{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261013-advance-20261019-r04-computational-model-0034",
  "pilot_number": "R0018-09684",
  "number": 9684,
  "family_id": "qf-ext19-model-trace-qualification",
  "title": {
    "zh-Hant": "第 9684 題：有限轉移計算模型",
    "en": "Question 9684: Legal Finite Trace Prefix and Post-Halt Continuation Guard"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261013-advance-20261019-r04-computational-model-0034",
    "batch_id": "batch-20261013-advance-20261019-r04-computational-model-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-computational-model"
    ],
    "title_zh": "有限轉移計算模型",
    "stem_zh": "完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1]],\"trace\":[0,1,2,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。",
    "answer": {
      "kind": "expression",
      "value": "([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 是)",
      "explanation_zh": "第二批擴展核對=([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；halt與stuck分離；有限prefix不證一般終止。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 2,
      "skills": [
        "有限轉移計算模型"
      ]
    },
    "variant": {
      "family_id": "qf-ext19-model-trace-qualification",
      "seed": 202610194034,
      "parameters": {
        "n": 6,
        "init": [
          0
        ],
        "halt": [
          5
        ],
        "steps": [
          [
            0,
            1
          ],
          [
            1,
            2
          ],
          [
            2,
            5
          ],
          [
            2,
            1
          ]
        ],
        "trace": [
          0,
          1,
          2,
          5
        ],
        "domain": "Fin_transition_model",
        "operation": "model-trace-qualification",
        "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]}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_finite_model",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication",
        "producer_json_schema"
      ],
      "warning_zh": "僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、Lean執行或形式Evidence。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "model_unknown",
      "generated_at": "2026-10-13",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "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."
    }
  },
  "givens": [
    {
      "id": "G001",
      "text": {
        "zh-Hant": "完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1]],\"trace\":[0,1,2,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。",
        "en": "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."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "n=6;raw Init=[0];raw Halt=[5];raw Step=[[0, 1], [1, 2], [2, 5], [2, 1]]",
      "after": "Init=[0];Halt=[5];canonical raw Step=[[0, 1], [1, 2], [2, 1], [2, 5]]",
      "relation": "implies",
      "rule_id": "finite_transition_normalization",
      "conditions": [],
      "explanation": {
        "zh-Hant": "整張有限資料先合型，再去重原有向邊。保留halt的原始出邊在資料中，但執行語意在halt停止；不把stuck當成功halt，也不由一條prefix推一般程式終止。",
        "en": "Type the complete finite data and deduplicate directed edges.Retain raw outgoing halt edges as data,but execution stops at halt.Stuck is not successful halt,and one prefix proves no general program termination."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "trace position=0;raw state=0;domain Fin(6)",
      "after": "typed=是",
      "relation": "implies",
      "rule_id": "trace_each_state_type_guard",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先核每個原trace位置的型別與域；域外或布林資料不拿來當合法整數索引。",
        "en": "Check type and domain at every original trace position.Outside or Boolean data is not a legal integer index."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "trace position=1;raw state=1;domain Fin(6)",
      "after": "typed=是",
      "relation": "implies",
      "rule_id": "trace_each_state_type_guard",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先核每個原trace位置的型別與域；域外或布林資料不拿來當合法整數索引。",
        "en": "Check type and domain at every original trace position.Outside or Boolean data is not a legal integer index."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "trace position=2;raw state=2;domain Fin(6)",
      "after": "typed=是",
      "relation": "implies",
      "rule_id": "trace_each_state_type_guard",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先核每個原trace位置的型別與域；域外或布林資料不拿來當合法整數索引。",
        "en": "Check type and domain at every original trace position.Outside or Boolean data is not a legal integer index."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "trace position=3;raw state=5;domain Fin(6)",
      "after": "typed=是",
      "relation": "implies",
      "rule_id": "trace_each_state_type_guard",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先核每個原trace位置的型別與域；域外或布林資料不拿來當合法整數索引。",
        "en": "Check type and domain at every original trace position.Outside or Boolean data is not a legal integer index."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "trace pair index=0;pair=[0, 1];both typed=是",
      "after": "raw Step edge=是;continues from Halt=否",
      "relation": "implies",
      "rule_id": "trace_edge_and_halt_continuation_separate",
      "conditions": [],
      "explanation": {
        "zh-Hant": "原邊存在與禁止halt後繼續是兩個條件。即使有halt原始出邊，trace走它仍不合法。",
        "en": "Raw edge existence and the ban on continuing after Halt are separate.Even a listed raw halt edge cannot legally extend execution."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "trace pair index=1;pair=[1, 2];both typed=是",
      "after": "raw Step edge=是;continues from Halt=否",
      "relation": "implies",
      "rule_id": "trace_edge_and_halt_continuation_separate",
      "conditions": [],
      "explanation": {
        "zh-Hant": "原邊存在與禁止halt後繼續是兩個條件。即使有halt原始出邊，trace走它仍不合法。",
        "en": "Raw edge existence and the ban on continuing after Halt are separate.Even a listed raw halt edge cannot legally extend execution."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "trace pair index=2;pair=[2, 5];both typed=是",
      "after": "raw Step edge=是;continues from Halt=否",
      "relation": "implies",
      "rule_id": "trace_edge_and_halt_continuation_separate",
      "conditions": [],
      "explanation": {
        "zh-Hant": "原邊存在與禁止halt後繼續是兩個條件。即使有halt原始出邊，trace走它仍不合法。",
        "en": "Raw edge existence and the ban on continuing after Halt are separate.Even a listed raw halt edge cannot legally extend execution."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "nonempty=是;initial in Init=是;state masks=[是, 是, 是, 是];edge flags=[是, 是, 是];continued after halt=否",
      "after": "legal finite prefix=是",
      "relation": "implies",
      "rule_id": "finite_trace_prefix_not_termination",
      "conditions": [],
      "explanation": {
        "zh-Hant": "非空、全合型、起於Init、相鄰邊皆合法且不越halt才是合法prefix；prefix不必已到halt，亦不構成所有分支終止的證明。",
        "en": "A legal prefix is nonempty,typed,starts in Init,follows each edge and never continues after halt.It need not yet reach Halt and does not prove all branches terminate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": [
      [
        0,
        1,
        2,
        5
      ],
      [
        true,
        true,
        true,
        true
      ],
      true,
      true,
      [
        true,
        true,
        true
      ],
      false,
      true
    ]
  },
  "conclusion": {
    "canonical_value": "([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 是)",
    "explanation": {
      "zh-Hant": "依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。",
      "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged."
    }
  },
  "definition_note": {
    "zh-Hant": "沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。",
    "en": "Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate."
  },
  "source": {
    "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db",
    "question_binding": {
      "batch_id": "batch-20261013-advance-20261019-r04-computational-model-foundations",
      "batch_path": "public/data/questions/batches/batch-20261013-advance-20261019-r04-computational-model-foundations/questions.jsonl",
      "batch_sha256": "cd8be3fc874c2679c687b7da60c375690d2be058604ca0ac451e2b4fef43d5f3",
      "original_line": 34,
      "original_line_sha256": "5d9677ab25f4649afb679e7571d1fd52969fa356abc9789c2d4521b8662f784e",
      "question_compact_sha256": "454d50a5b9181a42fec64423868412dcd2dc6033092c338defc4e7c476b7b17b",
      "english_row_compact_sha256": "b17fcda738750d76bffd77d1134a160907d54c0149fca41699b7b2fc3433b07e",
      "english_manifest_path": "public/data/i18n/editions/batch-20261013-advance-20261019-r04-computational-model-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261013-advance-20261019-r04-computational-model-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-computational-model": {
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        "english_sha256": "ebf84673ae14cdac5d40d5169fdf883572ebfb975b108019f7d01964682ca3ef",
        "original_path": "public/data/mko/computational-model.json",
        "english_path": "public/data/i18n/editions/mko-computational-model.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "2cf5df7bf9c3d48dfd41d968723b60d910c4ecfec9c2089d22ac1cda059a6086",
    "original_candidate_sha256": "7c34f20c75d5ee67648244279e9aecda3e85c146854f0f94eb150ec22b21db87",
    "original_candidate_line_sha256": "7c34f20c75d5ee67648244279e9aecda3e85c146854f0f94eb150ec22b21db87"
  },
  "historical_source_state": {
    "review_state": {
      "derivation": "candidate_authored_and_locally_checked",
      "source_question_state": "candidate",
      "independent_AI_or_human_review": "NOT_PERFORMED",
      "formalization": "not_formalized",
      "Lean": "NOT_RUN"
    },
    "scope_note": {
      "zh-Hant": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。",
      "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human review or general formal proof.Original questions,answers,MKOs,formulas,ASTs and history remain unchanged."
    },
    "label": "Frozen producer metadata; current per-question review is separate below."
  },
  "revision": {
    "id": "review-20261026-006-p19",
    "review_date": "2026-10-26",
    "owner_authorized_reader_publication": true,
    "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.",
    "review_receipts": {
      "semantic_review_sha256": "bd35da62087a15d6b89b45585dc46e89b9efbe097cba7b3c707b5030496f013c",
      "question_first_witness_sha256": "fab45a10d8ac95c7d61d32e47d1bdd3ca862c17c3289a6bf4b01d4dc9492fbb6"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 9,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "2ab6ccd0073cc6544c6446b5e0e917349432627f06b55ce7217819c08003cd7d",
      "arithmetic_steps": 0
    },
    "uses_answer_as_premise": false,
    "human_review": "NOT_PERFORMED",
    "formalization": "not_formalized",
    "Lean": "NOT_RUN",
    "Canonical_truth_promotion": false,
    "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged."
  }
}