{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261019-r04-computational-model-0001","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cae83bb4e41973e5dafae6207cc43191a0db99f3d42ceae9058d3aa9101ff68f","family_id":"qf-ext19-model-reachable-states","seed":202610194001,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 5]], [0, 1, 2, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 5]], [0, 1, 2, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0002","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"68dbe1840539492c07cb59072dba8f87c74a1c27d13c434ce4ac792ea2142785","family_id":"qf-ext19-model-reachable-states","seed":202610194002,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5]], [0, 1, 2, 3, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5]], [0, 1, 2, 3, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0003","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4fd91b2b3173fc06a5961ff83ca75653667c8f8979baae28de3dcb1a25482d4f","family_id":"qf-ext19-model-reachable-states","seed":202610194003,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[3,4]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0004","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ec17e272412f6dffdc4c72e536e39d7fdd2df0ed30950f5d8562a5de9226812a","family_id":"qf-ext19-model-reachable-states","seed":202610194004,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0005","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d92902e1d3e89dfa4241139736148f980e05e2fa4f3f7edba7e3f6db4bc48fb6","family_id":"qf-ext19-model-reachable-states","seed":202610194005,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[4,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0006","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c7c2a7bcea7f463aac9a1be0cedbb7405e5ee4406b6c1a5b43ff1303531d0af6","family_id":"qf-ext19-model-reachable-states","seed":202610194006,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[4,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0007","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"75921f02a5a87ec1eee70121db93aee06366ba8118a7ced253ba2b835df55512","family_id":"qf-ext19-model-reachable-states","seed":202610194007,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0008","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d7c86c5d03ef4741cfc5e46fed6e7f44d13d8241655e19641bab4ab6322cb2d4","family_id":"qf-ext19-model-reachable-states","seed":202610194008,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4],[4,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0009","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3d70c9b4e17fb10fa2d667474cc9c1f25fa7ba47d761370cafe2c59383345a87","family_id":"qf-ext19-model-reachable-states","seed":202610194009,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0010","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dbf196b9cc68489e6e27b89a47a0fbdfe070b1a9fb6affc80d67eaadd79b91da","family_id":"qf-ext19-model-reachable-states","seed":202610194010,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 3, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 3, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0011","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"128fccfe6964a2c5ea5653c09068259b98d14b0a82dfd9d5e785312b10a09f22","family_id":"qf-ext19-model-reachable-states","seed":202610194011,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0012","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4cd2da8e10d01c8c278d6315e84593f627fc6a07df97615bafb165f968c70a6f","family_id":"qf-ext19-model-reachable-states","seed":202610194012,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0013","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3622922c386c05718e4f94f940f4a28518e9aa112388f81a750b812f5293155b","family_id":"qf-ext19-model-reachable-states","seed":202610194013,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[4,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0014","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ddc02806e5c67c04d5e175bac2e80015d86ae83305f4d7074f724556304beaa0","family_id":"qf-ext19-model-reachable-states","seed":202610194014,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[4,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 3, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 3, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0015","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"06c7bfad77ecbe5712e6b2e0ee00648990c2ea26f79e166dfdb81093625477c7","family_id":"qf-ext19-model-reachable-states","seed":202610194015,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4],[4,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0016","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"31080a57e0ac3934e8839574ea200f9a465da04c48322e4b49535c75136addd2","family_id":"qf-ext19-model-reachable-states","seed":202610194016,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4],[4,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0017","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6957e2d65b2dc28d0327a4a96f6ef69ab64be08024dc741d83c6f60b39065c09","family_id":"qf-ext19-model-reachable-states","seed":202610194017,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0018","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"897fbb306c9e417d8e095ac5c204725be8b4c6aed24b8133471b6a2f92181d20","family_id":"qf-ext19-model-reachable-states","seed":202610194018,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 3, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 3, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0019","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d32bd7f4ec8a4726076dc25e4db38e883f4471ab5a7a9729a1139cfea92df570","family_id":"qf-ext19-model-reachable-states","seed":202610194019,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0020","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"21b59418938054c4d180f8263321c3244d2970959efb3c9911db47875a09540d","family_id":"qf-ext19-model-reachable-states","seed":202610194020,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0021","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"95a15a959bd6de0da424c726005cb8879dac1a25df66917362b0c4d7d4cfefdf","family_id":"qf-ext19-model-reachable-states","seed":202610194021,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[4,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0022","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3e11c7782be45027e87c39cc5d5e1539e3a1c8af9c44081a9158be379f41426c","family_id":"qf-ext19-model-reachable-states","seed":202610194022,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[4,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0023","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c49333b98e1eae46bdfc534a130b482400256997a5a05a1f75410dfc0501f35b","family_id":"qf-ext19-model-reachable-states","seed":202610194023,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4],[4,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0024","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"68060b185acef3fba64a21e315592cc6531c08f11fd8d5b4dcb84450efc24772","family_id":"qf-ext19-model-reachable-states","seed":202610194024,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4],[4,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0025","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"71f0ce966342846fa9703b10a63d6fe8d4c4b93d3189689d2504bb2cb1c60a46","family_id":"qf-ext19-model-reachable-states","seed":202610194025,"semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,1],[2,5]]}"},"fields":{"title":"Complete Reachability with Halt Outgoing Edges Truncated","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5])","explanation":"Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5])."},"skills":["Complete Reachability with Halt Outgoing Edges Truncated"],"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-20261019-r04-computational-model-0026","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ca0d93e5357dbddf95e9079003e7782216d034aa8ab559685b2aead8a9276ad","family_id":"qf-ext19-model-trace-qualification","seed":202610194026,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5]],\"trace\":[0,1,2,5]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0027","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ae76df675dbedb3f75fdcbe5d2d0bf71a83983aa197549c4579671e09853c18d","family_id":"qf-ext19-model-trace-qualification","seed":202610194027,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5]],\"trace\":[0,4]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0028","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"75fd2783a3ef801c2699d0f2886321ef64567eb9d8d2746d21187350e0a331c2","family_id":"qf-ext19-model-trace-qualification","seed":202610194028,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[3,4]],\"trace\":[0,1,2,5,5]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0029","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b104e5fc500e5d0e07f89493be77fdbb620d67fc24c09d9b5dd1d695537eb337","family_id":"qf-ext19-model-trace-qualification","seed":202610194029,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4]],\"trace\":[0,6]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 6], [Yes, No], Yes, Yes, [No], No, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0030","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"879d5cf9411a235812150bddbecbe6a8d103da64d28a0c3273afae03ced0f61a","family_id":"qf-ext19-model-trace-qualification","seed":202610194030,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[4,5]],\"trace\":[0,1,2,5]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0031","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ffa8a9faaf31d6f6888e8b4ba05dfc4329faa93cb5906dcd507378e4c074ead9","family_id":"qf-ext19-model-trace-qualification","seed":202610194031,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[4,5]],\"trace\":[0,4]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0032","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bfba48aec7b3fc9b281cac0077b285d3e4d8ac92bfb0745812256dd84073d685","family_id":"qf-ext19-model-trace-qualification","seed":202610194032,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]],\"trace\":[0,1,2,5,5]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0033","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"10ea800831fb426f216ca31f56458a7e023267517142543c5f5218e1f0961f98","family_id":"qf-ext19-model-trace-qualification","seed":202610194033,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4],[4,5]],\"trace\":[0,6]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 6], [Yes, No], Yes, Yes, [No], No, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0034","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"454d50a5b9181a42fec64423868412dcd2dc6033092c338defc4e7c476b7b17b","family_id":"qf-ext19-model-trace-qualification","seed":202610194034,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5]],\"trace\":[0,1,2,5]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0035","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aef56a63996f91553c42ead81bff322173f866749e5855ed1eee3e511defd15b","family_id":"qf-ext19-model-trace-qualification","seed":202610194035,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5]],\"trace\":[0,4]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0036","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a5270e31665fde797323ee99db5deddb2f2f612438a1a8280f5a181919a66581","family_id":"qf-ext19-model-trace-qualification","seed":202610194036,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4]],\"trace\":[0,1,2,5,5]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0037","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1b7caccc68e3ae84c01ed38ff0db1d7b5a33911d902a4540451fe0d26abc3fdf","family_id":"qf-ext19-model-trace-qualification","seed":202610194037,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4]],\"trace\":[0,6]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 6], [Yes, No], Yes, Yes, [No], No, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0038","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e668eeb5061cc319a3be216d5d6d6b957bbfd0258d620fa7a8c3583731c9c502","family_id":"qf-ext19-model-trace-qualification","seed":202610194038,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[4,5]],\"trace\":[0,1,2,5]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0039","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"55b3d7f095146a7f3c043e101415e1a340124d368738ef3092aa39b680cb2f25","family_id":"qf-ext19-model-trace-qualification","seed":202610194039,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[4,5]],\"trace\":[0,4]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0040","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5df328259300452bf387da0e6e01420b9e77917f8118b4ceaa1be0eb0e8332be","family_id":"qf-ext19-model-trace-qualification","seed":202610194040,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4],[4,5]],\"trace\":[0,1,2,5,5]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0041","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"08ddb350900b54ce3d8501c509ff33018edb1e6c09f7dd6fd22d9da36dc9e25b","family_id":"qf-ext19-model-trace-qualification","seed":202610194041,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4],[4,5]],\"trace\":[0,6]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 6], [Yes, No], Yes, Yes, [No], No, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0042","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4f950c3b0e13e2ea0778f955df42b05f016c548760fba84f6b58081633b68a87","family_id":"qf-ext19-model-trace-qualification","seed":202610194042,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5]],\"trace\":[0,1,2,5]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0043","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e73cb9c4a8fd285f1a96695e6e07d59e25549c3b23bb4315f6e8647e0151250c","family_id":"qf-ext19-model-trace-qualification","seed":202610194043,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5]],\"trace\":[0,4]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0044","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"233c8a14b03e2970dd2ec31985d0a51420e63ece56e2aafa82752064d2410484","family_id":"qf-ext19-model-trace-qualification","seed":202610194044,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4]],\"trace\":[0,1,2,5,5]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0045","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9f0190c5f2b1a74cc5c57dcf759b0a966b7f336e8b0706f51787bbaa2eb622e3","family_id":"qf-ext19-model-trace-qualification","seed":202610194045,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4]],\"trace\":[0,6]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 6], [Yes, No], Yes, Yes, [No], No, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0046","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"507bf15e06cf8f64446da09f55d46b22c923e4f506ea8473e8fb7f4523cd25be","family_id":"qf-ext19-model-trace-qualification","seed":202610194046,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[4,5]],\"trace\":[0,1,2,5]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0047","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7b66c4bce5a5cd0bd3588faa87f77be6ddfeb40b3d7301732629f1d6ff5a73d3","family_id":"qf-ext19-model-trace-qualification","seed":202610194047,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[4,5]],\"trace\":[0,4]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0048","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a519c457e86def23a387e973f96b698a089477330af1d027fde4e072183e1df8","family_id":"qf-ext19-model-trace-qualification","seed":202610194048,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4],[4,5]],\"trace\":[0,1,2,5,5]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0049","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7a6a8b70ac92de7aa17aaba3439cbc0c9a9da08b45163ea3dd56db91561ae17d","family_id":"qf-ext19-model-trace-qualification","seed":202610194049,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4],[4,5]],\"trace\":[0,6]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 6], [Yes, No], Yes, Yes, [No], No, No)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0050","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a871b3ae2f079f44656d8f4c522ff871d9951637d318b98b34a9a6098346046f","family_id":"qf-ext19-model-trace-qualification","seed":202610194050,"semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,1],[2,5]],\"trace\":[0,1,2,5]}"},"fields":{"title":"Legal Finite Trace Prefix and Post-Halt Continuation Guard","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)","explanation":"Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)."},"skills":["Legal Finite Trace Prefix and Post-Halt Continuation Guard"],"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-20261019-r04-computational-model-0051","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0b216b19f9714f012a9aad8ae159b0a3a4732288885d20f74da3ceecb794fb9b","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194051,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0052","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e382bfbda5589445d6abe1e7b978b592322d47f6c6d004550e39dc9b33846ab2","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194052,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0053","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4a7450d5c89c501e72a414024f41fcbbe4e7c608e1254a2c03012b80f51a2bf0","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194053,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[3,4]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0054","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d4fe0bef0f04ea310fb7fc61417665ab65b5094e2f2a3fd01d23b0197e123058","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194054,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0055","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d14b230ed0a9bac9d99e742f7945edb298ac0ee0255a61193ea88492b902ccfd","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194055,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[4,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0056","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4dc8be75b9a998a1d9b8cc53c44eb2bc0f14f2b280f3216a6ec5cf142dd7c066","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194056,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[4,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0057","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"610b2873d7b8c1201e6080e5fbcc34cc5312d84016773473dc9cb044855936c9","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194057,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0058","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aa26aa3afe76a9252a573e7366f04f21a5592c0146acf95242b3cde26a824bc8","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194058,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4],[4,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0059","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7448fed2b7c90c3b3e78599fa9c1b2da00e1e226cf01a3c425a59f30a1d8e52f","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194059,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0060","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"18c52df4b20389f7cee86107bfff1920b0ae2bdff02b7d91cf12307aaea95d75","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194060,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0061","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9798592eed2c07796baec2aa5ef7b10bd0dee14e781adf407c3aba801fbb703f","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194061,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0062","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"41c07a33ccbd802f6939cdbc7d300995dc595a2aa436887a746f706229a286a5","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194062,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0063","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"89a43b9ad7f4399e30f081e4f08be3e446b82cacf7113a31951985b42eb44d0a","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194063,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[4,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0064","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0889600262a297fada91e6d41bb863c15399f583dc08572dea0d3dcb57aca5db","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194064,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[4,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0065","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a4cb85ff3e22a4f2995074d3684e2b1b2f55f633ea8708dd60814ff44f48ea6d","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194065,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4],[4,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0066","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4e9182cc4a67268067ef6634c492d10007ebd8d85ff90586208ce28556531571","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194066,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4],[4,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0067","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"14a097f43534e89efed5d5c2e277cd5b847b1aae10a740367241e20bebb69be6","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194067,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0068","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d211e41877f10e805f0e02f03b40c4369c64330720ed67e81d8e4ea20192e5be","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194068,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0069","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87d75ce9611eb421a2a9cf7bc8108ce5731068c375838493bcac89e704bb5e02","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194069,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0070","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"755568655816037bf856258b238555cbe8018bf7704caaed3fdb84437fdf16b2","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194070,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0071","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cb072c62da09d837858960d74730bf82d9d9255f911f9eadf4e30e6035141017","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194071,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[4,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0072","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aaf140edc2abf892667edcdd68f201f91f04cc86233ff631c1389a0f7f4628ac","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194072,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[4,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0073","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4aefdcaa57daf6ef1e36d7739c6222f74578805ecaa0d69468e183e612bffef4","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194073,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4],[4,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0074","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"22988fb7bcc62e41287e3569afb9e4eabe97facc02da368edc53e5cbb932cbf2","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194074,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4],[4,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0075","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9cf117978848e69a21ae42dc841e50d444bd99180e924d7515678493e653d554","family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194075,"semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,1],[2,5]]}"},"fields":{"title":"Reachable Halt, Stuck, and Active States","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation":"A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2])."},"skills":["Reachable Halt, Stuck, and Active States"],"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-20261019-r04-computational-model-0076","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cfbd441beb94664fb01b4d68f2b442645c45ff9cfe502f84d60564d7a54efdaf","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194076,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0077","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"69bc95a24cfa5558d137db173e1420a08183490f396b82c27f907b4400d13c7a","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194077,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [3], No, No, reachable stuck-nonhalting-state)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], No, No, reachable stuck-nonhalting-state)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0078","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6585606aab97edd2705dd3da0170080279427e0667c25ee08ca912973787c600","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194078,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[3,4]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0079","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3263b23121be7894888edef104acedfb07749450c511e9b4c59a3b57bf638d9a","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194079,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [4], No, No, reachable stuck-nonhalting-state)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [4], No, No, reachable stuck-nonhalting-state)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0080","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9df439c62cff182420eb5bb1ba26f97af11ec8bd1667e055302b86089349940f","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194080,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[4,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0081","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"003f377aceffb6ee7975fc9c17bce6a31112d56e12be9ed4d58277d566cda7cb","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194081,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[4,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [3], No, No, reachable stuck-nonhalting-state)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], No, No, reachable stuck-nonhalting-state)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0082","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"29a6b20a5b14bbc97327d62b75a1482807c0e6dfa271503e55833685c34ddfa5","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194082,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0083","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9d40df8c2972c6f62e60db9ebb5b817f0a97c5ce74ec2b29c115416786e0e752","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194083,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4],[4,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [], No, Yes, all-finite-model-paths-reach-halt)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [], No, Yes, all-finite-model-paths-reach-halt)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0084","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ff90e8241bd801f7e305aa050a632475a76dc8646dfc99f8929f23e3873b4146","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194084,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0085","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8679e204e374d65dd13a3379f70b1007a55f697ed12d06e5e40b509376e96a08","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194085,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0086","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c849953db53c9a0c72d41faa0ff3c6ee9dd9d5eca15f1a59038b453d00cc96f","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194086,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0087","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6e2803f19e50cbadcbe2bad08e13fd9a892f581be2e277d71e1037a379b9f254","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194087,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [4], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [4], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0088","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"18001b93d02f12077a1bc6fd06bbe442a46a41cd4dac50f3533116fad431fcbe","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194088,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[4,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0089","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0f2a2775420d0463dfbe69047b535ccc23faf581135b988b5475c240bf49c187","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194089,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[4,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0090","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8bafc27f65a52978d392cddb9bea9baaf59701a94d9e01c9e60e679902529e63","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194090,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4],[4,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0091","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"181afaa65a72a8827743185a83886de8a82f365887c7b7d10f2101eeb3ba90ac","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194091,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4],[4,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0092","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3c9dce1ef9506b078f17335744b05dd4c5ee297520ed777987277042487539f2","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194092,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0093","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7237a9969e8ea34e6e43f2b34b852b5e026777948962d289934f4feb8af35ac0","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194093,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0094","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"50501ead9e319ecf4a066eecb82234228d3b54b7d80ea76919ea315ebe42fbc3","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194094,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0095","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ee2a0a3b31104a347d0f9e229a5c687bd40e4701510298e6e27b593124fad798","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194095,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [4], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [4], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0096","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"389f3a6a92d8b849f2e436820d1d4dc6102ceecc8d50284b11ba2470c0b64b07","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194096,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[4,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0097","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"feec89dc15658050f30ce141a66aefa2fb63f495889c909ae3456b02b0af2caf","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194097,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[4,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0098","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"89678e4666d85e49edea0a9564040fba4ceb7bf74aa4db4cf536579729912eff","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194098,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4],[4,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0099","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f6705e5ba453daa9165c7271fc5f68ba000d39a059cbb0786d5ceaec31ae426f","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194099,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4],[4,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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-20261019-r04-computational-model-0100","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"91842efab9dc554b92d57efcc2214af94aae64beabf09b9a11a21b0edf50e13c","family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194100,"semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,1],[2,5]]}"},"fields":{"title":"All-Path Finite Termination and Reachable Nonhalting Cycles","stem":"Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)","explanation":"Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)."},"skills":["All-Path Finite Termination and Reachable Nonhalting Cycles"],"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."}}