{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261018-r06-decision-problem-0001","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"acaf3a8def5e522d73bb12956187da2650ca1d534a332401ffb7ed7f2479ba23","family_id":"qf-ext18-decision-yes-set-table","seed":202610186001,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [], [[0, No], [1, No], [2, No], [3, No], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [], [[0, No], [1, No], [2, No], [3, No], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0002","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"64acf1f9af86679c521024302a5d6bf15e11003f989910780e1d67e8f9a3899f","family_id":"qf-ext18-decision-yes-set-table","seed":202610186002,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[0]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [0], [[0, Yes], [1, No], [2, No], [3, No], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [[0, Yes], [1, No], [2, No], [3, No], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0003","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d64b3860d856f61dd8c97e7bc4b1bda45fdcf5859689a30278b771f882366c6f","family_id":"qf-ext18-decision-yes-set-table","seed":202610186003,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[1]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [1], [[0, No], [1, Yes], [2, No], [3, No], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1], [[0, No], [1, Yes], [2, No], [3, No], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0004","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f4d472d7472b26604a4ae037f1d31d0387981988df1be4c151e3b04206c52fe1","family_id":"qf-ext18-decision-yes-set-table","seed":202610186004,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[0,1]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [0, 1], [[0, Yes], [1, Yes], [2, No], [3, No], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1], [[0, Yes], [1, Yes], [2, No], [3, No], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0005","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c106d999bf080f5c4924514428d38abe3e82de5f497328f1915d3a14b2a114f8","family_id":"qf-ext18-decision-yes-set-table","seed":202610186005,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[2]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [2], [[0, No], [1, No], [2, Yes], [3, No], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2], [[0, No], [1, No], [2, Yes], [3, No], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0006","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"001954daf066b215df4e0daa79a4aa8ade1c748cac827fbda69fb5b7adc3c43a","family_id":"qf-ext18-decision-yes-set-table","seed":202610186006,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[0,2]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [0, 2], [[0, Yes], [1, No], [2, Yes], [3, No], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2], [[0, Yes], [1, No], [2, Yes], [3, No], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0007","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bfdf89911ed3133c005985b257faf539e2f547495838081ff80c7543aab0def6","family_id":"qf-ext18-decision-yes-set-table","seed":202610186007,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[1,2]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [1, 2], [[0, No], [1, Yes], [2, Yes], [3, No], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2], [[0, No], [1, Yes], [2, Yes], [3, No], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0008","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5d5812ee90f79b3db771201e43ac5e278bb8dfb77fc5d7b82325772cf6e8c274","family_id":"qf-ext18-decision-yes-set-table","seed":202610186008,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[0,1,2]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [0, 1, 2], [[0, Yes], [1, Yes], [2, Yes], [3, No], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 2], [[0, Yes], [1, Yes], [2, Yes], [3, No], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0009","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eaf1566fe04fe833df1adac34ddd3db7575dfe53ff037bdf00aad22f033d58cf","family_id":"qf-ext18-decision-yes-set-table","seed":202610186009,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[3]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [3], [[0, No], [1, No], [2, No], [3, Yes], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [3], [[0, No], [1, No], [2, No], [3, Yes], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0010","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0f4cda57607e18673494d376be3915703bc9e5fed80a2022f5d51cec4c9d33af","family_id":"qf-ext18-decision-yes-set-table","seed":202610186010,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[0,3]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [0, 3], [[0, Yes], [1, No], [2, No], [3, Yes], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3], [[0, Yes], [1, No], [2, No], [3, Yes], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0011","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"85d9ec298c82525614790354481947ef98ec45080bf00fc68dbb2f6e98e7bf03","family_id":"qf-ext18-decision-yes-set-table","seed":202610186011,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[1,3]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [1, 3], [[0, No], [1, Yes], [2, No], [3, Yes], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 3], [[0, No], [1, Yes], [2, No], [3, Yes], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0012","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"75c1dfe28dbfb4e18a6f845dc2b27898ab4869a4d8ad25cc838065f5b573fe49","family_id":"qf-ext18-decision-yes-set-table","seed":202610186012,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[0,1,3]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [0, 1, 3], [[0, Yes], [1, Yes], [2, No], [3, Yes], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 3], [[0, Yes], [1, Yes], [2, No], [3, Yes], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0013","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4f8fc07b8cec5313ad0221e9629131810499786e30460815c1f92503b29102cd","family_id":"qf-ext18-decision-yes-set-table","seed":202610186013,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[2,3]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [2, 3], [[0, No], [1, No], [2, Yes], [3, Yes], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 3], [[0, No], [1, No], [2, Yes], [3, Yes], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0014","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3e00ab261a26af4b5836c4e70885098ffe42b78ba0295fac0eb85c86245dca2d","family_id":"qf-ext18-decision-yes-set-table","seed":202610186014,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[0,2,3]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [0, 2, 3], [[0, Yes], [1, No], [2, Yes], [3, Yes], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 3], [[0, Yes], [1, No], [2, Yes], [3, Yes], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0015","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a00fd036b9d209b5c2c706038762d6af40325d11a1ded2e8f21eac759fa4aaed","family_id":"qf-ext18-decision-yes-set-table","seed":202610186015,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[1,2,3]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [1, 2, 3], [[0, No], [1, Yes], [2, Yes], [3, Yes], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 3], [[0, No], [1, Yes], [2, Yes], [3, Yes], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0016","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8a0263b19f89fa509579eaa4d073a045719128b44c4c4bbfc3e7ed2532b86765","family_id":"qf-ext18-decision-yes-set-table","seed":202610186016,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[0,1,2,3]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [0, 1, 2, 3], [[0, Yes], [1, Yes], [2, Yes], [3, Yes], [4, No], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 2, 3], [[0, Yes], [1, Yes], [2, Yes], [3, Yes], [4, No], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0017","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4bb85fac6a9165990350f6bde26a674b251d785be156916a85500cd0f4b26bff","family_id":"qf-ext18-decision-yes-set-table","seed":202610186017,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[4]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [4], [[0, No], [1, No], [2, No], [3, No], [4, Yes], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [4], [[0, No], [1, No], [2, No], [3, No], [4, Yes], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0018","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"18403e40870a7ee981b62531fcf08e888fec38530958b0abcadd5158f422ec80","family_id":"qf-ext18-decision-yes-set-table","seed":202610186018,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[0,4]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [0, 4], [[0, Yes], [1, No], [2, No], [3, No], [4, Yes], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 4], [[0, Yes], [1, No], [2, No], [3, No], [4, Yes], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0019","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9d15397130cb871621ce824d90375908111aa6e5122502b38a9f166a0f6bafec","family_id":"qf-ext18-decision-yes-set-table","seed":202610186019,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[1,4]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [1, 4], [[0, No], [1, Yes], [2, No], [3, No], [4, Yes], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4], [[0, No], [1, Yes], [2, No], [3, No], [4, Yes], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0020","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3e76b11eacd13f471d0fbfdabfd2a813878765ac1015de42d3cf9cf2ef4d9ba3","family_id":"qf-ext18-decision-yes-set-table","seed":202610186020,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[0,1,4]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [0, 1, 4], [[0, Yes], [1, Yes], [2, No], [3, No], [4, Yes], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 4], [[0, Yes], [1, Yes], [2, No], [3, No], [4, Yes], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0021","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7ebae7cb2b293b34c660e56dfc07a4cdef176fa6e5e820b0f96d941375830e3a","family_id":"qf-ext18-decision-yes-set-table","seed":202610186021,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[2,4]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [2, 4], [[0, No], [1, No], [2, Yes], [3, No], [4, Yes], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 4], [[0, No], [1, No], [2, Yes], [3, No], [4, Yes], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0022","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"465203d60e6b43d0a69aa97a57e5cf7d6a787976d97f70c0711fe9b6deb39712","family_id":"qf-ext18-decision-yes-set-table","seed":202610186022,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[0,2,4]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [0, 2, 4], [[0, Yes], [1, No], [2, Yes], [3, No], [4, Yes], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 4], [[0, Yes], [1, No], [2, Yes], [3, No], [4, Yes], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0023","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"949c6fc719992edf6f9840abb789fa5fcf52de435be5c74cfc0ecfdfad328107","family_id":"qf-ext18-decision-yes-set-table","seed":202610186023,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[1,2,4]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [1, 2, 4], [[0, No], [1, Yes], [2, Yes], [3, No], [4, Yes], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 4], [[0, No], [1, Yes], [2, Yes], [3, No], [4, Yes], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0024","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"434392f79a0a5a01599e3d2db459741b517efa35d4f1f1a7a74b7b0636da7c6f","family_id":"qf-ext18-decision-yes-set-table","seed":202610186024,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[0,1,2,4]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [0, 1, 2, 4], [[0, Yes], [1, Yes], [2, Yes], [3, No], [4, Yes], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 2, 4], [[0, Yes], [1, Yes], [2, Yes], [3, No], [4, Yes], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0025","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7c3d7554a1dd169c0b02060a6d502edbccee88b308bf99e9b66278cb68259d04","family_id":"qf-ext18-decision-yes-set-table","seed":202610186025,"semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[3,4]}"},"fields":{"title":"Finite Decision Specification and Complete Truth Table","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).","answer":{"kind":"expression","value":"(6, [3, 4], [[0, No], [1, No], [2, No], [3, Yes], [4, Yes], [5, No]])","explanation":"Enumerate every legal input against the specification; this is not execution of an arbitrary program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [3, 4], [[0, No], [1, No], [2, No], [3, Yes], [4, Yes], [5, No]])."},"skills":["Finite Decision Specification and Complete Truth Table"],"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-20261013-advance-20261018-r06-decision-problem-0026","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"10c1dc311c55ef86383e7b1967bc2922e4a7e0e458cae06816d0fe64d593aeec","family_id":"qf-ext18-decision-decider-agreement","seed":202610186026,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,false,false,false,false,false],\"n\":6,\"yes\":[]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [], [No, No, No, No, No, No], [], Yes)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [], [No, No, No, No, No, No], [], Yes)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0027","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8496ab676ee04a453f376df4cc9760904d9547a441f6c3a43774821a773eb1fc","family_id":"qf-ext18-decision-decider-agreement","seed":202610186027,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,true,false,false,false,false],\"n\":6,\"yes\":[0]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [0], [Yes, Yes, No, No, No, No], [1], No)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [Yes, Yes, No, No, No, No], [1], No)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0028","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cc1d15fc747145683dafd61caecc105971ef5d118d3612417c477f7699bc3061","family_id":"qf-ext18-decision-decider-agreement","seed":202610186028,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,true,false,false,false,false],\"n\":6,\"yes\":[1]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [1], [No, Yes, No, No, No, No], [], Yes)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1], [No, Yes, No, No, No, No], [], Yes)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0029","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"77cdc3aa0ed27ef175a2c2675b6352d3828e83a0a9343315387ad770cc383ed6","family_id":"qf-ext18-decision-decider-agreement","seed":202610186029,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,true,false,true,false,false],\"n\":6,\"yes\":[0,1]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, true, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [0, 1], [Yes, Yes, No, Yes, No, No], [3], No)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1], [Yes, Yes, No, Yes, No, No], [3], No)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0030","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5ac65ebdac60e81540e7e0ab830350b993975468c7f62eaec3629c9848c0ad96","family_id":"qf-ext18-decision-decider-agreement","seed":202610186030,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,false,true,false,false,false],\"n\":6,\"yes\":[2]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [2], [No, No, Yes, No, No, No], [], Yes)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2], [No, No, Yes, No, No, No], [], Yes)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0031","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b92b20af06e5aba31f42056a41619722a12bcc71c6f966d79603c549f6dd3ce5","family_id":"qf-ext18-decision-decider-agreement","seed":202610186031,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,false,true,false,false,true],\"n\":6,\"yes\":[0,2]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, false, true]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [0, 2], [Yes, No, Yes, No, No, Yes], [5], No)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2], [Yes, No, Yes, No, No, Yes], [5], No)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0032","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ebbdb2125bac4da1ab0d34847ade11a92a74cc288250796b07b4327045c315cd","family_id":"qf-ext18-decision-decider-agreement","seed":202610186032,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,true,true,false,false,false],\"n\":6,\"yes\":[1,2]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [1, 2], [No, Yes, Yes, No, No, No], [], Yes)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2], [No, Yes, Yes, No, No, No], [], Yes)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0033","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8be8d90fb5a159f6c28afbcd04df55249720c86dc6d336d01e3b8abcf9c74708","family_id":"qf-ext18-decision-decider-agreement","seed":202610186033,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,false,true,false,false,false],\"n\":6,\"yes\":[0,1,2]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [0, 1, 2], [Yes, No, Yes, No, No, No], [1], No)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 2], [Yes, No, Yes, No, No, No], [1], No)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0034","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b1dc1a87ecb7b3b20b96c01b92aaff07fc79dcfba38830c684b6c6690233ec06","family_id":"qf-ext18-decision-decider-agreement","seed":202610186034,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,false,false,true,false,false],\"n\":6,\"yes\":[3]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [3], [No, No, No, Yes, No, No], [], Yes)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [3], [No, No, No, Yes, No, No], [], Yes)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0035","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7dc93ca9b626082fdecbd475da7e6d3fb2805f91836535734f9b77125d364ecf","family_id":"qf-ext18-decision-decider-agreement","seed":202610186035,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,false,false,false,false,false],\"n\":6,\"yes\":[0,3]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [0, 3], [Yes, No, No, No, No, No], [3], No)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3], [Yes, No, No, No, No, No], [3], No)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0036","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"171bad11a8945d803f645ec3872f0947a4e60d2d40f7bd8c0a9a58d445f3e326","family_id":"qf-ext18-decision-decider-agreement","seed":202610186036,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,true,false,true,false,false],\"n\":6,\"yes\":[1,3]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, true, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [1, 3], [No, Yes, No, Yes, No, No], [], Yes)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 3], [No, Yes, No, Yes, No, No], [], Yes)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0037","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9b4ed6f70d9462b5d5bcd726a9805582288dc87aa9f73a3c3b1805a23ecf0bc7","family_id":"qf-ext18-decision-decider-agreement","seed":202610186037,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,true,false,true,false,true],\"n\":6,\"yes\":[0,1,3]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, true, false, true]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [0, 1, 3], [Yes, Yes, No, Yes, No, Yes], [5], No)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 3], [Yes, Yes, No, Yes, No, Yes], [5], No)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0038","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"db2a657a76bb6852aabb76092fed88defa0b4c9a8cd29121bdc54ab78ea30143","family_id":"qf-ext18-decision-decider-agreement","seed":202610186038,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,false,true,true,false,false],\"n\":6,\"yes\":[2,3]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, true, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [2, 3], [No, No, Yes, Yes, No, No], [], Yes)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 3], [No, No, Yes, Yes, No, No], [], Yes)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0039","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0710fe4e62adcda103938456e43c33686c51527efab98c4f7a8c6fa7815f8860","family_id":"qf-ext18-decision-decider-agreement","seed":202610186039,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,true,true,true,false,false],\"n\":6,\"yes\":[0,2,3]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, true, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [0, 2, 3], [Yes, Yes, Yes, Yes, No, No], [1], No)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 3], [Yes, Yes, Yes, Yes, No, No], [1], No)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0040","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"70dba4daa940cd1b543275feb9b5458b055a443550c2377e2828457200a3897c","family_id":"qf-ext18-decision-decider-agreement","seed":202610186040,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,true,true,true,false,false],\"n\":6,\"yes\":[1,2,3]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, true, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [1, 2, 3], [No, Yes, Yes, Yes, No, No], [], Yes)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 3], [No, Yes, Yes, Yes, No, No], [], Yes)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0041","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3eacb4177a135df96392e706e7ac82953c4d3329abdb8cd6948b9a39a9f5af92","family_id":"qf-ext18-decision-decider-agreement","seed":202610186041,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,true,true,false,false,false],\"n\":6,\"yes\":[0,1,2,3]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, false, false, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [0, 1, 2, 3], [Yes, Yes, Yes, No, No, No], [3], No)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 2, 3], [Yes, Yes, Yes, No, No, No], [3], No)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0042","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df42bfc71bd8b3e58e655785ad84dd1e9b7ae321a67a2a36130a8b8d8988d3bf","family_id":"qf-ext18-decision-decider-agreement","seed":202610186042,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,false,false,false,true,false],\"n\":6,\"yes\":[4]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, false, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [4], [No, No, No, No, Yes, No], [], Yes)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [4], [No, No, No, No, Yes, No], [], Yes)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0043","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c9b3f66d5768d0e9a33ff987d2050a3c19cefea02c58eee827aa2330fae35271","family_id":"qf-ext18-decision-decider-agreement","seed":202610186043,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,false,false,false,true,true],\"n\":6,\"yes\":[0,4]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, false, true, true]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [0, 4], [Yes, No, No, No, Yes, Yes], [5], No)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 4], [Yes, No, No, No, Yes, Yes], [5], No)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0044","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4dd92ede4b4c80f75294f3f3ab5798e0c445529b50db518604ace901a86d1119","family_id":"qf-ext18-decision-decider-agreement","seed":202610186044,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,true,false,false,true,false],\"n\":6,\"yes\":[1,4]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, false, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [1, 4], [No, Yes, No, No, Yes, No], [], Yes)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4], [No, Yes, No, No, Yes, No], [], Yes)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0045","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"581975b10573f960812e45600755173af7a063d579c331ffec552144adfa9d0c","family_id":"qf-ext18-decision-decider-agreement","seed":202610186045,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,false,false,false,true,false],\"n\":6,\"yes\":[0,1,4]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, false, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [0, 1, 4], [Yes, No, No, No, Yes, No], [1], No)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 4], [Yes, No, No, No, Yes, No], [1], No)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0046","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"57e334087bb038459b134f51f90e811648758a0c0340db692253758749dfa7d3","family_id":"qf-ext18-decision-decider-agreement","seed":202610186046,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,false,true,false,true,false],\"n\":6,\"yes\":[2,4]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [2, 4], [No, No, Yes, No, Yes, No], [], Yes)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 4], [No, No, Yes, No, Yes, No], [], Yes)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0047","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b10099916535ef0d8178b1e5e333def8338c2845caedc40e50410eda5b30df69","family_id":"qf-ext18-decision-decider-agreement","seed":202610186047,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,false,true,true,true,false],\"n\":6,\"yes\":[0,2,4]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, true, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [0, 2, 4], [Yes, No, Yes, Yes, Yes, No], [3], No)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 4], [Yes, No, Yes, Yes, Yes, No], [3], No)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0048","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"441e7c8eae9113d1712e6e716bc8cf1032b8fce11f61ef820d34febcc2c86002","family_id":"qf-ext18-decision-decider-agreement","seed":202610186048,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,true,true,false,true,false],\"n\":6,\"yes\":[1,2,4]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, false, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [1, 2, 4], [No, Yes, Yes, No, Yes, No], [], Yes)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 4], [No, Yes, Yes, No, Yes, No], [], Yes)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0049","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dbdac68748cb936fa57931fde676d6e799697c5dc08cec80af70b5a0ed3e70b3","family_id":"qf-ext18-decision-decider-agreement","seed":202610186049,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,true,true,false,true,true],\"n\":6,\"yes\":[0,1,2,4]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, false, true, true]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [0, 1, 2, 4], [Yes, Yes, Yes, No, Yes, Yes], [5], No)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 2, 4], [Yes, Yes, Yes, No, Yes, Yes], [5], No)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0050","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"92e4355d6ed2bbd7ed0b2df14d9b0d454450091ad39b7a27e988ff1b8ce76ea3","family_id":"qf-ext18-decision-decider-agreement","seed":202610186050,"semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,false,false,true,true,false],\"n\":6,\"yes\":[3,4]}"},"fields":{"title":"Whole Finite Decider Table against Its Specification","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).","answer":{"kind":"expression","value":"(6, [3, 4], [No, No, No, Yes, Yes, No], [], Yes)","explanation":"Check every table cell, not a sample; the explicit finite table does not establish termination of a general program. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [3, 4], [No, No, No, Yes, Yes, No], [], Yes)."},"skills":["Whole Finite Decider Table against Its Specification"],"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-20261013-advance-20261018-r06-decision-problem-0051","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"54db2f3d30b8b64d70c3a64ecccc6d25616307a82c480c2a638920b4997aec5d","family_id":"qf-ext18-decision-domain-restriction","seed":202610186051,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,false,true,false,false,false],\"n\":6,\"subset\":[0,1,3],\"yes\":[]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, false, false], retained subset=[0, 1, 3]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [0, 1, 3], [], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 3], [], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0052","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc4a93d0c5b3b0c2f3784ebd6d00cca9f280d83a206dc94b3a11d7f4afb71799","family_id":"qf-ext18-decision-domain-restriction","seed":202610186052,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,false,true,false,false],\"n\":6,\"subset\":[1,2,4],\"yes\":[0]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, true, false, false], retained subset=[1, 2, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [1, 2, 4], [], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 4], [], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0053","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"64a46427655edb4e23b231e407d6b3bec384cb065f3cf28bd33d02835f811c26","family_id":"qf-ext18-decision-domain-restriction","seed":202610186053,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,true,false,false,true,false],\"n\":6,\"subset\":[2,3,5],\"yes\":[1]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, false, true, false], retained subset=[2, 3, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [2, 3, 5], [], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 3, 5], [], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0054","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"17d4a7843ed4efa7c91d844acf35b9254a5af16ee428a8b041af5265d9326170","family_id":"qf-ext18-decision-domain-restriction","seed":202610186054,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,false,false,false,true],\"n\":6,\"subset\":[0,3,4],\"yes\":[0,1]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, false, false, true], retained subset=[0, 3, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [0, 3, 4], [0], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3, 4], [0], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0055","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2f823622cbe32d718ae22e6515af6a7b0ec5dd6fa0864ec8cb0b1206308bfd6b","family_id":"qf-ext18-decision-domain-restriction","seed":202610186055,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,true,false,false,false],\"n\":6,\"subset\":[1,4,5],\"yes\":[2]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, false, false], retained subset=[1, 4, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [1, 4, 5], [], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4, 5], [], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0056","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f44287e8b2ae005f7287d1f14f5f6dab1317188126501df37a1d4d07e74c5ec6","family_id":"qf-ext18-decision-domain-restriction","seed":202610186056,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,true,false,false,false],\"n\":6,\"subset\":[0,2,5],\"yes\":[0,2]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, false, false, false], retained subset=[0, 2, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [0, 2, 5], [0, 2], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 5], [0, 2], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0057","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ebfc8f7d306a072c9aaf01dae1c4b813a0a773395f8e5bb9cf007d42de9f2e1e","family_id":"qf-ext18-decision-domain-restriction","seed":202610186057,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,true,false,false,false,false],\"n\":6,\"subset\":[0,1,3],\"yes\":[1,2]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, false, false, false], retained subset=[0, 1, 3]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [0, 1, 3], [1], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 3], [1], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0058","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"82f2772b9f604d3d1395d4d46e9909f83c9d05acb57fe0bf171f3fb839e7c737","family_id":"qf-ext18-decision-domain-restriction","seed":202610186058,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,true,true,false,false],\"n\":6,\"subset\":[1,2,4],\"yes\":[0,1,2]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, true, false, false], retained subset=[1, 2, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [1, 2, 4], [1, 2], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 4], [1, 2], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0059","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"641ef37e698011f44779c1aa47f1b6677a30f3d9b2a44db0a719846c7697d1f3","family_id":"qf-ext18-decision-domain-restriction","seed":202610186059,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,false,false,true,true,false],\"n\":6,\"subset\":[2,3,5],\"yes\":[3]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, true, false], retained subset=[2, 3, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [2, 3, 5], [3], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 3, 5], [3], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0060","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3bcbe87fbd891f870b0ed20da0a2ab22f44c04c4451c356050825586f79384de","family_id":"qf-ext18-decision-domain-restriction","seed":202610186060,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,false,true,false,true],\"n\":6,\"subset\":[0,3,4],\"yes\":[0,3]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, true, false, true], retained subset=[0, 3, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [0, 3, 4], [0, 3], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3, 4], [0, 3], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0061","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a05096936ba6fa263e663b1b213c0355565e99fdbfb8525e0439b2d665d6c414","family_id":"qf-ext18-decision-domain-restriction","seed":202610186061,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,false,true,false,false],\"n\":6,\"subset\":[1,4,5],\"yes\":[1,3]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, true, false, false], retained subset=[1, 4, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [1, 4, 5], [1], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4, 5], [1], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0062","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b5a8ea0b8c31daa36274e6f880138a1be7582733a12145b4e7e406c13da8108d","family_id":"qf-ext18-decision-domain-restriction","seed":202610186062,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,false,true,false,false],\"n\":6,\"subset\":[0,2,5],\"yes\":[0,1,3]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, true, false, false], retained subset=[0, 2, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [0, 2, 5], [0], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 5], [0], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0063","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e53b9815e29d7f8185d385b232020407e51f2c985f4737a13e3198377a1c4820","family_id":"qf-ext18-decision-domain-restriction","seed":202610186063,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,false,false,true,false,false],\"n\":6,\"subset\":[0,1,3],\"yes\":[2,3]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, false, false], retained subset=[0, 1, 3]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [0, 1, 3], [3], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 3], [3], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0064","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f60221386c2c8f11ad448d92a75805be2c8bdde7641aaaa805146a83edb622ea","family_id":"qf-ext18-decision-domain-restriction","seed":202610186064,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,true,false,false,false],\"n\":6,\"subset\":[1,2,4],\"yes\":[0,2,3]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, false, false], retained subset=[1, 2, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [1, 2, 4], [2], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 4], [2], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0065","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d3986cab3dbc7e0b4af73a9532a0ea64d0c00460ccbbb2eae926bcef09204fc3","family_id":"qf-ext18-decision-domain-restriction","seed":202610186065,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,true,true,true,true,false],\"n\":6,\"subset\":[2,3,5],\"yes\":[1,2,3]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, true, true, false], retained subset=[2, 3, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [2, 3, 5], [2, 3], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 3, 5], [2, 3], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0066","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4f8723a99dcb5eee97b873474818091afbdef9b4ba8aa1e6adbe565c41517513","family_id":"qf-ext18-decision-domain-restriction","seed":202610186066,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,true,true,false,true],\"n\":6,\"subset\":[0,3,4],\"yes\":[0,1,2,3]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, true, false, true], retained subset=[0, 3, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [0, 3, 4], [0, 3], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3, 4], [0, 3], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0067","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2dbec55b2d5cee61f6af2f6efb1b95630043c335c2f3be4b334bb6855445d189","family_id":"qf-ext18-decision-domain-restriction","seed":202610186067,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,false,false,true,false],\"n\":6,\"subset\":[1,4,5],\"yes\":[4]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, false, true, false], retained subset=[1, 4, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [1, 4, 5], [4], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4, 5], [4], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0068","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0e7c00ea2499933b1806d2561fe222205ef33f6bd16bd74e34ec9654b991d8a7","family_id":"qf-ext18-decision-domain-restriction","seed":202610186068,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,false,false,true,false],\"n\":6,\"subset\":[0,2,5],\"yes\":[0,4]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, false, true, false], retained subset=[0, 2, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [0, 2, 5], [0], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 5], [0], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0069","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d78bbe14669c851597633fa0d06869d225fe114885f9232a74ebc308d1a64d54","family_id":"qf-ext18-decision-domain-restriction","seed":202610186069,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,true,true,false,true,false],\"n\":6,\"subset\":[0,1,3],\"yes\":[1,4]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, false, true, false], retained subset=[0, 1, 3]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [0, 1, 3], [1], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 3], [1], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0070","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4ce31471140b60067c2cba7bfbc8478af938d85c8083cc6865e9d1c1777cd173","family_id":"qf-ext18-decision-domain-restriction","seed":202610186070,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,false,true,true,false],\"n\":6,\"subset\":[1,2,4],\"yes\":[0,1,4]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, true, true, false], retained subset=[1, 2, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [1, 2, 4], [1, 4], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2, 4], [1, 4], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0071","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"093de5184629213f79db5dc034d3aa09671ea0ed669634e7f708ed80becd00a7","family_id":"qf-ext18-decision-domain-restriction","seed":202610186071,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,false,true,false,false,false],\"n\":6,\"subset\":[2,3,5],\"yes\":[2,4]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, false, false], retained subset=[2, 3, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [2, 3, 5], [2], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 3, 5], [2], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0072","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"46ee82bcee910d83fd25edb92e06703a1352f384dc74d7eea192f4e3ba9dfec3","family_id":"qf-ext18-decision-domain-restriction","seed":202610186072,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,true,false,true,true],\"n\":6,\"subset\":[0,3,4],\"yes\":[0,2,4]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, true, true], retained subset=[0, 3, 4]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [0, 3, 4], [0, 4], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3, 4], [0, 4], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0073","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"819712fb279bd573db64822facc5930b992071324135f16c877ec445c8c64c39","family_id":"qf-ext18-decision-domain-restriction","seed":202610186073,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,true,false,true,false],\"n\":6,\"subset\":[1,4,5],\"yes\":[1,2,4]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, false, true, false], retained subset=[1, 4, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [1, 4, 5], [1, 4], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4, 5], [1, 4], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0074","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2397afb1ee365681fd65dc56edb76c89ee68a3d0270c80d4cdd0ed29e761cad5","family_id":"qf-ext18-decision-domain-restriction","seed":202610186074,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,true,false,true,false],\"n\":6,\"subset\":[0,2,5],\"yes\":[0,1,2,4]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, true, false], retained subset=[0, 2, 5]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [0, 2, 5], [0, 2], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2, 5], [0, 2], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0075","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7b70589228f737bbfc5b1e87f80fb4ab83d29a02ccb1c80811c93d1cb05ac2a9","family_id":"qf-ext18-decision-domain-restriction","seed":202610186075,"semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,false,true,true,true,false],\"n\":6,\"subset\":[0,1,3],\"yes\":[3,4]}"},"fields":{"title":"Restricted Decision Domain with Original Input Labels","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, true, true, false], retained subset=[0, 1, 3]. Give (n, sorted retained labels, restricted yes-instance set, restricted mismatches, restricted agreement?).","answer":{"kind":"expression","value":"(6, [0, 1, 3], [3], [], Yes)","explanation":"Normalize the subset as a set but do not renumber it; mismatches outside the restriction do not become restricted witnesses. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1, 3], [3], [], Yes)."},"skills":["Restricted Decision Domain with Original Input Labels"],"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-20261013-advance-20261018-r06-decision-problem-0076","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"246a2fc1c8d1b80d9a328b46747862bfcb3e3d5f143e74e584df55950086d583","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186076,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,1],\"decider\":[false,false,false,true,false,false],\"n\":6,\"yes\":[]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, false, false], checked subset=[0, 1]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0077","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c19eb67645af33680ac192664ea92a56dbce5588dd7b9cd51cca507e4e074e8e","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186077,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,4],\"decider\":[true,false,false,false,true,false],\"n\":6,\"yes\":[0]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, false, true, false], checked subset=[1, 4]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [1, 4], [4], [4], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4], [4], [4], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0078","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"baecdca587a371a4c77a04518c0989d93a70a355f9e8f9dc1c7e3a6bbe43df12","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186078,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,2],\"decider\":[false,true,false,false,false,true],\"n\":6,\"yes\":[1]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, false, false, true], checked subset=[0, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [0, 2], [], [5], Yes, No, sample-passed-full-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2], [], [5], Yes, No, sample-passed-full-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0079","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f585af7a54aef231a2b1ad2f9751d4c74ddeee93ec2dd69e61378fb3c1d8cf32","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186079,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,3],\"decider\":[false,true,false,false,false,false],\"n\":6,\"yes\":[0,1]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, false, false, false], checked subset=[0, 3]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [0, 3], [0], [0], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3], [0], [0], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0080","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bee817e9289bd06e7b81f54fd00cd572b00303451629836a6c83c567a3e452b8","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186080,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,2],\"decider\":[false,true,true,false,false,false],\"n\":6,\"yes\":[2]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, false, false, false], checked subset=[1, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [1, 2], [1], [1], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2], [1], [1], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0081","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4ae2e7cee5dd3c4c5e930c3d0237d83baa48d5c1f035de07ffb8e28ad7c63602","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186081,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[2,5],\"decider\":[true,false,false,false,false,false],\"n\":6,\"yes\":[0,2]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, false, false, false, false], checked subset=[2, 5]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [2, 5], [2], [2], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 5], [2], [2], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0082","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"64c373455866180c1b6af6a96bad68f64adda81cca5142cec00103284f4a0734","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186082,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,1],\"decider\":[false,true,true,true,false,false],\"n\":6,\"yes\":[1,2]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, true, false, false], checked subset=[0, 1]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0083","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"617be928d629df08c7a56cab264d8caccd44071c7170228f084d12fa0113006a","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186083,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,4],\"decider\":[true,true,true,false,true,false],\"n\":6,\"yes\":[0,1,2]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, false, true, false], checked subset=[1, 4]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [1, 4], [4], [4], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4], [4], [4], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0084","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"099f5bb87d68d6a2a933c9866240bafd1539c2872869da289f07646263b03cf0","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186084,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,2],\"decider\":[false,false,false,true,false,true],\"n\":6,\"yes\":[3]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, false, true], checked subset=[0, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [0, 2], [], [5], Yes, No, sample-passed-full-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2], [], [5], Yes, No, sample-passed-full-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0085","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"44cf7cb756cfadc349a214969d9e574cbe5de4060ca7aa1e5c494d334fac3672","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186085,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,3],\"decider\":[false,false,false,true,false,false],\"n\":6,\"yes\":[0,3]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, false, false], checked subset=[0, 3]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [0, 3], [0], [0], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3], [0], [0], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0086","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"51e9953c2f797740b12fac7f13e49a44ec5818c075b432626cea3542bc5514a7","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186086,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,2],\"decider\":[false,false,false,true,false,false],\"n\":6,\"yes\":[1,3]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, true, false, false], checked subset=[1, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [1, 2], [1], [1], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2], [1], [1], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0087","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"077a574391283c19022141e82bceb7fa832e14aa715b3ffbea2e946bdb81580d","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186087,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[2,5],\"decider\":[true,true,true,true,false,false],\"n\":6,\"yes\":[0,1,3]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, true, true, false, false], checked subset=[2, 5]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [2, 5], [2], [2], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 5], [2], [2], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0088","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"28ce62a54b008d22436474b5eee3bfa4ed198fb41c06542dcc1448ca3bfec77e","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186088,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,1],\"decider\":[false,false,true,false,false,false],\"n\":6,\"yes\":[2,3]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, false, false], checked subset=[0, 1]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0089","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e68a7ac95877aae6dbf08f4969781593d029fc9754f9b83c9305d9ac82475bda","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186089,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,4],\"decider\":[true,false,true,true,true,false],\"n\":6,\"yes\":[0,2,3]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, true, true, false], checked subset=[1, 4]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [1, 4], [4], [4], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4], [4], [4], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0090","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8de49f58367a22896f48fc43d8bdff5b0b8147ef477ec9662d8c46268a4c6dd9","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186090,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,2],\"decider\":[false,true,true,true,false,true],\"n\":6,\"yes\":[1,2,3]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, true, false, true], checked subset=[0, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [0, 2], [], [5], Yes, No, sample-passed-full-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2], [], [5], Yes, No, sample-passed-full-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0091","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2644b789149a56fdb6641f5155d5b898b6000d76dfabdb9855f38b7dc98be560","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186091,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,3],\"decider\":[false,true,true,true,false,false],\"n\":6,\"yes\":[0,1,2,3]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, true, true, false, false], checked subset=[0, 3]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [0, 3], [0], [0], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3], [0], [0], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0092","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a713fe585188dedb626c8e7a38212c6604bd4da6cb57d54d3ed048b561dcfe54","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186092,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,2],\"decider\":[false,true,false,false,true,false],\"n\":6,\"yes\":[4]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, false, true, false], checked subset=[1, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [1, 2], [1], [1], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2], [1], [1], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0093","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f12433869b9c75b89c71f7309677ffc342278b0f1a6a85dcbcfd33fe3badbeaf","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186093,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[2,5],\"decider\":[true,false,true,false,true,false],\"n\":6,\"yes\":[0,4]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, false, true, false, true, false], checked subset=[2, 5]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [2, 5], [2], [2], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 5], [2], [2], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0094","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d069eb0d6d9dc222f1d62426537ebf6312b27524e0ecd150db957956f32b2443","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186094,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,1],\"decider\":[false,true,false,true,true,false],\"n\":6,\"yes\":[1,4]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, true, false, true, true, false], checked subset=[0, 1]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0095","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e01b701cc9bd1435d4206f162485b4b1867e190c45a0e9ef0c6c1e84b9ae4fae","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186095,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,4],\"decider\":[true,true,false,false,false,false],\"n\":6,\"yes\":[0,1,4]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, false, false, false], checked subset=[1, 4]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [1, 4], [4], [4], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 4], [4], [4], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0096","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7c02a6aa908d9671ebef5e5415361e8391f8494336550fb45b765d4fc6f5541e","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186096,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,2],\"decider\":[false,false,true,false,true,true],\"n\":6,\"yes\":[2,4]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, true, true], checked subset=[0, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [0, 2], [], [5], Yes, No, sample-passed-full-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 2], [], [5], Yes, No, sample-passed-full-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0097","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f9e1b3e2618f8ce5ac5b67276ccfdb50d132965350d38cab6001315392495c5e","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186097,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,3],\"decider\":[false,false,true,false,true,false],\"n\":6,\"yes\":[0,2,4]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, true, false], checked subset=[0, 3]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [0, 3], [0], [0], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 3], [0], [0], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0098","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d2f803c735fe3b6b8842dcafa1beee6efd27d572d8bd94ff1ec4a384b329f6e4","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186098,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,2],\"decider\":[false,false,true,false,true,false],\"n\":6,\"yes\":[1,2,4]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, true, false], checked subset=[1, 2]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [1, 2], [1], [1], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [1, 2], [1], [1], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0099","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3b41258abbe1bc752a5aab92781dcfdae9d1c7378b41a764d468740766991331","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186099,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[2,5],\"decider\":[true,true,false,false,true,false],\"n\":6,\"yes\":[0,1,2,4]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[true, true, false, false, true, false], checked subset=[2, 5]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [2, 5], [2], [2], No, No, sample-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [2, 5], [2], [2], No, No, sample-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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-20261013-advance-20261018-r06-decision-problem-0100","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"699eee3c8d072871d0e25b07f9d492c482169aeea27cabe44974516abdb60500","family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186100,"semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,1],\"decider\":[false,false,false,false,true,false],\"n\":6,\"yes\":[3,4]}"},"fields":{"title":"Sample Agreement Is Not Complete Finite Agreement","stem":"The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, false, false, true, false], checked subset=[0, 1]. Give (n, checked labels, sampled mismatches, complete mismatches, sample agreement?, complete agreement?, complete-agreement/sample-passed-full-failed/sample-failed).","answer":{"kind":"expression","value":"(6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)","explanation":"Compare sampled and full mismatch inventories independently, including an empty checked set. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0, 1], [], [3], Yes, No, sample-passed-full-failed)."},"skills":["Sample Agreement Is Not Complete Finite Agreement"],"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."}}