{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0001","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fe096bf5242eb6ecc00672cc5f75afcf29a6d61b34a4050c43eacd09aeeb4b9f","family_id":"qf-mod44-tm-signature-qualification","seed":202611135001,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa0\",\"blank\":\"_0\",\"input_alphabet\":[\"00\"],\"reject_state\":\"qr0\",\"start_state\":\"q00\",\"states\":[\"q00\",\"q10\",\"qa0\",\"qr0\"],\"tape_alphabet\":[\"00\",\"X0\",\"_0\"],\"transitions\":[[\"q00\",\"_0\",\"qr0\",\"_0\",\"S\"],[\"q00\",\"00\",\"q10\",\"X0\",\"R\"],[\"q10\",\"_0\",\"qa0\",\"_0\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q00, q10, qa0, qr0], input_alphabet=[00], tape_alphabet=[00, X0, _0], blank=_0, start=q00, accept=qa0, reject=qr0, transitions=[[q00, 00, q10, X0, R], [q00, _0, qr0, _0, S], [q10, _0, qa0, _0, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q00, q10, qa0, qr0], [00], [00, X0, _0], _0, q00, qa0, qr0, [[q00, _0, qr0, _0, S], [q00, 00, q10, X0, R], [q10, _0, qa0, _0, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q00, q10, qa0, qr0], [00], [00, X0, _0], _0, q00, qa0, qr0, [[q00, _0, qr0, _0, S], [q00, 00, q10, X0, R], [q10, _0, qa0, _0, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0002","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"939a9444b969f204a00c322ce39ed220d21fb81d568166267f5ad1d0cc1e0b2a","family_id":"qf-mod44-tm-signature-qualification","seed":202611135002,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa1\",\"blank\":\"_1\",\"input_alphabet\":[\"01\"],\"reject_state\":\"qr1\",\"start_state\":\"q01\",\"states\":[\"q01\",\"q11\",\"qa1\",\"qr1\"],\"tape_alphabet\":[\"01\",\"X1\",\"_1\"],\"transitions\":[[\"q01\",\"_1\",\"qr1\",\"_1\",\"S\"],[\"q01\",\"01\",\"q11\",\"X1\",\"R\"],[\"q11\",\"_1\",\"qa1\",\"_1\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q01, q11, qa1, qr1], input_alphabet=[01], tape_alphabet=[01, X1, _1], blank=_1, start=q01, accept=qa1, reject=qr1, transitions=[[q01, 01, q11, X1, R], [q01, _1, qr1, _1, S], [q11, _1, qa1, _1, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q01, q11, qa1, qr1], [01], [01, X1, _1], _1, q01, qa1, qr1, [[q01, _1, qr1, _1, S], [q01, 01, q11, X1, R], [q11, _1, qa1, _1, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q01, q11, qa1, qr1], [01], [01, X1, _1], _1, q01, qa1, qr1, [[q01, _1, qr1, _1, S], [q01, 01, q11, X1, R], [q11, _1, qa1, _1, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0003","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"017c94cc0b69e48434a74dd21a74330c21d7a675b00b15c6ed5d543cae6073d8","family_id":"qf-mod44-tm-signature-qualification","seed":202611135003,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa2\",\"blank\":\"_2\",\"input_alphabet\":[\"02\"],\"reject_state\":\"qr2\",\"start_state\":\"q02\",\"states\":[\"q02\",\"q12\",\"qa2\",\"qr2\"],\"tape_alphabet\":[\"02\",\"X2\",\"_2\"],\"transitions\":[[\"q02\",\"_2\",\"qr2\",\"_2\",\"S\"],[\"q02\",\"02\",\"q12\",\"X2\",\"R\"],[\"q12\",\"_2\",\"qa2\",\"_2\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q02, q12, qa2, qr2], input_alphabet=[02], tape_alphabet=[02, X2, _2], blank=_2, start=q02, accept=qa2, reject=qr2, transitions=[[q02, 02, q12, X2, R], [q02, _2, qr2, _2, S], [q12, _2, qa2, _2, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q02, q12, qa2, qr2], [02], [02, X2, _2], _2, q02, qa2, qr2, [[q02, _2, qr2, _2, S], [q02, 02, q12, X2, R], [q12, _2, qa2, _2, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q02, q12, qa2, qr2], [02], [02, X2, _2], _2, q02, qa2, qr2, [[q02, _2, qr2, _2, S], [q02, 02, q12, X2, R], [q12, _2, qa2, _2, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0004","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"09fa76f4bd8b621980021487c7178c3157bf9929fed916092a91dbd86167107a","family_id":"qf-mod44-tm-signature-qualification","seed":202611135004,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa3\",\"blank\":\"_3\",\"input_alphabet\":[\"03\"],\"reject_state\":\"qr3\",\"start_state\":\"q03\",\"states\":[\"q03\",\"q13\",\"qa3\",\"qr3\"],\"tape_alphabet\":[\"03\",\"X3\",\"_3\"],\"transitions\":[[\"q03\",\"_3\",\"qr3\",\"_3\",\"S\"],[\"q03\",\"03\",\"q13\",\"X3\",\"R\"],[\"q13\",\"_3\",\"qa3\",\"_3\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q03, q13, qa3, qr3], input_alphabet=[03], tape_alphabet=[03, X3, _3], blank=_3, start=q03, accept=qa3, reject=qr3, transitions=[[q03, 03, q13, X3, R], [q03, _3, qr3, _3, S], [q13, _3, qa3, _3, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q03, q13, qa3, qr3], [03], [03, X3, _3], _3, q03, qa3, qr3, [[q03, _3, qr3, _3, S], [q03, 03, q13, X3, R], [q13, _3, qa3, _3, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q03, q13, qa3, qr3], [03], [03, X3, _3], _3, q03, qa3, qr3, [[q03, _3, qr3, _3, S], [q03, 03, q13, X3, R], [q13, _3, qa3, _3, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0005","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"63a362bf3849d2ef9f674110ef8897a95cb5d9d305e08e716d6c4dc8c7ec7362","family_id":"qf-mod44-tm-signature-qualification","seed":202611135005,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa4\",\"blank\":\"_4\",\"input_alphabet\":[\"04\"],\"reject_state\":\"qr4\",\"start_state\":\"q04\",\"states\":[\"q04\",\"q14\",\"qa4\",\"qr4\"],\"tape_alphabet\":[\"04\",\"X4\",\"_4\"],\"transitions\":[[\"q04\",\"_4\",\"qr4\",\"_4\",\"S\"],[\"q04\",\"04\",\"q14\",\"X4\",\"R\"],[\"q14\",\"_4\",\"qa4\",\"_4\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q04, q14, qa4, qr4], input_alphabet=[04], tape_alphabet=[04, X4, _4], blank=_4, start=q04, accept=qa4, reject=qr4, transitions=[[q04, 04, q14, X4, R], [q04, _4, qr4, _4, S], [q14, _4, qa4, _4, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q04, q14, qa4, qr4], [04], [04, X4, _4], _4, q04, qa4, qr4, [[q04, _4, qr4, _4, S], [q04, 04, q14, X4, R], [q14, _4, qa4, _4, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q04, q14, qa4, qr4], [04], [04, X4, _4], _4, q04, qa4, qr4, [[q04, _4, qr4, _4, S], [q04, 04, q14, X4, R], [q14, _4, qa4, _4, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0006","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c477d0eea8e4cc32695164a12a2e2c8c486ca9870f5d69dd4cb1c204dd305df2","family_id":"qf-mod44-tm-signature-qualification","seed":202611135006,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa5\",\"blank\":\"_5\",\"input_alphabet\":[\"05\"],\"reject_state\":\"qr5\",\"start_state\":\"q05\",\"states\":[\"q05\",\"q15\",\"qa5\",\"qr5\"],\"tape_alphabet\":[\"05\",\"X5\",\"_5\"],\"transitions\":[[\"q05\",\"_5\",\"qr5\",\"_5\",\"S\"],[\"q05\",\"05\",\"q15\",\"X5\",\"R\"],[\"q15\",\"_5\",\"qa5\",\"_5\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q05, q15, qa5, qr5], input_alphabet=[05], tape_alphabet=[05, X5, _5], blank=_5, start=q05, accept=qa5, reject=qr5, transitions=[[q05, 05, q15, X5, R], [q05, _5, qr5, _5, S], [q15, _5, qa5, _5, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q05, q15, qa5, qr5], [05], [05, X5, _5], _5, q05, qa5, qr5, [[q05, _5, qr5, _5, S], [q05, 05, q15, X5, R], [q15, _5, qa5, _5, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q05, q15, qa5, qr5], [05], [05, X5, _5], _5, q05, qa5, qr5, [[q05, _5, qr5, _5, S], [q05, 05, q15, X5, R], [q15, _5, qa5, _5, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0007","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a23c9f75f44dc0165d09452e074fdf6a21f2cbb5d7738d0469d95467069d6415","family_id":"qf-mod44-tm-signature-qualification","seed":202611135007,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa6\",\"blank\":\"_6\",\"input_alphabet\":[\"06\"],\"reject_state\":\"qr6\",\"start_state\":\"q06\",\"states\":[\"q06\",\"q16\",\"qa6\",\"qr6\"],\"tape_alphabet\":[\"06\",\"X6\",\"_6\"],\"transitions\":[[\"q06\",\"_6\",\"qr6\",\"_6\",\"S\"],[\"q06\",\"06\",\"q16\",\"X6\",\"R\"],[\"q16\",\"_6\",\"qa6\",\"_6\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q06, q16, qa6, qr6], input_alphabet=[06], tape_alphabet=[06, X6, _6], blank=_6, start=q06, accept=qa6, reject=qr6, transitions=[[q06, 06, q16, X6, R], [q06, _6, qr6, _6, S], [q16, _6, qa6, _6, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q06, q16, qa6, qr6], [06], [06, X6, _6], _6, q06, qa6, qr6, [[q06, _6, qr6, _6, S], [q06, 06, q16, X6, R], [q16, _6, qa6, _6, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q06, q16, qa6, qr6], [06], [06, X6, _6], _6, q06, qa6, qr6, [[q06, _6, qr6, _6, S], [q06, 06, q16, X6, R], [q16, _6, qa6, _6, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0008","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e183006f1cdb271a3bff277bcd8e851e60795e1e3253d23cb23ed3f5b4d3a981","family_id":"qf-mod44-tm-signature-qualification","seed":202611135008,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa7\",\"blank\":\"_7\",\"input_alphabet\":[\"07\"],\"reject_state\":\"qr7\",\"start_state\":\"q07\",\"states\":[\"q07\",\"q17\",\"qa7\",\"qr7\"],\"tape_alphabet\":[\"07\",\"X7\",\"_7\"],\"transitions\":[[\"q07\",\"_7\",\"qr7\",\"_7\",\"S\"],[\"q07\",\"07\",\"q17\",\"X7\",\"R\"],[\"q17\",\"_7\",\"qa7\",\"_7\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q07, q17, qa7, qr7], input_alphabet=[07], tape_alphabet=[07, X7, _7], blank=_7, start=q07, accept=qa7, reject=qr7, transitions=[[q07, 07, q17, X7, R], [q07, _7, qr7, _7, S], [q17, _7, qa7, _7, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q07, q17, qa7, qr7], [07], [07, X7, _7], _7, q07, qa7, qr7, [[q07, _7, qr7, _7, S], [q07, 07, q17, X7, R], [q17, _7, qa7, _7, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q07, q17, qa7, qr7], [07], [07, X7, _7], _7, q07, qa7, qr7, [[q07, _7, qr7, _7, S], [q07, 07, q17, X7, R], [q17, _7, qa7, _7, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0009","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c4126b87b8dcbbc78f8210f25b4cb6be5e268f14a6e16ce36b295cc37ed5e4dd","family_id":"qf-mod44-tm-signature-qualification","seed":202611135009,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa8\",\"blank\":\"_8\",\"input_alphabet\":[\"08\"],\"reject_state\":\"qr8\",\"start_state\":\"q08\",\"states\":[\"q08\",\"q18\",\"qa8\",\"qr8\"],\"tape_alphabet\":[\"08\",\"X8\",\"_8\"],\"transitions\":[[\"q08\",\"_8\",\"qr8\",\"_8\",\"S\"],[\"q08\",\"08\",\"q18\",\"X8\",\"R\"],[\"q18\",\"_8\",\"qa8\",\"_8\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q08, q18, qa8, qr8], input_alphabet=[08], tape_alphabet=[08, X8, _8], blank=_8, start=q08, accept=qa8, reject=qr8, transitions=[[q08, 08, q18, X8, R], [q08, _8, qr8, _8, S], [q18, _8, qa8, _8, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q08, q18, qa8, qr8], [08], [08, X8, _8], _8, q08, qa8, qr8, [[q08, _8, qr8, _8, S], [q08, 08, q18, X8, R], [q18, _8, qa8, _8, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q08, q18, qa8, qr8], [08], [08, X8, _8], _8, q08, qa8, qr8, [[q08, _8, qr8, _8, S], [q08, 08, q18, X8, R], [q18, _8, qa8, _8, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0010","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d6e7b22fd26e0c4e4e03fbed77d47832914c9403cc404f590d35e96f2aa86794","family_id":"qf-mod44-tm-signature-qualification","seed":202611135010,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa9\",\"blank\":\"_9\",\"input_alphabet\":[\"09\"],\"reject_state\":\"qr9\",\"start_state\":\"q09\",\"states\":[\"q09\",\"q19\",\"qa9\",\"qr9\"],\"tape_alphabet\":[\"09\",\"X9\",\"_9\"],\"transitions\":[[\"q09\",\"_9\",\"qr9\",\"_9\",\"S\"],[\"q09\",\"09\",\"q19\",\"X9\",\"R\"],[\"q19\",\"_9\",\"qa9\",\"_9\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q09, q19, qa9, qr9], input_alphabet=[09], tape_alphabet=[09, X9, _9], blank=_9, start=q09, accept=qa9, reject=qr9, transitions=[[q09, 09, q19, X9, R], [q09, _9, qr9, _9, S], [q19, _9, qa9, _9, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q09, q19, qa9, qr9], [09], [09, X9, _9], _9, q09, qa9, qr9, [[q09, _9, qr9, _9, S], [q09, 09, q19, X9, R], [q19, _9, qa9, _9, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q09, q19, qa9, qr9], [09], [09, X9, _9], _9, q09, qa9, qr9, [[q09, _9, qr9, _9, S], [q09, 09, q19, X9, R], [q19, _9, qa9, _9, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0011","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6fbd6256fcab8b77194ae08a789410f295835499289ebe18e638b6d3480d5e49","family_id":"qf-mod44-tm-signature-qualification","seed":202611135011,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa10\",\"blank\":\"_10\",\"input_alphabet\":[\"010\"],\"reject_state\":\"qr10\",\"start_state\":\"q010\",\"states\":[\"q010\",\"q110\",\"qa10\",\"qr10\"],\"tape_alphabet\":[\"010\",\"X10\",\"_10\"],\"transitions\":[[\"q010\",\"_10\",\"qr10\",\"_10\",\"S\"],[\"q010\",\"010\",\"q110\",\"X10\",\"R\"],[\"q110\",\"_10\",\"qa10\",\"_10\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q010, q110, qa10, qr10], input_alphabet=[010], tape_alphabet=[010, X10, _10], blank=_10, start=q010, accept=qa10, reject=qr10, transitions=[[q010, 010, q110, X10, R], [q010, _10, qr10, _10, S], [q110, _10, qa10, _10, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q010, q110, qa10, qr10], [010], [010, X10, _10], _10, q010, qa10, qr10, [[q010, _10, qr10, _10, S], [q010, 010, q110, X10, R], [q110, _10, qa10, _10, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q010, q110, qa10, qr10], [010], [010, X10, _10], _10, q010, qa10, qr10, [[q010, _10, qr10, _10, S], [q010, 010, q110, X10, R], [q110, _10, qa10, _10, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0012","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"314ad47ea423d4822f82ce0bc3f21eb5ad2214c65134df5be3327c00ff5e17c0","family_id":"qf-mod44-tm-signature-qualification","seed":202611135012,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa11\",\"blank\":\"_11\",\"input_alphabet\":[\"011\"],\"reject_state\":\"qr11\",\"start_state\":\"q011\",\"states\":[\"q011\",\"q111\",\"qa11\",\"qr11\"],\"tape_alphabet\":[\"011\",\"X11\",\"_11\"],\"transitions\":[[\"q011\",\"_11\",\"qr11\",\"_11\",\"S\"],[\"q011\",\"011\",\"q111\",\"X11\",\"R\"],[\"q111\",\"_11\",\"qa11\",\"_11\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q011, q111, qa11, qr11], input_alphabet=[011], tape_alphabet=[011, X11, _11], blank=_11, start=q011, accept=qa11, reject=qr11, transitions=[[q011, 011, q111, X11, R], [q011, _11, qr11, _11, S], [q111, _11, qa11, _11, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q011, q111, qa11, qr11], [011], [011, X11, _11], _11, q011, qa11, qr11, [[q011, _11, qr11, _11, S], [q011, 011, q111, X11, R], [q111, _11, qa11, _11, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q011, q111, qa11, qr11], [011], [011, X11, _11], _11, q011, qa11, qr11, [[q011, _11, qr11, _11, S], [q011, 011, q111, X11, R], [q111, _11, qa11, _11, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0013","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"78de041a76246e7c19bb5833bb8d39a18be3147b801ea3eca21c13985d7241ff","family_id":"qf-mod44-tm-signature-qualification","seed":202611135013,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa12\",\"blank\":\"_12\",\"input_alphabet\":[\"012\"],\"reject_state\":\"qr12\",\"start_state\":\"q012\",\"states\":[\"q012\",\"q112\",\"qa12\",\"qr12\"],\"tape_alphabet\":[\"012\",\"X12\",\"_12\"],\"transitions\":[[\"q012\",\"_12\",\"qr12\",\"_12\",\"S\"],[\"q012\",\"012\",\"q112\",\"X12\",\"R\"],[\"q112\",\"_12\",\"qa12\",\"_12\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q012, q112, qa12, qr12], input_alphabet=[012], tape_alphabet=[012, X12, _12], blank=_12, start=q012, accept=qa12, reject=qr12, transitions=[[q012, 012, q112, X12, R], [q012, _12, qr12, _12, S], [q112, _12, qa12, _12, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q012, q112, qa12, qr12], [012], [012, X12, _12], _12, q012, qa12, qr12, [[q012, _12, qr12, _12, S], [q012, 012, q112, X12, R], [q112, _12, qa12, _12, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q012, q112, qa12, qr12], [012], [012, X12, _12], _12, q012, qa12, qr12, [[q012, _12, qr12, _12, S], [q012, 012, q112, X12, R], [q112, _12, qa12, _12, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0014","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"720e102456a2681c97788b05b32dd26d2f7adbc8ac39aaaa127b6298ad46fdd1","family_id":"qf-mod44-tm-signature-qualification","seed":202611135014,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa13\",\"blank\":\"_13\",\"input_alphabet\":[\"013\"],\"reject_state\":\"qr13\",\"start_state\":\"q013\",\"states\":[\"q013\",\"q113\",\"qa13\",\"qr13\"],\"tape_alphabet\":[\"013\",\"X13\",\"_13\"],\"transitions\":[[\"q013\",\"_13\",\"qr13\",\"_13\",\"S\"],[\"q013\",\"013\",\"q113\",\"X13\",\"R\"],[\"q113\",\"_13\",\"qa13\",\"_13\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q013, q113, qa13, qr13], input_alphabet=[013], tape_alphabet=[013, X13, _13], blank=_13, start=q013, accept=qa13, reject=qr13, transitions=[[q013, 013, q113, X13, R], [q013, _13, qr13, _13, S], [q113, _13, qa13, _13, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q013, q113, qa13, qr13], [013], [013, X13, _13], _13, q013, qa13, qr13, [[q013, _13, qr13, _13, S], [q013, 013, q113, X13, R], [q113, _13, qa13, _13, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q013, q113, qa13, qr13], [013], [013, X13, _13], _13, q013, qa13, qr13, [[q013, _13, qr13, _13, S], [q013, 013, q113, X13, R], [q113, _13, qa13, _13, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0015","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3e24422fc874c21766a2e2adf260f2347884e50f86f96af6ad940899cac4c14f","family_id":"qf-mod44-tm-signature-qualification","seed":202611135015,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa14\",\"blank\":\"_14\",\"input_alphabet\":[\"014\"],\"reject_state\":\"qr14\",\"start_state\":\"q014\",\"states\":[\"q014\",\"q114\",\"qa14\",\"qr14\"],\"tape_alphabet\":[\"014\",\"X14\",\"_14\"],\"transitions\":[[\"q014\",\"_14\",\"qr14\",\"_14\",\"S\"],[\"q014\",\"014\",\"q114\",\"X14\",\"R\"],[\"q114\",\"_14\",\"qa14\",\"_14\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q014, q114, qa14, qr14], input_alphabet=[014], tape_alphabet=[014, X14, _14], blank=_14, start=q014, accept=qa14, reject=qr14, transitions=[[q014, 014, q114, X14, R], [q014, _14, qr14, _14, S], [q114, _14, qa14, _14, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q014, q114, qa14, qr14], [014], [014, X14, _14], _14, q014, qa14, qr14, [[q014, _14, qr14, _14, S], [q014, 014, q114, X14, R], [q114, _14, qa14, _14, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q014, q114, qa14, qr14], [014], [014, X14, _14], _14, q014, qa14, qr14, [[q014, _14, qr14, _14, S], [q014, 014, q114, X14, R], [q114, _14, qa14, _14, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0016","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9ed59b45d3c3aaf4069d2c7c558310cc1bb54f5f1b6d1ca3b0f11df779d83951","family_id":"qf-mod44-tm-signature-qualification","seed":202611135016,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa15\",\"blank\":\"_15\",\"input_alphabet\":[\"015\"],\"reject_state\":\"qr15\",\"start_state\":\"q015\",\"states\":[\"q015\",\"q115\",\"qa15\",\"qr15\"],\"tape_alphabet\":[\"015\",\"X15\",\"_15\"],\"transitions\":[[\"q015\",\"_15\",\"qr15\",\"_15\",\"S\"],[\"q015\",\"015\",\"q115\",\"X15\",\"R\"],[\"q115\",\"_15\",\"qa15\",\"_15\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q015, q115, qa15, qr15], input_alphabet=[015], tape_alphabet=[015, X15, _15], blank=_15, start=q015, accept=qa15, reject=qr15, transitions=[[q015, 015, q115, X15, R], [q015, _15, qr15, _15, S], [q115, _15, qa15, _15, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q015, q115, qa15, qr15], [015], [015, X15, _15], _15, q015, qa15, qr15, [[q015, _15, qr15, _15, S], [q015, 015, q115, X15, R], [q115, _15, qa15, _15, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q015, q115, qa15, qr15], [015], [015, X15, _15], _15, q015, qa15, qr15, [[q015, _15, qr15, _15, S], [q015, 015, q115, X15, R], [q115, _15, qa15, _15, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0017","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bf3464e51a1b4334a7a696d4378d741d299a5267c2c0df7223edad1cd28d2edd","family_id":"qf-mod44-tm-signature-qualification","seed":202611135017,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa16\",\"blank\":\"_16\",\"input_alphabet\":[\"016\"],\"reject_state\":\"qr16\",\"start_state\":\"q016\",\"states\":[\"q016\",\"q116\",\"qa16\",\"qr16\"],\"tape_alphabet\":[\"016\",\"X16\",\"_16\"],\"transitions\":[[\"q016\",\"_16\",\"qr16\",\"_16\",\"S\"],[\"q016\",\"016\",\"q116\",\"X16\",\"R\"],[\"q116\",\"_16\",\"qa16\",\"_16\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q016, q116, qa16, qr16], input_alphabet=[016], tape_alphabet=[016, X16, _16], blank=_16, start=q016, accept=qa16, reject=qr16, transitions=[[q016, 016, q116, X16, R], [q016, _16, qr16, _16, S], [q116, _16, qa16, _16, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q016, q116, qa16, qr16], [016], [016, X16, _16], _16, q016, qa16, qr16, [[q016, _16, qr16, _16, S], [q016, 016, q116, X16, R], [q116, _16, qa16, _16, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q016, q116, qa16, qr16], [016], [016, X16, _16], _16, q016, qa16, qr16, [[q016, _16, qr16, _16, S], [q016, 016, q116, X16, R], [q116, _16, qa16, _16, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0018","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f74a26beabbbed3e6d3401060776a86491864afe322dc270737bcb3cac58e907","family_id":"qf-mod44-tm-signature-qualification","seed":202611135018,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa17\",\"blank\":\"_17\",\"input_alphabet\":[\"017\"],\"reject_state\":\"qr17\",\"start_state\":\"q017\",\"states\":[\"q017\",\"q117\",\"qa17\",\"qr17\"],\"tape_alphabet\":[\"017\",\"X17\",\"_17\"],\"transitions\":[[\"q017\",\"_17\",\"qr17\",\"_17\",\"S\"],[\"q017\",\"017\",\"q117\",\"X17\",\"R\"],[\"q117\",\"_17\",\"qa17\",\"_17\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q017, q117, qa17, qr17], input_alphabet=[017], tape_alphabet=[017, X17, _17], blank=_17, start=q017, accept=qa17, reject=qr17, transitions=[[q017, 017, q117, X17, R], [q017, _17, qr17, _17, S], [q117, _17, qa17, _17, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q017, q117, qa17, qr17], [017], [017, X17, _17], _17, q017, qa17, qr17, [[q017, _17, qr17, _17, S], [q017, 017, q117, X17, R], [q117, _17, qa17, _17, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q017, q117, qa17, qr17], [017], [017, X17, _17], _17, q017, qa17, qr17, [[q017, _17, qr17, _17, S], [q017, 017, q117, X17, R], [q117, _17, qa17, _17, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0019","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d27f188bfa06e7e115876b7056947d2760472e5172755b86f75ebf42e9794f00","family_id":"qf-mod44-tm-signature-qualification","seed":202611135019,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa18\",\"blank\":\"_18\",\"input_alphabet\":[\"018\"],\"reject_state\":\"qr18\",\"start_state\":\"q018\",\"states\":[\"q018\",\"q118\",\"qa18\",\"qr18\"],\"tape_alphabet\":[\"018\",\"X18\",\"_18\"],\"transitions\":[[\"q018\",\"_18\",\"qr18\",\"_18\",\"S\"],[\"q018\",\"018\",\"q118\",\"X18\",\"R\"],[\"q118\",\"_18\",\"qa18\",\"_18\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q018, q118, qa18, qr18], input_alphabet=[018], tape_alphabet=[018, X18, _18], blank=_18, start=q018, accept=qa18, reject=qr18, transitions=[[q018, 018, q118, X18, R], [q018, _18, qr18, _18, S], [q118, _18, qa18, _18, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q018, q118, qa18, qr18], [018], [018, X18, _18], _18, q018, qa18, qr18, [[q018, _18, qr18, _18, S], [q018, 018, q118, X18, R], [q118, _18, qa18, _18, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q018, q118, qa18, qr18], [018], [018, X18, _18], _18, q018, qa18, qr18, [[q018, _18, qr18, _18, S], [q018, 018, q118, X18, R], [q118, _18, qa18, _18, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0020","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"57edb118e03c27e604fc4f6c65e36073305988cbd7792cebe592a13fba89b97d","family_id":"qf-mod44-tm-signature-qualification","seed":202611135020,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa19\",\"blank\":\"_19\",\"input_alphabet\":[\"019\"],\"reject_state\":\"qr19\",\"start_state\":\"q019\",\"states\":[\"q019\",\"q119\",\"qa19\",\"qr19\"],\"tape_alphabet\":[\"019\",\"X19\",\"_19\"],\"transitions\":[[\"q019\",\"_19\",\"qr19\",\"_19\",\"S\"],[\"q019\",\"019\",\"q119\",\"X19\",\"R\"],[\"q119\",\"_19\",\"qa19\",\"_19\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q019, q119, qa19, qr19], input_alphabet=[019], tape_alphabet=[019, X19, _19], blank=_19, start=q019, accept=qa19, reject=qr19, transitions=[[q019, 019, q119, X19, R], [q019, _19, qr19, _19, S], [q119, _19, qa19, _19, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q019, q119, qa19, qr19], [019], [019, X19, _19], _19, q019, qa19, qr19, [[q019, _19, qr19, _19, S], [q019, 019, q119, X19, R], [q119, _19, qa19, _19, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q019, q119, qa19, qr19], [019], [019, X19, _19], _19, q019, qa19, qr19, [[q019, _19, qr19, _19, S], [q019, 019, q119, X19, R], [q119, _19, qa19, _19, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0021","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"06842603426c5df8394c9df38ba377f93ac0cf565335a2c5bc9355534a069aef","family_id":"qf-mod44-tm-signature-qualification","seed":202611135021,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa20\",\"blank\":\"_20\",\"input_alphabet\":[\"020\"],\"reject_state\":\"qr20\",\"start_state\":\"q020\",\"states\":[\"q020\",\"q120\",\"qa20\",\"qr20\"],\"tape_alphabet\":[\"020\",\"X20\",\"_20\"],\"transitions\":[[\"q020\",\"_20\",\"qr20\",\"_20\",\"S\"],[\"q020\",\"020\",\"q120\",\"X20\",\"R\"],[\"q120\",\"_20\",\"qa20\",\"_20\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q020, q120, qa20, qr20], input_alphabet=[020], tape_alphabet=[020, X20, _20], blank=_20, start=q020, accept=qa20, reject=qr20, transitions=[[q020, 020, q120, X20, R], [q020, _20, qr20, _20, S], [q120, _20, qa20, _20, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q020, q120, qa20, qr20], [020], [020, X20, _20], _20, q020, qa20, qr20, [[q020, _20, qr20, _20, S], [q020, 020, q120, X20, R], [q120, _20, qa20, _20, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q020, q120, qa20, qr20], [020], [020, X20, _20], _20, q020, qa20, qr20, [[q020, _20, qr20, _20, S], [q020, 020, q120, X20, R], [q120, _20, qa20, _20, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0022","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"75ddd79bb3801b0e4e32e03ff1fdb73a1bfd3e22b150e49a9c00a235ee4de29d","family_id":"qf-mod44-tm-signature-qualification","seed":202611135022,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa21\",\"blank\":\"_21\",\"input_alphabet\":[\"021\"],\"reject_state\":\"qr21\",\"start_state\":\"q021\",\"states\":[\"q021\",\"q121\",\"qa21\",\"qr21\"],\"tape_alphabet\":[\"021\",\"X21\",\"_21\"],\"transitions\":[[\"q021\",\"_21\",\"qr21\",\"_21\",\"S\"],[\"q021\",\"021\",\"q121\",\"X21\",\"R\"],[\"q121\",\"_21\",\"qa21\",\"_21\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q021, q121, qa21, qr21], input_alphabet=[021], tape_alphabet=[021, X21, _21], blank=_21, start=q021, accept=qa21, reject=qr21, transitions=[[q021, 021, q121, X21, R], [q021, _21, qr21, _21, S], [q121, _21, qa21, _21, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q021, q121, qa21, qr21], [021], [021, X21, _21], _21, q021, qa21, qr21, [[q021, _21, qr21, _21, S], [q021, 021, q121, X21, R], [q121, _21, qa21, _21, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q021, q121, qa21, qr21], [021], [021, X21, _21], _21, q021, qa21, qr21, [[q021, _21, qr21, _21, S], [q021, 021, q121, X21, R], [q121, _21, qa21, _21, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0023","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"437fab974d629f008c0d9bebcbb22c0d05ca6cb3d8655d3f3adf9ba7ab031b94","family_id":"qf-mod44-tm-signature-qualification","seed":202611135023,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa22\",\"blank\":\"_22\",\"input_alphabet\":[\"022\"],\"reject_state\":\"qr22\",\"start_state\":\"q022\",\"states\":[\"q022\",\"q122\",\"qa22\",\"qr22\"],\"tape_alphabet\":[\"022\",\"X22\",\"_22\"],\"transitions\":[[\"q022\",\"_22\",\"qr22\",\"_22\",\"S\"],[\"q022\",\"022\",\"q122\",\"X22\",\"R\"],[\"q122\",\"_22\",\"qa22\",\"_22\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q022, q122, qa22, qr22], input_alphabet=[022], tape_alphabet=[022, X22, _22], blank=_22, start=q022, accept=qa22, reject=qr22, transitions=[[q022, 022, q122, X22, R], [q022, _22, qr22, _22, S], [q122, _22, qa22, _22, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q022, q122, qa22, qr22], [022], [022, X22, _22], _22, q022, qa22, qr22, [[q022, _22, qr22, _22, S], [q022, 022, q122, X22, R], [q122, _22, qa22, _22, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q022, q122, qa22, qr22], [022], [022, X22, _22], _22, q022, qa22, qr22, [[q022, _22, qr22, _22, S], [q022, 022, q122, X22, R], [q122, _22, qa22, _22, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0024","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a16788cc0c5d73d56b95aa9a51652f04701d597213b7efe5a94efa260c4620d2","family_id":"qf-mod44-tm-signature-qualification","seed":202611135024,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa23\",\"blank\":\"_23\",\"input_alphabet\":[\"023\"],\"reject_state\":\"qr23\",\"start_state\":\"q023\",\"states\":[\"q023\",\"q123\",\"qa23\",\"qr23\"],\"tape_alphabet\":[\"023\",\"X23\",\"_23\"],\"transitions\":[[\"q023\",\"_23\",\"qr23\",\"_23\",\"S\"],[\"q023\",\"023\",\"q123\",\"X23\",\"R\"],[\"q123\",\"_23\",\"qa23\",\"_23\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q023, q123, qa23, qr23], input_alphabet=[023], tape_alphabet=[023, X23, _23], blank=_23, start=q023, accept=qa23, reject=qr23, transitions=[[q023, 023, q123, X23, R], [q023, _23, qr23, _23, S], [q123, _23, qa23, _23, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q023, q123, qa23, qr23], [023], [023, X23, _23], _23, q023, qa23, qr23, [[q023, _23, qr23, _23, S], [q023, 023, q123, X23, R], [q123, _23, qa23, _23, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q023, q123, qa23, qr23], [023], [023, X23, _23], _23, q023, qa23, qr23, [[q023, _23, qr23, _23, S], [q023, 023, q123, X23, R], [q123, _23, qa23, _23, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0025","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0ac2b59c3850037871eb9d0e615ce91cc027ab12534b01615c0aaae68de79c46","family_id":"qf-mod44-tm-signature-qualification","seed":202611135025,"semantic_template":"qf-mod44-tm-signature-qualification/{\"accept_state\":\"qa24\",\"blank\":\"_24\",\"input_alphabet\":[\"024\"],\"reject_state\":\"qr24\",\"start_state\":\"q024\",\"states\":[\"q024\",\"q124\",\"qa24\",\"qr24\"],\"tape_alphabet\":[\"024\",\"X24\",\"_24\"],\"transitions\":[[\"q024\",\"_24\",\"qr24\",\"_24\",\"S\"],[\"q024\",\"024\",\"q124\",\"X24\",\"R\"],[\"q124\",\"_24\",\"qa24\",\"_24\",\"L\"]]}"},"fields":{"title":"A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider","stem":"Use deterministic single-tape states=[q024, q124, qa24, qr24], input_alphabet=[024], tape_alphabet=[024, X24, _24], blank=_24, start=q024, accept=qa24, reject=qr24, transitions=[[q024, 024, q124, X24, R], [q024, _24, qr24, _24, S], [q124, _24, qa24, _24, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).","answer":{"kind":"expression","value":"([q024, q124, qa24, qr24], [024], [024, X24, _24], _24, q024, qa24, qr24, [[q024, _24, qr24, _24, S], [q024, 024, q124, X24, R], [q124, _24, qa24, _24, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)","explanation":"Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q024, q124, qa24, qr24], [024], [024, X24, _24], _24, q024, qa24, qr24, [[q024, _24, qr24, _24, S], [q024, 024, q124, X24, R], [q124, _24, qa24, _24, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)."},"skills":["A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0026","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a552d6ae6d494f4565760bde9441241507b786d5c08b584e99f0bfa7ff67dcea","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135026,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa0\",\"blank\":\"_0\",\"input\":[\"00\"],\"input_alphabet\":[\"00\"],\"reject_state\":\"qr0\",\"start_state\":\"q00\",\"states\":[\"q00\",\"q10\",\"qa0\",\"qr0\"],\"steps\":2,\"tape_alphabet\":[\"00\",\"X0\",\"_0\"],\"transitions\":[[\"q00\",\"_0\",\"qr0\",\"_0\",\"S\"],[\"q00\",\"00\",\"q10\",\"X0\",\"R\"],[\"q10\",\"_0\",\"qa0\",\"_0\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q00, q10, qa0, qr0], input_alphabet=[00], tape_alphabet=[00, X0, _0], blank=_0, start=q00, accept=qa0, reject=qr0, transitions=[[q00, 00, q10, X0, R], [q00, _0, qr0, _0, S], [q10, _0, qa0, _0, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[00], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([00], 2, [[q00, 0, [[0, 00]]], [q10, 1, [[0, X0]]], [qa0, 0, [[0, X0]]]], [step, step], qa0, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([00], 2, [[q00, 0, [[0, 00]]], [q10, 1, [[0, X0]]], [qa0, 0, [[0, X0]]]], [step, step], qa0, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0027","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dd229035d85c152615d224fe5bf240e99fdad213659a6bbce880a3df38b7411e","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135027,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa1\",\"blank\":\"_1\",\"input\":[\"01\"],\"input_alphabet\":[\"01\"],\"reject_state\":\"qr1\",\"start_state\":\"q01\",\"states\":[\"q01\",\"q11\",\"qa1\",\"qr1\"],\"steps\":2,\"tape_alphabet\":[\"01\",\"X1\",\"_1\"],\"transitions\":[[\"q01\",\"_1\",\"qr1\",\"_1\",\"S\"],[\"q01\",\"01\",\"q11\",\"X1\",\"R\"],[\"q11\",\"_1\",\"qa1\",\"_1\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q01, q11, qa1, qr1], input_alphabet=[01], tape_alphabet=[01, X1, _1], blank=_1, start=q01, accept=qa1, reject=qr1, transitions=[[q01, 01, q11, X1, R], [q01, _1, qr1, _1, S], [q11, _1, qa1, _1, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[01], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([01], 2, [[q01, 0, [[0, 01]]], [q11, 1, [[0, X1]]], [qa1, 0, [[0, X1]]]], [step, step], qa1, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([01], 2, [[q01, 0, [[0, 01]]], [q11, 1, [[0, X1]]], [qa1, 0, [[0, X1]]]], [step, step], qa1, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0028","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9b5db7c488bb4c0a0c3386ae29e253054b328c027323ad50f6a480180ce11406","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135028,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa2\",\"blank\":\"_2\",\"input\":[\"02\"],\"input_alphabet\":[\"02\"],\"reject_state\":\"qr2\",\"start_state\":\"q02\",\"states\":[\"q02\",\"q12\",\"qa2\",\"qr2\"],\"steps\":2,\"tape_alphabet\":[\"02\",\"X2\",\"_2\"],\"transitions\":[[\"q02\",\"_2\",\"qr2\",\"_2\",\"S\"],[\"q02\",\"02\",\"q12\",\"X2\",\"R\"],[\"q12\",\"_2\",\"qa2\",\"_2\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q02, q12, qa2, qr2], input_alphabet=[02], tape_alphabet=[02, X2, _2], blank=_2, start=q02, accept=qa2, reject=qr2, transitions=[[q02, 02, q12, X2, R], [q02, _2, qr2, _2, S], [q12, _2, qa2, _2, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[02], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([02], 2, [[q02, 0, [[0, 02]]], [q12, 1, [[0, X2]]], [qa2, 0, [[0, X2]]]], [step, step], qa2, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([02], 2, [[q02, 0, [[0, 02]]], [q12, 1, [[0, X2]]], [qa2, 0, [[0, X2]]]], [step, step], qa2, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0029","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8af194f1f1a96f3cfe28b8ea4eed673ef8b61104f0fee9776af9e4738580874","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135029,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa3\",\"blank\":\"_3\",\"input\":[\"03\"],\"input_alphabet\":[\"03\"],\"reject_state\":\"qr3\",\"start_state\":\"q03\",\"states\":[\"q03\",\"q13\",\"qa3\",\"qr3\"],\"steps\":2,\"tape_alphabet\":[\"03\",\"X3\",\"_3\"],\"transitions\":[[\"q03\",\"_3\",\"qr3\",\"_3\",\"S\"],[\"q03\",\"03\",\"q13\",\"X3\",\"R\"],[\"q13\",\"_3\",\"qa3\",\"_3\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q03, q13, qa3, qr3], input_alphabet=[03], tape_alphabet=[03, X3, _3], blank=_3, start=q03, accept=qa3, reject=qr3, transitions=[[q03, 03, q13, X3, R], [q03, _3, qr3, _3, S], [q13, _3, qa3, _3, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[03], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([03], 2, [[q03, 0, [[0, 03]]], [q13, 1, [[0, X3]]], [qa3, 0, [[0, X3]]]], [step, step], qa3, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([03], 2, [[q03, 0, [[0, 03]]], [q13, 1, [[0, X3]]], [qa3, 0, [[0, X3]]]], [step, step], qa3, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0030","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4a625d88b1a98dff41c20c141b629ee1c1dd76ecd833872af238472d6972486e","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135030,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa4\",\"blank\":\"_4\",\"input\":[\"04\"],\"input_alphabet\":[\"04\"],\"reject_state\":\"qr4\",\"start_state\":\"q04\",\"states\":[\"q04\",\"q14\",\"qa4\",\"qr4\"],\"steps\":2,\"tape_alphabet\":[\"04\",\"X4\",\"_4\"],\"transitions\":[[\"q04\",\"_4\",\"qr4\",\"_4\",\"S\"],[\"q04\",\"04\",\"q14\",\"X4\",\"R\"],[\"q14\",\"_4\",\"qa4\",\"_4\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q04, q14, qa4, qr4], input_alphabet=[04], tape_alphabet=[04, X4, _4], blank=_4, start=q04, accept=qa4, reject=qr4, transitions=[[q04, 04, q14, X4, R], [q04, _4, qr4, _4, S], [q14, _4, qa4, _4, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[04], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([04], 2, [[q04, 0, [[0, 04]]], [q14, 1, [[0, X4]]], [qa4, 0, [[0, X4]]]], [step, step], qa4, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([04], 2, [[q04, 0, [[0, 04]]], [q14, 1, [[0, X4]]], [qa4, 0, [[0, X4]]]], [step, step], qa4, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0031","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5b82846dd4e53a6606ddfc007d51ce7fe3a4dfdb8c0f1a03bb1cd0a0d88104fe","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135031,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa5\",\"blank\":\"_5\",\"input\":[\"05\"],\"input_alphabet\":[\"05\"],\"reject_state\":\"qr5\",\"start_state\":\"q05\",\"states\":[\"q05\",\"q15\",\"qa5\",\"qr5\"],\"steps\":2,\"tape_alphabet\":[\"05\",\"X5\",\"_5\"],\"transitions\":[[\"q05\",\"_5\",\"qr5\",\"_5\",\"S\"],[\"q05\",\"05\",\"q15\",\"X5\",\"R\"],[\"q15\",\"_5\",\"qa5\",\"_5\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q05, q15, qa5, qr5], input_alphabet=[05], tape_alphabet=[05, X5, _5], blank=_5, start=q05, accept=qa5, reject=qr5, transitions=[[q05, 05, q15, X5, R], [q05, _5, qr5, _5, S], [q15, _5, qa5, _5, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[05], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([05], 2, [[q05, 0, [[0, 05]]], [q15, 1, [[0, X5]]], [qa5, 0, [[0, X5]]]], [step, step], qa5, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([05], 2, [[q05, 0, [[0, 05]]], [q15, 1, [[0, X5]]], [qa5, 0, [[0, X5]]]], [step, step], qa5, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0032","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"66a320d3a46bb54d6cd11a8c54f0679c1c57f128fe82d690deb75d6db2350b57","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135032,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa6\",\"blank\":\"_6\",\"input\":[\"06\"],\"input_alphabet\":[\"06\"],\"reject_state\":\"qr6\",\"start_state\":\"q06\",\"states\":[\"q06\",\"q16\",\"qa6\",\"qr6\"],\"steps\":2,\"tape_alphabet\":[\"06\",\"X6\",\"_6\"],\"transitions\":[[\"q06\",\"_6\",\"qr6\",\"_6\",\"S\"],[\"q06\",\"06\",\"q16\",\"X6\",\"R\"],[\"q16\",\"_6\",\"qa6\",\"_6\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q06, q16, qa6, qr6], input_alphabet=[06], tape_alphabet=[06, X6, _6], blank=_6, start=q06, accept=qa6, reject=qr6, transitions=[[q06, 06, q16, X6, R], [q06, _6, qr6, _6, S], [q16, _6, qa6, _6, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[06], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([06], 2, [[q06, 0, [[0, 06]]], [q16, 1, [[0, X6]]], [qa6, 0, [[0, X6]]]], [step, step], qa6, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([06], 2, [[q06, 0, [[0, 06]]], [q16, 1, [[0, X6]]], [qa6, 0, [[0, X6]]]], [step, step], qa6, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0033","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6db1c0b639918b749cd22064b03b60858327cbe263ed1eb988d09bab79586946","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135033,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa7\",\"blank\":\"_7\",\"input\":[\"07\"],\"input_alphabet\":[\"07\"],\"reject_state\":\"qr7\",\"start_state\":\"q07\",\"states\":[\"q07\",\"q17\",\"qa7\",\"qr7\"],\"steps\":2,\"tape_alphabet\":[\"07\",\"X7\",\"_7\"],\"transitions\":[[\"q07\",\"_7\",\"qr7\",\"_7\",\"S\"],[\"q07\",\"07\",\"q17\",\"X7\",\"R\"],[\"q17\",\"_7\",\"qa7\",\"_7\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q07, q17, qa7, qr7], input_alphabet=[07], tape_alphabet=[07, X7, _7], blank=_7, start=q07, accept=qa7, reject=qr7, transitions=[[q07, 07, q17, X7, R], [q07, _7, qr7, _7, S], [q17, _7, qa7, _7, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[07], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([07], 2, [[q07, 0, [[0, 07]]], [q17, 1, [[0, X7]]], [qa7, 0, [[0, X7]]]], [step, step], qa7, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([07], 2, [[q07, 0, [[0, 07]]], [q17, 1, [[0, X7]]], [qa7, 0, [[0, X7]]]], [step, step], qa7, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0034","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"63f8d3cb82805140e5e1c0b16513551994f98e5353ceac86d343c65338392903","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135034,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa8\",\"blank\":\"_8\",\"input\":[\"08\"],\"input_alphabet\":[\"08\"],\"reject_state\":\"qr8\",\"start_state\":\"q08\",\"states\":[\"q08\",\"q18\",\"qa8\",\"qr8\"],\"steps\":2,\"tape_alphabet\":[\"08\",\"X8\",\"_8\"],\"transitions\":[[\"q08\",\"_8\",\"qr8\",\"_8\",\"S\"],[\"q08\",\"08\",\"q18\",\"X8\",\"R\"],[\"q18\",\"_8\",\"qa8\",\"_8\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q08, q18, qa8, qr8], input_alphabet=[08], tape_alphabet=[08, X8, _8], blank=_8, start=q08, accept=qa8, reject=qr8, transitions=[[q08, 08, q18, X8, R], [q08, _8, qr8, _8, S], [q18, _8, qa8, _8, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[08], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([08], 2, [[q08, 0, [[0, 08]]], [q18, 1, [[0, X8]]], [qa8, 0, [[0, X8]]]], [step, step], qa8, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([08], 2, [[q08, 0, [[0, 08]]], [q18, 1, [[0, X8]]], [qa8, 0, [[0, X8]]]], [step, step], qa8, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0035","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2055ce3af8695848359c5e6e3ce8f12723412e793c0faaf5a3152137a7e043ac","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135035,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa9\",\"blank\":\"_9\",\"input\":[\"09\"],\"input_alphabet\":[\"09\"],\"reject_state\":\"qr9\",\"start_state\":\"q09\",\"states\":[\"q09\",\"q19\",\"qa9\",\"qr9\"],\"steps\":2,\"tape_alphabet\":[\"09\",\"X9\",\"_9\"],\"transitions\":[[\"q09\",\"_9\",\"qr9\",\"_9\",\"S\"],[\"q09\",\"09\",\"q19\",\"X9\",\"R\"],[\"q19\",\"_9\",\"qa9\",\"_9\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q09, q19, qa9, qr9], input_alphabet=[09], tape_alphabet=[09, X9, _9], blank=_9, start=q09, accept=qa9, reject=qr9, transitions=[[q09, 09, q19, X9, R], [q09, _9, qr9, _9, S], [q19, _9, qa9, _9, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[09], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([09], 2, [[q09, 0, [[0, 09]]], [q19, 1, [[0, X9]]], [qa9, 0, [[0, X9]]]], [step, step], qa9, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([09], 2, [[q09, 0, [[0, 09]]], [q19, 1, [[0, X9]]], [qa9, 0, [[0, X9]]]], [step, step], qa9, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0036","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2eba6523e33ebb818dd936b49f5767a474d71abab6b7d588d8dfc70c36dafd1f","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135036,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa10\",\"blank\":\"_10\",\"input\":[\"010\"],\"input_alphabet\":[\"010\"],\"reject_state\":\"qr10\",\"start_state\":\"q010\",\"states\":[\"q010\",\"q110\",\"qa10\",\"qr10\"],\"steps\":2,\"tape_alphabet\":[\"010\",\"X10\",\"_10\"],\"transitions\":[[\"q010\",\"_10\",\"qr10\",\"_10\",\"S\"],[\"q010\",\"010\",\"q110\",\"X10\",\"R\"],[\"q110\",\"_10\",\"qa10\",\"_10\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q010, q110, qa10, qr10], input_alphabet=[010], tape_alphabet=[010, X10, _10], blank=_10, start=q010, accept=qa10, reject=qr10, transitions=[[q010, 010, q110, X10, R], [q010, _10, qr10, _10, S], [q110, _10, qa10, _10, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[010], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([010], 2, [[q010, 0, [[0, 010]]], [q110, 1, [[0, X10]]], [qa10, 0, [[0, X10]]]], [step, step], qa10, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([010], 2, [[q010, 0, [[0, 010]]], [q110, 1, [[0, X10]]], [qa10, 0, [[0, X10]]]], [step, step], qa10, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0037","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"be40a25419c95dd3a3e117d784afa40e4f28c74f9cde6111d5fc6af45957d401","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135037,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa11\",\"blank\":\"_11\",\"input\":[\"011\"],\"input_alphabet\":[\"011\"],\"reject_state\":\"qr11\",\"start_state\":\"q011\",\"states\":[\"q011\",\"q111\",\"qa11\",\"qr11\"],\"steps\":2,\"tape_alphabet\":[\"011\",\"X11\",\"_11\"],\"transitions\":[[\"q011\",\"_11\",\"qr11\",\"_11\",\"S\"],[\"q011\",\"011\",\"q111\",\"X11\",\"R\"],[\"q111\",\"_11\",\"qa11\",\"_11\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q011, q111, qa11, qr11], input_alphabet=[011], tape_alphabet=[011, X11, _11], blank=_11, start=q011, accept=qa11, reject=qr11, transitions=[[q011, 011, q111, X11, R], [q011, _11, qr11, _11, S], [q111, _11, qa11, _11, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[011], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([011], 2, [[q011, 0, [[0, 011]]], [q111, 1, [[0, X11]]], [qa11, 0, [[0, X11]]]], [step, step], qa11, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([011], 2, [[q011, 0, [[0, 011]]], [q111, 1, [[0, X11]]], [qa11, 0, [[0, X11]]]], [step, step], qa11, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0038","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"31ac3d9fb9d0f4f559ea0c1b934c81353db24facfe0280703a6c6b9e3ff07268","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135038,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa12\",\"blank\":\"_12\",\"input\":[\"012\"],\"input_alphabet\":[\"012\"],\"reject_state\":\"qr12\",\"start_state\":\"q012\",\"states\":[\"q012\",\"q112\",\"qa12\",\"qr12\"],\"steps\":2,\"tape_alphabet\":[\"012\",\"X12\",\"_12\"],\"transitions\":[[\"q012\",\"_12\",\"qr12\",\"_12\",\"S\"],[\"q012\",\"012\",\"q112\",\"X12\",\"R\"],[\"q112\",\"_12\",\"qa12\",\"_12\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q012, q112, qa12, qr12], input_alphabet=[012], tape_alphabet=[012, X12, _12], blank=_12, start=q012, accept=qa12, reject=qr12, transitions=[[q012, 012, q112, X12, R], [q012, _12, qr12, _12, S], [q112, _12, qa12, _12, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[012], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([012], 2, [[q012, 0, [[0, 012]]], [q112, 1, [[0, X12]]], [qa12, 0, [[0, X12]]]], [step, step], qa12, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([012], 2, [[q012, 0, [[0, 012]]], [q112, 1, [[0, X12]]], [qa12, 0, [[0, X12]]]], [step, step], qa12, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0039","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1002b250b2baac38b65bffe1d8299803ed90b49f0e50058d7ae967cd484c6d53","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135039,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa13\",\"blank\":\"_13\",\"input\":[\"013\"],\"input_alphabet\":[\"013\"],\"reject_state\":\"qr13\",\"start_state\":\"q013\",\"states\":[\"q013\",\"q113\",\"qa13\",\"qr13\"],\"steps\":2,\"tape_alphabet\":[\"013\",\"X13\",\"_13\"],\"transitions\":[[\"q013\",\"_13\",\"qr13\",\"_13\",\"S\"],[\"q013\",\"013\",\"q113\",\"X13\",\"R\"],[\"q113\",\"_13\",\"qa13\",\"_13\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q013, q113, qa13, qr13], input_alphabet=[013], tape_alphabet=[013, X13, _13], blank=_13, start=q013, accept=qa13, reject=qr13, transitions=[[q013, 013, q113, X13, R], [q013, _13, qr13, _13, S], [q113, _13, qa13, _13, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[013], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([013], 2, [[q013, 0, [[0, 013]]], [q113, 1, [[0, X13]]], [qa13, 0, [[0, X13]]]], [step, step], qa13, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([013], 2, [[q013, 0, [[0, 013]]], [q113, 1, [[0, X13]]], [qa13, 0, [[0, X13]]]], [step, step], qa13, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0040","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"089d86312ebc271c73159c74fd1488d5fef65d191992e6e470e242028d18329e","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135040,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa14\",\"blank\":\"_14\",\"input\":[\"014\"],\"input_alphabet\":[\"014\"],\"reject_state\":\"qr14\",\"start_state\":\"q014\",\"states\":[\"q014\",\"q114\",\"qa14\",\"qr14\"],\"steps\":2,\"tape_alphabet\":[\"014\",\"X14\",\"_14\"],\"transitions\":[[\"q014\",\"_14\",\"qr14\",\"_14\",\"S\"],[\"q014\",\"014\",\"q114\",\"X14\",\"R\"],[\"q114\",\"_14\",\"qa14\",\"_14\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q014, q114, qa14, qr14], input_alphabet=[014], tape_alphabet=[014, X14, _14], blank=_14, start=q014, accept=qa14, reject=qr14, transitions=[[q014, 014, q114, X14, R], [q014, _14, qr14, _14, S], [q114, _14, qa14, _14, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[014], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([014], 2, [[q014, 0, [[0, 014]]], [q114, 1, [[0, X14]]], [qa14, 0, [[0, X14]]]], [step, step], qa14, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([014], 2, [[q014, 0, [[0, 014]]], [q114, 1, [[0, X14]]], [qa14, 0, [[0, X14]]]], [step, step], qa14, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0041","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"61c3314531370d65ddf1e462791706ee0165686b50ae1139625068411b825c8a","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135041,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa15\",\"blank\":\"_15\",\"input\":[\"015\"],\"input_alphabet\":[\"015\"],\"reject_state\":\"qr15\",\"start_state\":\"q015\",\"states\":[\"q015\",\"q115\",\"qa15\",\"qr15\"],\"steps\":2,\"tape_alphabet\":[\"015\",\"X15\",\"_15\"],\"transitions\":[[\"q015\",\"_15\",\"qr15\",\"_15\",\"S\"],[\"q015\",\"015\",\"q115\",\"X15\",\"R\"],[\"q115\",\"_15\",\"qa15\",\"_15\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q015, q115, qa15, qr15], input_alphabet=[015], tape_alphabet=[015, X15, _15], blank=_15, start=q015, accept=qa15, reject=qr15, transitions=[[q015, 015, q115, X15, R], [q015, _15, qr15, _15, S], [q115, _15, qa15, _15, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[015], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([015], 2, [[q015, 0, [[0, 015]]], [q115, 1, [[0, X15]]], [qa15, 0, [[0, X15]]]], [step, step], qa15, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([015], 2, [[q015, 0, [[0, 015]]], [q115, 1, [[0, X15]]], [qa15, 0, [[0, X15]]]], [step, step], qa15, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0042","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"720ffcd085f58df741c8b62309cca1be24ea98f7c4b5cc2538fc1f1d2a03aaef","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135042,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa16\",\"blank\":\"_16\",\"input\":[\"016\"],\"input_alphabet\":[\"016\"],\"reject_state\":\"qr16\",\"start_state\":\"q016\",\"states\":[\"q016\",\"q116\",\"qa16\",\"qr16\"],\"steps\":2,\"tape_alphabet\":[\"016\",\"X16\",\"_16\"],\"transitions\":[[\"q016\",\"_16\",\"qr16\",\"_16\",\"S\"],[\"q016\",\"016\",\"q116\",\"X16\",\"R\"],[\"q116\",\"_16\",\"qa16\",\"_16\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q016, q116, qa16, qr16], input_alphabet=[016], tape_alphabet=[016, X16, _16], blank=_16, start=q016, accept=qa16, reject=qr16, transitions=[[q016, 016, q116, X16, R], [q016, _16, qr16, _16, S], [q116, _16, qa16, _16, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[016], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([016], 2, [[q016, 0, [[0, 016]]], [q116, 1, [[0, X16]]], [qa16, 0, [[0, X16]]]], [step, step], qa16, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([016], 2, [[q016, 0, [[0, 016]]], [q116, 1, [[0, X16]]], [qa16, 0, [[0, X16]]]], [step, step], qa16, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0043","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"258d7b91f8ebfc0b207d15e752feb5d9c288ae98f9a29d56b3260bd9b5e26b29","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135043,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa17\",\"blank\":\"_17\",\"input\":[\"017\"],\"input_alphabet\":[\"017\"],\"reject_state\":\"qr17\",\"start_state\":\"q017\",\"states\":[\"q017\",\"q117\",\"qa17\",\"qr17\"],\"steps\":2,\"tape_alphabet\":[\"017\",\"X17\",\"_17\"],\"transitions\":[[\"q017\",\"_17\",\"qr17\",\"_17\",\"S\"],[\"q017\",\"017\",\"q117\",\"X17\",\"R\"],[\"q117\",\"_17\",\"qa17\",\"_17\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q017, q117, qa17, qr17], input_alphabet=[017], tape_alphabet=[017, X17, _17], blank=_17, start=q017, accept=qa17, reject=qr17, transitions=[[q017, 017, q117, X17, R], [q017, _17, qr17, _17, S], [q117, _17, qa17, _17, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[017], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([017], 2, [[q017, 0, [[0, 017]]], [q117, 1, [[0, X17]]], [qa17, 0, [[0, X17]]]], [step, step], qa17, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([017], 2, [[q017, 0, [[0, 017]]], [q117, 1, [[0, X17]]], [qa17, 0, [[0, X17]]]], [step, step], qa17, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0044","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0e92e54d3677b5056e4f7f7d204f3cb0cc1607409cb8ab7ed55971a270abebab","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135044,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa18\",\"blank\":\"_18\",\"input\":[\"018\"],\"input_alphabet\":[\"018\"],\"reject_state\":\"qr18\",\"start_state\":\"q018\",\"states\":[\"q018\",\"q118\",\"qa18\",\"qr18\"],\"steps\":2,\"tape_alphabet\":[\"018\",\"X18\",\"_18\"],\"transitions\":[[\"q018\",\"_18\",\"qr18\",\"_18\",\"S\"],[\"q018\",\"018\",\"q118\",\"X18\",\"R\"],[\"q118\",\"_18\",\"qa18\",\"_18\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q018, q118, qa18, qr18], input_alphabet=[018], tape_alphabet=[018, X18, _18], blank=_18, start=q018, accept=qa18, reject=qr18, transitions=[[q018, 018, q118, X18, R], [q018, _18, qr18, _18, S], [q118, _18, qa18, _18, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[018], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([018], 2, [[q018, 0, [[0, 018]]], [q118, 1, [[0, X18]]], [qa18, 0, [[0, X18]]]], [step, step], qa18, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([018], 2, [[q018, 0, [[0, 018]]], [q118, 1, [[0, X18]]], [qa18, 0, [[0, X18]]]], [step, step], qa18, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0045","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"29cfb55dddc1e1fb339f24307613414918559705ceb5b894c46ba83dfaf63d00","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135045,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa19\",\"blank\":\"_19\",\"input\":[\"019\"],\"input_alphabet\":[\"019\"],\"reject_state\":\"qr19\",\"start_state\":\"q019\",\"states\":[\"q019\",\"q119\",\"qa19\",\"qr19\"],\"steps\":2,\"tape_alphabet\":[\"019\",\"X19\",\"_19\"],\"transitions\":[[\"q019\",\"_19\",\"qr19\",\"_19\",\"S\"],[\"q019\",\"019\",\"q119\",\"X19\",\"R\"],[\"q119\",\"_19\",\"qa19\",\"_19\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q019, q119, qa19, qr19], input_alphabet=[019], tape_alphabet=[019, X19, _19], blank=_19, start=q019, accept=qa19, reject=qr19, transitions=[[q019, 019, q119, X19, R], [q019, _19, qr19, _19, S], [q119, _19, qa19, _19, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[019], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([019], 2, [[q019, 0, [[0, 019]]], [q119, 1, [[0, X19]]], [qa19, 0, [[0, X19]]]], [step, step], qa19, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([019], 2, [[q019, 0, [[0, 019]]], [q119, 1, [[0, X19]]], [qa19, 0, [[0, X19]]]], [step, step], qa19, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0046","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e584ba8ef5fa90ade0e329ef4716175720373c39eca34e862bdadcb8fe6e7ea0","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135046,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa20\",\"blank\":\"_20\",\"input\":[\"020\"],\"input_alphabet\":[\"020\"],\"reject_state\":\"qr20\",\"start_state\":\"q020\",\"states\":[\"q020\",\"q120\",\"qa20\",\"qr20\"],\"steps\":2,\"tape_alphabet\":[\"020\",\"X20\",\"_20\"],\"transitions\":[[\"q020\",\"_20\",\"qr20\",\"_20\",\"S\"],[\"q020\",\"020\",\"q120\",\"X20\",\"R\"],[\"q120\",\"_20\",\"qa20\",\"_20\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q020, q120, qa20, qr20], input_alphabet=[020], tape_alphabet=[020, X20, _20], blank=_20, start=q020, accept=qa20, reject=qr20, transitions=[[q020, 020, q120, X20, R], [q020, _20, qr20, _20, S], [q120, _20, qa20, _20, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[020], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([020], 2, [[q020, 0, [[0, 020]]], [q120, 1, [[0, X20]]], [qa20, 0, [[0, X20]]]], [step, step], qa20, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([020], 2, [[q020, 0, [[0, 020]]], [q120, 1, [[0, X20]]], [qa20, 0, [[0, X20]]]], [step, step], qa20, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0047","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"da6606dc3de8c69ab4a9b304093843a06f1f04c454feff5999ef6632366399a4","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135047,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa21\",\"blank\":\"_21\",\"input\":[\"021\"],\"input_alphabet\":[\"021\"],\"reject_state\":\"qr21\",\"start_state\":\"q021\",\"states\":[\"q021\",\"q121\",\"qa21\",\"qr21\"],\"steps\":2,\"tape_alphabet\":[\"021\",\"X21\",\"_21\"],\"transitions\":[[\"q021\",\"_21\",\"qr21\",\"_21\",\"S\"],[\"q021\",\"021\",\"q121\",\"X21\",\"R\"],[\"q121\",\"_21\",\"qa21\",\"_21\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q021, q121, qa21, qr21], input_alphabet=[021], tape_alphabet=[021, X21, _21], blank=_21, start=q021, accept=qa21, reject=qr21, transitions=[[q021, 021, q121, X21, R], [q021, _21, qr21, _21, S], [q121, _21, qa21, _21, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[021], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([021], 2, [[q021, 0, [[0, 021]]], [q121, 1, [[0, X21]]], [qa21, 0, [[0, X21]]]], [step, step], qa21, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([021], 2, [[q021, 0, [[0, 021]]], [q121, 1, [[0, X21]]], [qa21, 0, [[0, X21]]]], [step, step], qa21, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0048","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e13371e814bcae723b55446cf4ac6a4ad6aa300c73698d8fce5c34ab716a52a3","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135048,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa22\",\"blank\":\"_22\",\"input\":[\"022\"],\"input_alphabet\":[\"022\"],\"reject_state\":\"qr22\",\"start_state\":\"q022\",\"states\":[\"q022\",\"q122\",\"qa22\",\"qr22\"],\"steps\":2,\"tape_alphabet\":[\"022\",\"X22\",\"_22\"],\"transitions\":[[\"q022\",\"_22\",\"qr22\",\"_22\",\"S\"],[\"q022\",\"022\",\"q122\",\"X22\",\"R\"],[\"q122\",\"_22\",\"qa22\",\"_22\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q022, q122, qa22, qr22], input_alphabet=[022], tape_alphabet=[022, X22, _22], blank=_22, start=q022, accept=qa22, reject=qr22, transitions=[[q022, 022, q122, X22, R], [q022, _22, qr22, _22, S], [q122, _22, qa22, _22, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[022], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([022], 2, [[q022, 0, [[0, 022]]], [q122, 1, [[0, X22]]], [qa22, 0, [[0, X22]]]], [step, step], qa22, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([022], 2, [[q022, 0, [[0, 022]]], [q122, 1, [[0, X22]]], [qa22, 0, [[0, X22]]]], [step, step], qa22, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0049","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a49478c569e71578b3690482d688ee693af2dc016fe1335d78aa6e8b053d1f53","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135049,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa23\",\"blank\":\"_23\",\"input\":[\"023\"],\"input_alphabet\":[\"023\"],\"reject_state\":\"qr23\",\"start_state\":\"q023\",\"states\":[\"q023\",\"q123\",\"qa23\",\"qr23\"],\"steps\":2,\"tape_alphabet\":[\"023\",\"X23\",\"_23\"],\"transitions\":[[\"q023\",\"_23\",\"qr23\",\"_23\",\"S\"],[\"q023\",\"023\",\"q123\",\"X23\",\"R\"],[\"q123\",\"_23\",\"qa23\",\"_23\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q023, q123, qa23, qr23], input_alphabet=[023], tape_alphabet=[023, X23, _23], blank=_23, start=q023, accept=qa23, reject=qr23, transitions=[[q023, 023, q123, X23, R], [q023, _23, qr23, _23, S], [q123, _23, qa23, _23, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[023], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([023], 2, [[q023, 0, [[0, 023]]], [q123, 1, [[0, X23]]], [qa23, 0, [[0, X23]]]], [step, step], qa23, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([023], 2, [[q023, 0, [[0, 023]]], [q123, 1, [[0, X23]]], [qa23, 0, [[0, X23]]]], [step, step], qa23, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0050","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6290005d4276b8e399e8ca3538d36fffd5fcc215d382db83f969133948d43bce","family_id":"qf-mod44-tm-exact-step-trace","seed":202611135050,"semantic_template":"qf-mod44-tm-exact-step-trace/{\"accept_state\":\"qa24\",\"blank\":\"_24\",\"input\":[\"024\"],\"input_alphabet\":[\"024\"],\"reject_state\":\"qr24\",\"start_state\":\"q024\",\"states\":[\"q024\",\"q124\",\"qa24\",\"qr24\"],\"steps\":2,\"tape_alphabet\":[\"024\",\"X24\",\"_24\"],\"transitions\":[[\"q024\",\"_24\",\"qr24\",\"_24\",\"S\"],[\"q024\",\"024\",\"q124\",\"X24\",\"R\"],[\"q124\",\"_24\",\"qa24\",\"_24\",\"L\"]]}"},"fields":{"title":"A Finite Configuration Trace Has Only Its Declared Input and Budget Scope","stem":"Use deterministic single-tape states=[q024, q124, qa24, qr24], input_alphabet=[024], tape_alphabet=[024, X24, _24], blank=_24, start=q024, accept=qa24, reject=qr24, transitions=[[q024, 024, q124, X24, R], [q024, _24, qr24, _24, S], [q124, _24, qa24, _24, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[024], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).","answer":{"kind":"expression","value":"([024], 2, [[q024, 0, [[0, 024]]], [q124, 1, [[0, X24]]], [qa24, 0, [[0, X24]]]], [step, step], qa24, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)","explanation":"Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([024], 2, [[q024, 0, [[0, 024]]], [q124, 1, [[0, X24]]], [qa24, 0, [[0, X24]]]], [step, step], qa24, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)."},"skills":["A Finite Configuration Trace Has Only Its Declared Input and Budget Scope"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0051","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"44dfba14a09823e0e149a80132b24135d5d0971516487b9141276abb1a1be222","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135051,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a0\",\"b0\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a0\",\"b0\"],\"target_symbol\":\"b0\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a0\",\"scan\",\"a0\",\"R\"],[\"scan\",\"b0\",\"accept\",\"b0\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a0, b0], tape_alphabet=[a0, b0, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a0, scan, a0, R], [scan, b0, accept, b0, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b0. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a0, b0], [_, a0, b0], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a0, scan, a0, R], [scan, b0, accept, b0, S]], b0, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a0, b0], [_, a0, b0], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a0, scan, a0, R], [scan, b0, accept, b0, S]], b0, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0052","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3b502dcb9ad8bac3de206ea5931143c68f0a7cfa80887e8b362f5864b3562b34","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135052,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a1\",\"b1\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a1\",\"b1\"],\"target_symbol\":\"b1\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a1\",\"scan\",\"a1\",\"R\"],[\"scan\",\"b1\",\"accept\",\"b1\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a1, b1], tape_alphabet=[a1, b1, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a1, scan, a1, R], [scan, b1, accept, b1, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b1. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a1, b1], [_, a1, b1], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a1, scan, a1, R], [scan, b1, accept, b1, S]], b1, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a1, b1], [_, a1, b1], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a1, scan, a1, R], [scan, b1, accept, b1, S]], b1, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0053","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5664eb0d916a5507033901aa48e2bb5843baf1f2e897c8e648c75662ecf671fc","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135053,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a2\",\"b2\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a2\",\"b2\"],\"target_symbol\":\"b2\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a2\",\"scan\",\"a2\",\"R\"],[\"scan\",\"b2\",\"accept\",\"b2\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a2, b2], tape_alphabet=[a2, b2, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a2, scan, a2, R], [scan, b2, accept, b2, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b2. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a2, b2], [_, a2, b2], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a2, scan, a2, R], [scan, b2, accept, b2, S]], b2, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a2, b2], [_, a2, b2], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a2, scan, a2, R], [scan, b2, accept, b2, S]], b2, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0054","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8c491c89a5bb7f85710623c9cf7bbe91274dd7a8e1684e5385f0c9730e314b63","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135054,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a3\",\"b3\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a3\",\"b3\"],\"target_symbol\":\"b3\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a3\",\"scan\",\"a3\",\"R\"],[\"scan\",\"b3\",\"accept\",\"b3\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a3, b3], tape_alphabet=[a3, b3, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a3, scan, a3, R], [scan, b3, accept, b3, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b3. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a3, b3], [_, a3, b3], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a3, scan, a3, R], [scan, b3, accept, b3, S]], b3, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a3, b3], [_, a3, b3], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a3, scan, a3, R], [scan, b3, accept, b3, S]], b3, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0055","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ef3cbe9295aec3cf88904d60f8fb9019ea64f6c1f5cb222a705f097a72a2d6c4","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135055,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a4\",\"b4\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a4\",\"b4\"],\"target_symbol\":\"b4\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a4\",\"scan\",\"a4\",\"R\"],[\"scan\",\"b4\",\"accept\",\"b4\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a4, b4], tape_alphabet=[a4, b4, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a4, scan, a4, R], [scan, b4, accept, b4, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b4. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a4, b4], [_, a4, b4], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a4, scan, a4, R], [scan, b4, accept, b4, S]], b4, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a4, b4], [_, a4, b4], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a4, scan, a4, R], [scan, b4, accept, b4, S]], b4, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0056","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"524c0ed9714ce653172038c6d0280a2c5f3ddecef04c7304c5d0e356c5325e94","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135056,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a5\",\"b5\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a5\",\"b5\"],\"target_symbol\":\"b5\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a5\",\"scan\",\"a5\",\"R\"],[\"scan\",\"b5\",\"accept\",\"b5\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a5, b5], tape_alphabet=[a5, b5, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a5, scan, a5, R], [scan, b5, accept, b5, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b5. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a5, b5], [_, a5, b5], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a5, scan, a5, R], [scan, b5, accept, b5, S]], b5, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a5, b5], [_, a5, b5], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a5, scan, a5, R], [scan, b5, accept, b5, S]], b5, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0057","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"638baf0aa378cf0898fc29d73a382fb4446eb611fb9eea1015228e28ce80c423","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135057,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a6\",\"b6\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a6\",\"b6\"],\"target_symbol\":\"b6\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a6\",\"scan\",\"a6\",\"R\"],[\"scan\",\"b6\",\"accept\",\"b6\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a6, b6], tape_alphabet=[a6, b6, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a6, scan, a6, R], [scan, b6, accept, b6, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b6. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a6, b6], [_, a6, b6], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a6, scan, a6, R], [scan, b6, accept, b6, S]], b6, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a6, b6], [_, a6, b6], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a6, scan, a6, R], [scan, b6, accept, b6, S]], b6, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0058","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"035365b79c59bbd05ff87c1299708f9855e3e864d857fd0f46a3acdea85414a1","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135058,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a7\",\"b7\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a7\",\"b7\"],\"target_symbol\":\"b7\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a7\",\"scan\",\"a7\",\"R\"],[\"scan\",\"b7\",\"accept\",\"b7\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a7, b7], tape_alphabet=[a7, b7, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a7, scan, a7, R], [scan, b7, accept, b7, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b7. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a7, b7], [_, a7, b7], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a7, scan, a7, R], [scan, b7, accept, b7, S]], b7, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a7, b7], [_, a7, b7], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a7, scan, a7, R], [scan, b7, accept, b7, S]], b7, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0059","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"95ce8ca59b81e794857a0f8dd49ad8d7cfb2cf9803b2b948d153092fc805a67f","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135059,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a8\",\"b8\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a8\",\"b8\"],\"target_symbol\":\"b8\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a8\",\"scan\",\"a8\",\"R\"],[\"scan\",\"b8\",\"accept\",\"b8\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a8, b8], tape_alphabet=[a8, b8, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a8, scan, a8, R], [scan, b8, accept, b8, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b8. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a8, b8], [_, a8, b8], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a8, scan, a8, R], [scan, b8, accept, b8, S]], b8, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a8, b8], [_, a8, b8], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a8, scan, a8, R], [scan, b8, accept, b8, S]], b8, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0060","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"255aea63a73fb8394c5bcc9d42d829d8837f064f945cbf604ff0f3e26cb2914b","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135060,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a9\",\"b9\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a9\",\"b9\"],\"target_symbol\":\"b9\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a9\",\"scan\",\"a9\",\"R\"],[\"scan\",\"b9\",\"accept\",\"b9\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a9, b9], tape_alphabet=[a9, b9, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a9, scan, a9, R], [scan, b9, accept, b9, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b9. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a9, b9], [_, a9, b9], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a9, scan, a9, R], [scan, b9, accept, b9, S]], b9, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a9, b9], [_, a9, b9], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a9, scan, a9, R], [scan, b9, accept, b9, S]], b9, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0061","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"220a0549d899e3cd02c84e6a3a2bcc9ec88d7c355bd7195d9ed222459bbdcad1","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135061,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a10\",\"b10\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a10\",\"b10\"],\"target_symbol\":\"b10\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a10\",\"scan\",\"a10\",\"R\"],[\"scan\",\"b10\",\"accept\",\"b10\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a10, b10], tape_alphabet=[a10, b10, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a10, scan, a10, R], [scan, b10, accept, b10, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b10. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a10, b10], [_, a10, b10], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a10, scan, a10, R], [scan, b10, accept, b10, S]], b10, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a10, b10], [_, a10, b10], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a10, scan, a10, R], [scan, b10, accept, b10, S]], b10, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0062","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b61cb3e72a7e871dde0f776bd020b964fe30014a302e255f17bc85f295c47be2","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135062,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a11\",\"b11\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a11\",\"b11\"],\"target_symbol\":\"b11\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a11\",\"scan\",\"a11\",\"R\"],[\"scan\",\"b11\",\"accept\",\"b11\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a11, b11], tape_alphabet=[a11, b11, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a11, scan, a11, R], [scan, b11, accept, b11, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b11. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a11, b11], [_, a11, b11], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a11, scan, a11, R], [scan, b11, accept, b11, S]], b11, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a11, b11], [_, a11, b11], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a11, scan, a11, R], [scan, b11, accept, b11, S]], b11, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0063","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9b71da321f24af9a408e756a6ea03807cff5ad33852489d0cb457142e6395c8c","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135063,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a12\",\"b12\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a12\",\"b12\"],\"target_symbol\":\"b12\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a12\",\"scan\",\"a12\",\"R\"],[\"scan\",\"b12\",\"accept\",\"b12\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a12, b12], tape_alphabet=[a12, b12, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a12, scan, a12, R], [scan, b12, accept, b12, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b12. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a12, b12], [_, a12, b12], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a12, scan, a12, R], [scan, b12, accept, b12, S]], b12, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a12, b12], [_, a12, b12], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a12, scan, a12, R], [scan, b12, accept, b12, S]], b12, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0064","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3f1fe362c00533efa57b1ca8d5ab0c06642b9e0c38e05c7085d66b9d0de8da37","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135064,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a13\",\"b13\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a13\",\"b13\"],\"target_symbol\":\"b13\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a13\",\"scan\",\"a13\",\"R\"],[\"scan\",\"b13\",\"accept\",\"b13\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a13, b13], tape_alphabet=[a13, b13, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a13, scan, a13, R], [scan, b13, accept, b13, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b13. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a13, b13], [_, a13, b13], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a13, scan, a13, R], [scan, b13, accept, b13, S]], b13, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a13, b13], [_, a13, b13], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a13, scan, a13, R], [scan, b13, accept, b13, S]], b13, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0065","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3b76876ae763b1f4a2fd900a491d5b156a02d22a82aabb6b52cd13273ac6fddb","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135065,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a14\",\"b14\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a14\",\"b14\"],\"target_symbol\":\"b14\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a14\",\"scan\",\"a14\",\"R\"],[\"scan\",\"b14\",\"accept\",\"b14\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a14, b14], tape_alphabet=[a14, b14, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a14, scan, a14, R], [scan, b14, accept, b14, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b14. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a14, b14], [_, a14, b14], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a14, scan, a14, R], [scan, b14, accept, b14, S]], b14, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a14, b14], [_, a14, b14], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a14, scan, a14, R], [scan, b14, accept, b14, S]], b14, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0066","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"698f62906626a89f54d6a4b9f7960937db681572202bc8edbce9e9b183fc956b","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135066,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a15\",\"b15\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a15\",\"b15\"],\"target_symbol\":\"b15\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a15\",\"scan\",\"a15\",\"R\"],[\"scan\",\"b15\",\"accept\",\"b15\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a15, b15], tape_alphabet=[a15, b15, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a15, scan, a15, R], [scan, b15, accept, b15, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b15. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a15, b15], [_, a15, b15], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a15, scan, a15, R], [scan, b15, accept, b15, S]], b15, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a15, b15], [_, a15, b15], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a15, scan, a15, R], [scan, b15, accept, b15, S]], b15, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0067","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5c0605a65909f8c771d794e5f19a351a671b2806b6a780d6ad59bb33394ac4c5","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135067,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a16\",\"b16\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a16\",\"b16\"],\"target_symbol\":\"b16\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a16\",\"scan\",\"a16\",\"R\"],[\"scan\",\"b16\",\"accept\",\"b16\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a16, b16], tape_alphabet=[a16, b16, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a16, scan, a16, R], [scan, b16, accept, b16, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b16. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a16, b16], [_, a16, b16], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a16, scan, a16, R], [scan, b16, accept, b16, S]], b16, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a16, b16], [_, a16, b16], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a16, scan, a16, R], [scan, b16, accept, b16, S]], b16, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0068","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7624c1e9309c5dbe411ab173e61326c2fb1e860f0dbc6d3269fcae3d98fedf80","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135068,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a17\",\"b17\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a17\",\"b17\"],\"target_symbol\":\"b17\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a17\",\"scan\",\"a17\",\"R\"],[\"scan\",\"b17\",\"accept\",\"b17\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a17, b17], tape_alphabet=[a17, b17, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a17, scan, a17, R], [scan, b17, accept, b17, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b17. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a17, b17], [_, a17, b17], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a17, scan, a17, R], [scan, b17, accept, b17, S]], b17, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a17, b17], [_, a17, b17], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a17, scan, a17, R], [scan, b17, accept, b17, S]], b17, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0069","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9868eb9d665fc031d4c080dff2c7f080768b6d1fb8a2fd5a79bf9ffd663e7712","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135069,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a18\",\"b18\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a18\",\"b18\"],\"target_symbol\":\"b18\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a18\",\"scan\",\"a18\",\"R\"],[\"scan\",\"b18\",\"accept\",\"b18\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a18, b18], tape_alphabet=[a18, b18, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a18, scan, a18, R], [scan, b18, accept, b18, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b18. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a18, b18], [_, a18, b18], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a18, scan, a18, R], [scan, b18, accept, b18, S]], b18, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a18, b18], [_, a18, b18], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a18, scan, a18, R], [scan, b18, accept, b18, S]], b18, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0070","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dc78f63891e3cc6cb27dbf10150d8fb2a127d106035757c94e300a3e44578bd1","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135070,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a19\",\"b19\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a19\",\"b19\"],\"target_symbol\":\"b19\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a19\",\"scan\",\"a19\",\"R\"],[\"scan\",\"b19\",\"accept\",\"b19\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a19, b19], tape_alphabet=[a19, b19, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a19, scan, a19, R], [scan, b19, accept, b19, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b19. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a19, b19], [_, a19, b19], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a19, scan, a19, R], [scan, b19, accept, b19, S]], b19, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a19, b19], [_, a19, b19], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a19, scan, a19, R], [scan, b19, accept, b19, S]], b19, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0071","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"98f76dd8c237dd5fffc6b927b43f5aaeb944682c96e0db7b538b71bc23b85c63","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135071,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a20\",\"b20\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a20\",\"b20\"],\"target_symbol\":\"b20\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a20\",\"scan\",\"a20\",\"R\"],[\"scan\",\"b20\",\"accept\",\"b20\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a20, b20], tape_alphabet=[a20, b20, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a20, scan, a20, R], [scan, b20, accept, b20, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b20. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a20, b20], [_, a20, b20], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a20, scan, a20, R], [scan, b20, accept, b20, S]], b20, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a20, b20], [_, a20, b20], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a20, scan, a20, R], [scan, b20, accept, b20, S]], b20, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0072","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7dd758f4c044694db4fdce012c0dfa933e7b07231c4ce5a00b61a98254f4af09","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135072,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a21\",\"b21\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a21\",\"b21\"],\"target_symbol\":\"b21\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a21\",\"scan\",\"a21\",\"R\"],[\"scan\",\"b21\",\"accept\",\"b21\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a21, b21], tape_alphabet=[a21, b21, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a21, scan, a21, R], [scan, b21, accept, b21, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b21. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a21, b21], [_, a21, b21], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a21, scan, a21, R], [scan, b21, accept, b21, S]], b21, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a21, b21], [_, a21, b21], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a21, scan, a21, R], [scan, b21, accept, b21, S]], b21, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0073","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2409ec7d8907a6c06e5f06e440ff908a311f5dc7a0ac2f675c8e09e0078689f8","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135073,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a22\",\"b22\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a22\",\"b22\"],\"target_symbol\":\"b22\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a22\",\"scan\",\"a22\",\"R\"],[\"scan\",\"b22\",\"accept\",\"b22\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a22, b22], tape_alphabet=[a22, b22, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a22, scan, a22, R], [scan, b22, accept, b22, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b22. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a22, b22], [_, a22, b22], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a22, scan, a22, R], [scan, b22, accept, b22, S]], b22, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a22, b22], [_, a22, b22], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a22, scan, a22, R], [scan, b22, accept, b22, S]], b22, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0074","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"234aa93ef9ce23a46c12cdfba4f09c2b97e664f97984da44ba6346d91f21b866","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135074,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a23\",\"b23\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a23\",\"b23\"],\"target_symbol\":\"b23\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a23\",\"scan\",\"a23\",\"R\"],[\"scan\",\"b23\",\"accept\",\"b23\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a23, b23], tape_alphabet=[a23, b23, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a23, scan, a23, R], [scan, b23, accept, b23, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b23. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a23, b23], [_, a23, b23], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a23, scan, a23, R], [scan, b23, accept, b23, S]], b23, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a23, b23], [_, a23, b23], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a23, scan, a23, R], [scan, b23, accept, b23, S]], b23, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0075","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c2d8d4a7815cd359c9b8a34c14cc845442b81190e0ed701a675b207902d6d9f","family_id":"qf-mod44-tm-global-decider-ranking","seed":202611135075,"semantic_template":"qf-mod44-tm-global-decider-ranking/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input_alphabet\":[\"a24\",\"b24\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a24\",\"b24\"],\"target_symbol\":\"b24\",\"transitions\":[[\"scan\",\"_\",\"reject\",\"_\",\"S\"],[\"scan\",\"a24\",\"scan\",\"a24\",\"R\"],[\"scan\",\"b24\",\"accept\",\"b24\",\"S\"]]}"},"fields":{"title":"A Canonical Scan Schema Has an All-Input Ranking and Correct Answers","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a24, b24], tape_alphabet=[a24, b24, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a24, scan, a24, R], [scan, b24, accept, b24, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b24. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).","answer":{"kind":"expression","value":"([accept, reject, scan], [a24, b24], [_, a24, b24], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a24, scan, a24, R], [scan, b24, accept, b24, S]], b24, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)","explanation":"Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a24, b24], [_, a24, b24], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a24, scan, a24, R], [scan, b24, accept, b24, S]], b24, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)."},"skills":["A Canonical Scan Schema Has an All-Input Ranking and Correct Answers"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0076","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b03c114a518e559f775a9aa15e919a6342b980736a53dfc9fbd55bec863d3acd","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135076,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a0\",\"a0\"],\"input_alphabet\":[\"a0\",\"b0\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a0\",\"b0\"],\"target_symbol\":\"b0\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a0\",\"scan\",\"a0\",\"R\"],[\"scan\",\"b0\",\"accept\",\"b0\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a0, b0], tape_alphabet=[a0, b0, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a0, scan, a0, R], [scan, b0, accept, b0, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b0, legal target-free input=[a0, a0]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a0, b0], [_, a0, b0], [[scan, _, scan, _, S], [scan, a0, scan, a0, R], [scan, b0, accept, b0, S]], b0, [a0, a0], [scan, 2, [[0, a0], [1, a0]]], [scan, 2, [[0, a0], [1, a0]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a0, b0], [_, a0, b0], [[scan, _, scan, _, S], [scan, a0, scan, a0, R], [scan, b0, accept, b0, S]], b0, [a0, a0], [scan, 2, [[0, a0], [1, a0]]], [scan, 2, [[0, a0], [1, a0]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0077","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ccde0610c439c147d262f742c28745e844778df046cb5eb6e0ff600d3ab8203f","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135077,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a1\",\"a1\"],\"input_alphabet\":[\"a1\",\"b1\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a1\",\"b1\"],\"target_symbol\":\"b1\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a1\",\"scan\",\"a1\",\"R\"],[\"scan\",\"b1\",\"accept\",\"b1\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a1, b1], tape_alphabet=[a1, b1, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a1, scan, a1, R], [scan, b1, accept, b1, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b1, legal target-free input=[a1, a1]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a1, b1], [_, a1, b1], [[scan, _, scan, _, S], [scan, a1, scan, a1, R], [scan, b1, accept, b1, S]], b1, [a1, a1], [scan, 2, [[0, a1], [1, a1]]], [scan, 2, [[0, a1], [1, a1]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a1, b1], [_, a1, b1], [[scan, _, scan, _, S], [scan, a1, scan, a1, R], [scan, b1, accept, b1, S]], b1, [a1, a1], [scan, 2, [[0, a1], [1, a1]]], [scan, 2, [[0, a1], [1, a1]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0078","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"33f604010fb3771547ca58fa064cfcbd85afda98545f5ac7f9923457818c52b2","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135078,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a2\",\"a2\"],\"input_alphabet\":[\"a2\",\"b2\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a2\",\"b2\"],\"target_symbol\":\"b2\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a2\",\"scan\",\"a2\",\"R\"],[\"scan\",\"b2\",\"accept\",\"b2\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a2, b2], tape_alphabet=[a2, b2, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a2, scan, a2, R], [scan, b2, accept, b2, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b2, legal target-free input=[a2, a2]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a2, b2], [_, a2, b2], [[scan, _, scan, _, S], [scan, a2, scan, a2, R], [scan, b2, accept, b2, S]], b2, [a2, a2], [scan, 2, [[0, a2], [1, a2]]], [scan, 2, [[0, a2], [1, a2]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a2, b2], [_, a2, b2], [[scan, _, scan, _, S], [scan, a2, scan, a2, R], [scan, b2, accept, b2, S]], b2, [a2, a2], [scan, 2, [[0, a2], [1, a2]]], [scan, 2, [[0, a2], [1, a2]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0079","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"936434fa41952e99902424e5d040acfdeb967416ee84408a9dd5c6d33e4a06c6","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135079,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a3\",\"a3\"],\"input_alphabet\":[\"a3\",\"b3\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a3\",\"b3\"],\"target_symbol\":\"b3\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a3\",\"scan\",\"a3\",\"R\"],[\"scan\",\"b3\",\"accept\",\"b3\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a3, b3], tape_alphabet=[a3, b3, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a3, scan, a3, R], [scan, b3, accept, b3, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b3, legal target-free input=[a3, a3]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a3, b3], [_, a3, b3], [[scan, _, scan, _, S], [scan, a3, scan, a3, R], [scan, b3, accept, b3, S]], b3, [a3, a3], [scan, 2, [[0, a3], [1, a3]]], [scan, 2, [[0, a3], [1, a3]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a3, b3], [_, a3, b3], [[scan, _, scan, _, S], [scan, a3, scan, a3, R], [scan, b3, accept, b3, S]], b3, [a3, a3], [scan, 2, [[0, a3], [1, a3]]], [scan, 2, [[0, a3], [1, a3]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0080","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"09d737fc6b0a2f6f38448668bcd8f13f3fd0943924a842ca2b709e6e76a62f56","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135080,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a4\",\"a4\"],\"input_alphabet\":[\"a4\",\"b4\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a4\",\"b4\"],\"target_symbol\":\"b4\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a4\",\"scan\",\"a4\",\"R\"],[\"scan\",\"b4\",\"accept\",\"b4\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a4, b4], tape_alphabet=[a4, b4, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a4, scan, a4, R], [scan, b4, accept, b4, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b4, legal target-free input=[a4, a4]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a4, b4], [_, a4, b4], [[scan, _, scan, _, S], [scan, a4, scan, a4, R], [scan, b4, accept, b4, S]], b4, [a4, a4], [scan, 2, [[0, a4], [1, a4]]], [scan, 2, [[0, a4], [1, a4]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a4, b4], [_, a4, b4], [[scan, _, scan, _, S], [scan, a4, scan, a4, R], [scan, b4, accept, b4, S]], b4, [a4, a4], [scan, 2, [[0, a4], [1, a4]]], [scan, 2, [[0, a4], [1, a4]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0081","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5ebb10a0492535951a4bd392d779e43b1a9c4e1a1a5f3f69c4baed493162b77e","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135081,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a5\",\"a5\"],\"input_alphabet\":[\"a5\",\"b5\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a5\",\"b5\"],\"target_symbol\":\"b5\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a5\",\"scan\",\"a5\",\"R\"],[\"scan\",\"b5\",\"accept\",\"b5\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a5, b5], tape_alphabet=[a5, b5, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a5, scan, a5, R], [scan, b5, accept, b5, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b5, legal target-free input=[a5, a5]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a5, b5], [_, a5, b5], [[scan, _, scan, _, S], [scan, a5, scan, a5, R], [scan, b5, accept, b5, S]], b5, [a5, a5], [scan, 2, [[0, a5], [1, a5]]], [scan, 2, [[0, a5], [1, a5]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a5, b5], [_, a5, b5], [[scan, _, scan, _, S], [scan, a5, scan, a5, R], [scan, b5, accept, b5, S]], b5, [a5, a5], [scan, 2, [[0, a5], [1, a5]]], [scan, 2, [[0, a5], [1, a5]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0082","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9ac68d6807010365583d1c3640f83e1fba011897789dd458cd7be0e08224ec0b","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135082,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a6\",\"a6\"],\"input_alphabet\":[\"a6\",\"b6\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a6\",\"b6\"],\"target_symbol\":\"b6\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a6\",\"scan\",\"a6\",\"R\"],[\"scan\",\"b6\",\"accept\",\"b6\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a6, b6], tape_alphabet=[a6, b6, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a6, scan, a6, R], [scan, b6, accept, b6, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b6, legal target-free input=[a6, a6]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a6, b6], [_, a6, b6], [[scan, _, scan, _, S], [scan, a6, scan, a6, R], [scan, b6, accept, b6, S]], b6, [a6, a6], [scan, 2, [[0, a6], [1, a6]]], [scan, 2, [[0, a6], [1, a6]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a6, b6], [_, a6, b6], [[scan, _, scan, _, S], [scan, a6, scan, a6, R], [scan, b6, accept, b6, S]], b6, [a6, a6], [scan, 2, [[0, a6], [1, a6]]], [scan, 2, [[0, a6], [1, a6]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0083","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eb57d343964684167b7beb1791ec9e06628298e3b1a1b55092c946e951c1673d","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135083,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a7\",\"a7\"],\"input_alphabet\":[\"a7\",\"b7\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a7\",\"b7\"],\"target_symbol\":\"b7\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a7\",\"scan\",\"a7\",\"R\"],[\"scan\",\"b7\",\"accept\",\"b7\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a7, b7], tape_alphabet=[a7, b7, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a7, scan, a7, R], [scan, b7, accept, b7, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b7, legal target-free input=[a7, a7]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a7, b7], [_, a7, b7], [[scan, _, scan, _, S], [scan, a7, scan, a7, R], [scan, b7, accept, b7, S]], b7, [a7, a7], [scan, 2, [[0, a7], [1, a7]]], [scan, 2, [[0, a7], [1, a7]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a7, b7], [_, a7, b7], [[scan, _, scan, _, S], [scan, a7, scan, a7, R], [scan, b7, accept, b7, S]], b7, [a7, a7], [scan, 2, [[0, a7], [1, a7]]], [scan, 2, [[0, a7], [1, a7]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0084","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8a349f4aa6861c6387f435279f36af13417f70b8bfc02e4da82b370097b2e745","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135084,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a8\",\"a8\"],\"input_alphabet\":[\"a8\",\"b8\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a8\",\"b8\"],\"target_symbol\":\"b8\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a8\",\"scan\",\"a8\",\"R\"],[\"scan\",\"b8\",\"accept\",\"b8\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a8, b8], tape_alphabet=[a8, b8, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a8, scan, a8, R], [scan, b8, accept, b8, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b8, legal target-free input=[a8, a8]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a8, b8], [_, a8, b8], [[scan, _, scan, _, S], [scan, a8, scan, a8, R], [scan, b8, accept, b8, S]], b8, [a8, a8], [scan, 2, [[0, a8], [1, a8]]], [scan, 2, [[0, a8], [1, a8]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a8, b8], [_, a8, b8], [[scan, _, scan, _, S], [scan, a8, scan, a8, R], [scan, b8, accept, b8, S]], b8, [a8, a8], [scan, 2, [[0, a8], [1, a8]]], [scan, 2, [[0, a8], [1, a8]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0085","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3355b499fd27f5d508576a29f39e841dd0850186c75717bdb1636009a4f96c27","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135085,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a9\",\"a9\"],\"input_alphabet\":[\"a9\",\"b9\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a9\",\"b9\"],\"target_symbol\":\"b9\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a9\",\"scan\",\"a9\",\"R\"],[\"scan\",\"b9\",\"accept\",\"b9\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a9, b9], tape_alphabet=[a9, b9, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a9, scan, a9, R], [scan, b9, accept, b9, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b9, legal target-free input=[a9, a9]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a9, b9], [_, a9, b9], [[scan, _, scan, _, S], [scan, a9, scan, a9, R], [scan, b9, accept, b9, S]], b9, [a9, a9], [scan, 2, [[0, a9], [1, a9]]], [scan, 2, [[0, a9], [1, a9]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a9, b9], [_, a9, b9], [[scan, _, scan, _, S], [scan, a9, scan, a9, R], [scan, b9, accept, b9, S]], b9, [a9, a9], [scan, 2, [[0, a9], [1, a9]]], [scan, 2, [[0, a9], [1, a9]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0086","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"95de256b3255234c753ac24b3402400ea50df2c4748afc48a022ebdb7a03bd7a","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135086,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a10\",\"a10\"],\"input_alphabet\":[\"a10\",\"b10\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a10\",\"b10\"],\"target_symbol\":\"b10\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a10\",\"scan\",\"a10\",\"R\"],[\"scan\",\"b10\",\"accept\",\"b10\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a10, b10], tape_alphabet=[a10, b10, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a10, scan, a10, R], [scan, b10, accept, b10, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b10, legal target-free input=[a10, a10]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a10, b10], [_, a10, b10], [[scan, _, scan, _, S], [scan, a10, scan, a10, R], [scan, b10, accept, b10, S]], b10, [a10, a10], [scan, 2, [[0, a10], [1, a10]]], [scan, 2, [[0, a10], [1, a10]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a10, b10], [_, a10, b10], [[scan, _, scan, _, S], [scan, a10, scan, a10, R], [scan, b10, accept, b10, S]], b10, [a10, a10], [scan, 2, [[0, a10], [1, a10]]], [scan, 2, [[0, a10], [1, a10]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0087","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"11cc2713bf6f5da0b9b890d95547108d13accdbbc12791dd28c0f429843945d0","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135087,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a11\",\"a11\"],\"input_alphabet\":[\"a11\",\"b11\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a11\",\"b11\"],\"target_symbol\":\"b11\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a11\",\"scan\",\"a11\",\"R\"],[\"scan\",\"b11\",\"accept\",\"b11\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a11, b11], tape_alphabet=[a11, b11, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a11, scan, a11, R], [scan, b11, accept, b11, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b11, legal target-free input=[a11, a11]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a11, b11], [_, a11, b11], [[scan, _, scan, _, S], [scan, a11, scan, a11, R], [scan, b11, accept, b11, S]], b11, [a11, a11], [scan, 2, [[0, a11], [1, a11]]], [scan, 2, [[0, a11], [1, a11]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a11, b11], [_, a11, b11], [[scan, _, scan, _, S], [scan, a11, scan, a11, R], [scan, b11, accept, b11, S]], b11, [a11, a11], [scan, 2, [[0, a11], [1, a11]]], [scan, 2, [[0, a11], [1, a11]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0088","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"923fe9ab6e5759d2680580dfa80c8032d1064dd80a714e4c33a767c5a3b21808","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135088,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a12\",\"a12\"],\"input_alphabet\":[\"a12\",\"b12\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a12\",\"b12\"],\"target_symbol\":\"b12\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a12\",\"scan\",\"a12\",\"R\"],[\"scan\",\"b12\",\"accept\",\"b12\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a12, b12], tape_alphabet=[a12, b12, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a12, scan, a12, R], [scan, b12, accept, b12, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b12, legal target-free input=[a12, a12]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a12, b12], [_, a12, b12], [[scan, _, scan, _, S], [scan, a12, scan, a12, R], [scan, b12, accept, b12, S]], b12, [a12, a12], [scan, 2, [[0, a12], [1, a12]]], [scan, 2, [[0, a12], [1, a12]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a12, b12], [_, a12, b12], [[scan, _, scan, _, S], [scan, a12, scan, a12, R], [scan, b12, accept, b12, S]], b12, [a12, a12], [scan, 2, [[0, a12], [1, a12]]], [scan, 2, [[0, a12], [1, a12]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0089","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"becb30f2113ed0aab0398b96b35c0452a7f832813b44f3a0636bed8e478fa4fc","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135089,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a13\",\"a13\"],\"input_alphabet\":[\"a13\",\"b13\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a13\",\"b13\"],\"target_symbol\":\"b13\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a13\",\"scan\",\"a13\",\"R\"],[\"scan\",\"b13\",\"accept\",\"b13\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a13, b13], tape_alphabet=[a13, b13, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a13, scan, a13, R], [scan, b13, accept, b13, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b13, legal target-free input=[a13, a13]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a13, b13], [_, a13, b13], [[scan, _, scan, _, S], [scan, a13, scan, a13, R], [scan, b13, accept, b13, S]], b13, [a13, a13], [scan, 2, [[0, a13], [1, a13]]], [scan, 2, [[0, a13], [1, a13]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a13, b13], [_, a13, b13], [[scan, _, scan, _, S], [scan, a13, scan, a13, R], [scan, b13, accept, b13, S]], b13, [a13, a13], [scan, 2, [[0, a13], [1, a13]]], [scan, 2, [[0, a13], [1, a13]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0090","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6a2c8e9127171a933d2deb56c09ff694a0ea84706862ffdbc56615cfdbc5b0f8","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135090,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a14\",\"a14\"],\"input_alphabet\":[\"a14\",\"b14\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a14\",\"b14\"],\"target_symbol\":\"b14\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a14\",\"scan\",\"a14\",\"R\"],[\"scan\",\"b14\",\"accept\",\"b14\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a14, b14], tape_alphabet=[a14, b14, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a14, scan, a14, R], [scan, b14, accept, b14, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b14, legal target-free input=[a14, a14]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a14, b14], [_, a14, b14], [[scan, _, scan, _, S], [scan, a14, scan, a14, R], [scan, b14, accept, b14, S]], b14, [a14, a14], [scan, 2, [[0, a14], [1, a14]]], [scan, 2, [[0, a14], [1, a14]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a14, b14], [_, a14, b14], [[scan, _, scan, _, S], [scan, a14, scan, a14, R], [scan, b14, accept, b14, S]], b14, [a14, a14], [scan, 2, [[0, a14], [1, a14]]], [scan, 2, [[0, a14], [1, a14]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0091","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d088edd52ce7cf0dcc97a4c1044ce8e4474583048631e3211aa32e6add8ba23a","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135091,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a15\",\"a15\"],\"input_alphabet\":[\"a15\",\"b15\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a15\",\"b15\"],\"target_symbol\":\"b15\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a15\",\"scan\",\"a15\",\"R\"],[\"scan\",\"b15\",\"accept\",\"b15\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a15, b15], tape_alphabet=[a15, b15, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a15, scan, a15, R], [scan, b15, accept, b15, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b15, legal target-free input=[a15, a15]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a15, b15], [_, a15, b15], [[scan, _, scan, _, S], [scan, a15, scan, a15, R], [scan, b15, accept, b15, S]], b15, [a15, a15], [scan, 2, [[0, a15], [1, a15]]], [scan, 2, [[0, a15], [1, a15]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a15, b15], [_, a15, b15], [[scan, _, scan, _, S], [scan, a15, scan, a15, R], [scan, b15, accept, b15, S]], b15, [a15, a15], [scan, 2, [[0, a15], [1, a15]]], [scan, 2, [[0, a15], [1, a15]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0092","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"07a47076a8d3104681bf93fcf339e94cded92a83475171d520ae518e76f49a62","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135092,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a16\",\"a16\"],\"input_alphabet\":[\"a16\",\"b16\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a16\",\"b16\"],\"target_symbol\":\"b16\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a16\",\"scan\",\"a16\",\"R\"],[\"scan\",\"b16\",\"accept\",\"b16\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a16, b16], tape_alphabet=[a16, b16, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a16, scan, a16, R], [scan, b16, accept, b16, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b16, legal target-free input=[a16, a16]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a16, b16], [_, a16, b16], [[scan, _, scan, _, S], [scan, a16, scan, a16, R], [scan, b16, accept, b16, S]], b16, [a16, a16], [scan, 2, [[0, a16], [1, a16]]], [scan, 2, [[0, a16], [1, a16]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a16, b16], [_, a16, b16], [[scan, _, scan, _, S], [scan, a16, scan, a16, R], [scan, b16, accept, b16, S]], b16, [a16, a16], [scan, 2, [[0, a16], [1, a16]]], [scan, 2, [[0, a16], [1, a16]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0093","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"67674b32d49645d981b5a6049c31924f7fb0ffb1fd19d067f1b8d2e43ff5fe6d","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135093,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a17\",\"a17\"],\"input_alphabet\":[\"a17\",\"b17\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a17\",\"b17\"],\"target_symbol\":\"b17\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a17\",\"scan\",\"a17\",\"R\"],[\"scan\",\"b17\",\"accept\",\"b17\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a17, b17], tape_alphabet=[a17, b17, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a17, scan, a17, R], [scan, b17, accept, b17, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b17, legal target-free input=[a17, a17]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a17, b17], [_, a17, b17], [[scan, _, scan, _, S], [scan, a17, scan, a17, R], [scan, b17, accept, b17, S]], b17, [a17, a17], [scan, 2, [[0, a17], [1, a17]]], [scan, 2, [[0, a17], [1, a17]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a17, b17], [_, a17, b17], [[scan, _, scan, _, S], [scan, a17, scan, a17, R], [scan, b17, accept, b17, S]], b17, [a17, a17], [scan, 2, [[0, a17], [1, a17]]], [scan, 2, [[0, a17], [1, a17]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0094","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cd872ecea15c51e0a12618dea03e297a981d212edcb2ed07b58dbf9c3f28e2c3","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135094,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a18\",\"a18\"],\"input_alphabet\":[\"a18\",\"b18\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a18\",\"b18\"],\"target_symbol\":\"b18\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a18\",\"scan\",\"a18\",\"R\"],[\"scan\",\"b18\",\"accept\",\"b18\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a18, b18], tape_alphabet=[a18, b18, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a18, scan, a18, R], [scan, b18, accept, b18, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b18, legal target-free input=[a18, a18]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a18, b18], [_, a18, b18], [[scan, _, scan, _, S], [scan, a18, scan, a18, R], [scan, b18, accept, b18, S]], b18, [a18, a18], [scan, 2, [[0, a18], [1, a18]]], [scan, 2, [[0, a18], [1, a18]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a18, b18], [_, a18, b18], [[scan, _, scan, _, S], [scan, a18, scan, a18, R], [scan, b18, accept, b18, S]], b18, [a18, a18], [scan, 2, [[0, a18], [1, a18]]], [scan, 2, [[0, a18], [1, a18]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0095","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4a5265a38a8c55c6ee1efbe7002d0fb8667d9074c8c3feb56ef4541f5c84c096","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135095,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a19\",\"a19\"],\"input_alphabet\":[\"a19\",\"b19\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a19\",\"b19\"],\"target_symbol\":\"b19\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a19\",\"scan\",\"a19\",\"R\"],[\"scan\",\"b19\",\"accept\",\"b19\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a19, b19], tape_alphabet=[a19, b19, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a19, scan, a19, R], [scan, b19, accept, b19, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b19, legal target-free input=[a19, a19]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a19, b19], [_, a19, b19], [[scan, _, scan, _, S], [scan, a19, scan, a19, R], [scan, b19, accept, b19, S]], b19, [a19, a19], [scan, 2, [[0, a19], [1, a19]]], [scan, 2, [[0, a19], [1, a19]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a19, b19], [_, a19, b19], [[scan, _, scan, _, S], [scan, a19, scan, a19, R], [scan, b19, accept, b19, S]], b19, [a19, a19], [scan, 2, [[0, a19], [1, a19]]], [scan, 2, [[0, a19], [1, a19]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0096","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5062ecbaef13591337cbc1f9d5ed1704cecf26df33e33264a3c79956918eaea4","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135096,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a20\",\"a20\"],\"input_alphabet\":[\"a20\",\"b20\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a20\",\"b20\"],\"target_symbol\":\"b20\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a20\",\"scan\",\"a20\",\"R\"],[\"scan\",\"b20\",\"accept\",\"b20\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a20, b20], tape_alphabet=[a20, b20, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a20, scan, a20, R], [scan, b20, accept, b20, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b20, legal target-free input=[a20, a20]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a20, b20], [_, a20, b20], [[scan, _, scan, _, S], [scan, a20, scan, a20, R], [scan, b20, accept, b20, S]], b20, [a20, a20], [scan, 2, [[0, a20], [1, a20]]], [scan, 2, [[0, a20], [1, a20]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a20, b20], [_, a20, b20], [[scan, _, scan, _, S], [scan, a20, scan, a20, R], [scan, b20, accept, b20, S]], b20, [a20, a20], [scan, 2, [[0, a20], [1, a20]]], [scan, 2, [[0, a20], [1, a20]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0097","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b7872ce0569d9067abafa43fac9e04824f0e9558b537bcd426975bfbfe62d6fc","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135097,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a21\",\"a21\"],\"input_alphabet\":[\"a21\",\"b21\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a21\",\"b21\"],\"target_symbol\":\"b21\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a21\",\"scan\",\"a21\",\"R\"],[\"scan\",\"b21\",\"accept\",\"b21\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a21, b21], tape_alphabet=[a21, b21, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a21, scan, a21, R], [scan, b21, accept, b21, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b21, legal target-free input=[a21, a21]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a21, b21], [_, a21, b21], [[scan, _, scan, _, S], [scan, a21, scan, a21, R], [scan, b21, accept, b21, S]], b21, [a21, a21], [scan, 2, [[0, a21], [1, a21]]], [scan, 2, [[0, a21], [1, a21]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a21, b21], [_, a21, b21], [[scan, _, scan, _, S], [scan, a21, scan, a21, R], [scan, b21, accept, b21, S]], b21, [a21, a21], [scan, 2, [[0, a21], [1, a21]]], [scan, 2, [[0, a21], [1, a21]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0098","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ef48f37c4044748c0110d4ef03a32d1265c83748a5d6231caa25794bb55cf82e","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135098,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a22\",\"a22\"],\"input_alphabet\":[\"a22\",\"b22\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a22\",\"b22\"],\"target_symbol\":\"b22\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a22\",\"scan\",\"a22\",\"R\"],[\"scan\",\"b22\",\"accept\",\"b22\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a22, b22], tape_alphabet=[a22, b22, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a22, scan, a22, R], [scan, b22, accept, b22, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b22, legal target-free input=[a22, a22]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a22, b22], [_, a22, b22], [[scan, _, scan, _, S], [scan, a22, scan, a22, R], [scan, b22, accept, b22, S]], b22, [a22, a22], [scan, 2, [[0, a22], [1, a22]]], [scan, 2, [[0, a22], [1, a22]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a22, b22], [_, a22, b22], [[scan, _, scan, _, S], [scan, a22, scan, a22, R], [scan, b22, accept, b22, S]], b22, [a22, a22], [scan, 2, [[0, a22], [1, a22]]], [scan, 2, [[0, a22], [1, a22]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0099","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"71e156af2d1b308af8501cff0a755862898591517fe87d742e134d044e7c75c5","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135099,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a23\",\"a23\"],\"input_alphabet\":[\"a23\",\"b23\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a23\",\"b23\"],\"target_symbol\":\"b23\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a23\",\"scan\",\"a23\",\"R\"],[\"scan\",\"b23\",\"accept\",\"b23\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a23, b23], tape_alphabet=[a23, b23, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a23, scan, a23, R], [scan, b23, accept, b23, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b23, legal target-free input=[a23, a23]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a23, b23], [_, a23, b23], [[scan, _, scan, _, S], [scan, a23, scan, a23, R], [scan, b23, accept, b23, S]], b23, [a23, a23], [scan, 2, [[0, a23], [1, a23]]], [scan, 2, [[0, a23], [1, a23]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a23, b23], [_, a23, b23], [[scan, _, scan, _, S], [scan, a23, scan, a23, R], [scan, b23, accept, b23, S]], b23, [a23, a23], [scan, 2, [[0, a23], [1, a23]]], [scan, 2, [[0, a23], [1, a23]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261015-advance-20261113-r05-turing-machine-decision-model-0100","batch_id":"batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5cf81c4b659b5d35e3d1953408099992c1e8e38469d9c3d1d0f98fb6aa6fffaa","family_id":"qf-mod44-tm-recognizer-loop-boundary","seed":202611135100,"semantic_template":"qf-mod44-tm-recognizer-loop-boundary/{\"accept_state\":\"accept\",\"blank\":\"_\",\"input\":[\"a24\",\"a24\"],\"input_alphabet\":[\"a24\",\"b24\"],\"reject_state\":\"reject\",\"start_state\":\"scan\",\"states\":[\"accept\",\"reject\",\"scan\"],\"tape_alphabet\":[\"_\",\"a24\",\"b24\"],\"target_symbol\":\"b24\",\"transitions\":[[\"scan\",\"_\",\"scan\",\"_\",\"S\"],[\"scan\",\"a24\",\"scan\",\"a24\",\"R\"],[\"scan\",\"b24\",\"accept\",\"b24\",\"S\"]]}"},"fields":{"title":"An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider","stem":"Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a24, b24], tape_alphabet=[a24, b24, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a24, scan, a24, R], [scan, b24, accept, b24, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b24, legal target-free input=[a24, a24]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).","answer":{"kind":"expression","value":"([accept, reject, scan], [a24, b24], [_, a24, b24], [[scan, _, scan, _, S], [scan, a24, scan, a24, R], [scan, b24, accept, b24, S]], b24, [a24, a24], [scan, 2, [[0, a24], [1, a24]]], [scan, 2, [[0, a24], [1, a24]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)","explanation":"Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a24, b24], [_, a24, b24], [[scan, _, scan, _, S], [scan, a24, scan, a24, R], [scan, b24, accept, b24, S]], b24, [a24, a24], [scan, 2, [[0, a24], [1, a24]]], [scan, 2, [[0, a24], [1, a24]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)."},"skills":["An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}