{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261013-advance-20261018-r05-modular-congruence-0062",
  "pilot_number": "R0017-09012",
  "number": 9012,
  "family_id": "qf-ext18-modeq-add-preservation",
  "title": {
    "zh-Hant": "第 9012 題：正模數同餘",
    "en": "Question 9012: Additive Congruence Values, Premises, and Material Implication"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261013-advance-20261018-r05-modular-congruence-0062",
    "batch_id": "batch-20261013-advance-20261018-r05-modular-congruence-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-modular-congruence"
    ],
    "title_zh": "正模數同餘",
    "stem_zh": "固定模數。操作=modeq-add-preservation；資料={\"n\":4,\"a\":12,\"b\":24,\"c\":25,\"d\":29}。請依 [n,[a,b],[c,d],premises,[result_remainders],conclusion,implication] 的欄序回答。",
    "answer": {
      "kind": "expression",
      "value": "(4, [12, 24], [25, 29], 是, [1, 1], 是, 是)",
      "explanation_zh": "擴展基礎核對=(4, [12, 24], [25, 29], 是, [1, 1], 是, 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；正模數資格先行；不可無條件取消共同因子。"
    },
    "difficulty": {
      "band": "upper_secondary",
      "level": 2,
      "skills": [
        "正模數同餘"
      ]
    },
    "variant": {
      "family_id": "qf-ext18-modeq-add-preservation",
      "seed": 202610185062,
      "parameters": {
        "n": 4,
        "a": 12,
        "b": 24,
        "c": 25,
        "d": 29,
        "domain": "Nat_positive_mod_congruence",
        "operation": "modeq-add-preservation",
        "semantic_template": "qf-ext18-modeq-add-preservation/{\"a\":12,\"b\":24,\"c\":25,\"d\":29,\"n\":4}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_finite_arithmetic",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication",
        "producer_json_schema"
      ],
      "warning_zh": "僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、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-20261018-r05-modular-congruence-0062",
    "batch_id": "batch-20261013-advance-20261018-r05-modular-congruence-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "dccb7d729d5f6f61c0af0a86fb0e1c8c01394f85a109d6cd95053f58c7a16b45",
      "family_id": "qf-ext18-modeq-add-preservation",
      "seed": 202610185062,
      "semantic_template": "qf-ext18-modeq-add-preservation/{\"a\":12,\"b\":24,\"c\":25,\"d\":29,\"n\":4}"
    },
    "fields": {
      "title": "Additive Congruence Values, Premises, and Material Implication",
      "stem": "Use fixed positive modulus n=4, natural inputs a=12, b=24, c=25, d=29. Give (n, [a,b], [c,d], both a≡b and c≡d?, [(a+c) mod n,(b+d) mod n], sum congruence?, premises imply conclusion?).",
      "answer": {
        "kind": "expression",
        "value": "(4, [12, 24], [25, 29], Yes, [1, 1], Yes, Yes)",
        "explanation": "Recompute both premises and the conclusion separately. A false premise can make the material implication true even when it supplies no applicable preservation premise. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (4, [12, 24], [25, 29], Yes, [1, 1], Yes, Yes)."
      },
      "skills": [
        "Additive Congruence Values, Premises, and Material Implication"
      ],
      "verification_warning": "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": "固定模數。操作=modeq-add-preservation；資料={\"n\":4,\"a\":12,\"b\":24,\"c\":25,\"d\":29}。請依 [n,[a,b],[c,d],premises,[result_remainders],conclusion,implication] 的欄序回答。",
        "en": "Use fixed positive modulus n=4, natural inputs a=12, b=24, c=25, d=29. Give (n, [a,b], [c,d], both a≡b and c≡d?, [(a+c) mod n,(b+d) mod n], sum congruence?, premises imply conclusion?)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "fixed natural modulus candidate=4",
      "after": "positive modulus=是",
      "relation": "implies",
      "rule_id": "fixed_positive_modulus_scope",
      "conditions": [],
      "explanation": {
        "zh-Hant": "同餘在同一正模數下以餘數比較，不等於數值相等。乘法保持同餘不表示可無條件取消共同因子。",
        "en": "Congruence compares remainders at one positive modulus,not numerical equality.Multiplicative preservation does not permit unconditional cancellation of a common factor."
      },
      "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": "a remainder:natural dividend=12;positive divisor=4",
      "after": "12=3·4+0",
      "relation": "implies",
      "rule_id": "positive_euclidean_division",
      "conditions": [],
      "explanation": {
        "zh-Hant": "正除數下完整列商餘等式，0≤r<divisor；不把取模0當可求值。",
        "en": "With a positive divisor show the complete quotient/remainder equality and0≤r<divisor.Modulo zero is not evaluated."
      },
      "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": {
        "operation": "euclidean_division",
        "inputs": [
          "12",
          "4",
          "3"
        ],
        "output": "0",
        "label": "a remainder"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "b remainder:natural dividend=24;positive divisor=4",
      "after": "24=6·4+0",
      "relation": "implies",
      "rule_id": "positive_euclidean_division",
      "conditions": [],
      "explanation": {
        "zh-Hant": "正除數下完整列商餘等式，0≤r<divisor；不把取模0當可求值。",
        "en": "With a positive divisor show the complete quotient/remainder equality and0≤r<divisor.Modulo zero is not evaluated."
      },
      "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": {
        "operation": "euclidean_division",
        "inputs": [
          "24",
          "4",
          "6"
        ],
        "output": "0",
        "label": "b remainder"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "c remainder:natural dividend=25;positive divisor=4",
      "after": "25=6·4+1",
      "relation": "implies",
      "rule_id": "positive_euclidean_division",
      "conditions": [],
      "explanation": {
        "zh-Hant": "正除數下完整列商餘等式，0≤r<divisor；不把取模0當可求值。",
        "en": "With a positive divisor show the complete quotient/remainder equality and0≤r<divisor.Modulo zero is not evaluated."
      },
      "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": {
        "operation": "euclidean_division",
        "inputs": [
          "25",
          "4",
          "6"
        ],
        "output": "1",
        "label": "c remainder"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "d remainder:natural dividend=29;positive divisor=4",
      "after": "29=7·4+1",
      "relation": "implies",
      "rule_id": "positive_euclidean_division",
      "conditions": [],
      "explanation": {
        "zh-Hant": "正除數下完整列商餘等式，0≤r<divisor；不把取模0當可求值。",
        "en": "With a positive divisor show the complete quotient/remainder equality and0≤r<divisor.Modulo zero is not evaluated."
      },
      "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": {
        "operation": "euclidean_division",
        "inputs": [
          "29",
          "4",
          "7"
        ],
        "output": "1",
        "label": "d remainder"
      }
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "combined left value := sum(12, 25)",
      "after": "combined left value = 37",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步原始操作數及指定次序精確計算，不用近似值或替換候選。",
        "en": "Calculate exactly in the specified source-operand order without approximation or substituting a different candidate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 combined left value，不以小數近似替代。",
          "en": "Recompute combined left value with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "12",
          "25"
        ],
        "output": "37",
        "label": "combined left value"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "combined right value := sum(24, 29)",
      "after": "combined right value = 53",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步原始操作數及指定次序精確計算，不用近似值或替換候選。",
        "en": "Calculate exactly in the specified source-operand order without approximation or substituting a different candidate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 combined right value，不以小數近似替代。",
          "en": "Recompute combined right value with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "24",
          "29"
        ],
        "output": "53",
        "label": "combined right value"
      }
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "combined left remainder:natural dividend=37;positive divisor=4",
      "after": "37=9·4+1",
      "relation": "implies",
      "rule_id": "positive_euclidean_division",
      "conditions": [],
      "explanation": {
        "zh-Hant": "正除數下完整列商餘等式，0≤r<divisor；不把取模0當可求值。",
        "en": "With a positive divisor show the complete quotient/remainder equality and0≤r<divisor.Modulo zero is not evaluated."
      },
      "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": {
        "operation": "euclidean_division",
        "inputs": [
          "37",
          "4",
          "9"
        ],
        "output": "1",
        "label": "combined left remainder"
      }
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "combined right remainder:natural dividend=53;positive divisor=4",
      "after": "53=13·4+1",
      "relation": "implies",
      "rule_id": "positive_euclidean_division",
      "conditions": [],
      "explanation": {
        "zh-Hant": "正除數下完整列商餘等式，0≤r<divisor；不把取模0當可求值。",
        "en": "With a positive divisor show the complete quotient/remainder equality and0≤r<divisor.Modulo zero is not evaluated."
      },
      "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": {
        "operation": "euclidean_division",
        "inputs": [
          "53",
          "4",
          "13"
        ],
        "output": "1",
        "label": "combined right remainder"
      }
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "a,b remainders=[0, 0];c,d remainders=[1, 1]",
      "after": "both premises=是;conclusion=是",
      "relation": "implies",
      "rule_id": "modular_premises_and_conclusion_separate",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先各核兩個前提，再獨立算和或積的兩個餘數；前提不成立不表示結論一定不成立。",
        "en": "Audit both premises first,then independently compute the sum/product remainders.A failed premise does not force a false conclusion."
      },
      "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": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "first quotient difference := sub(3, 6)",
      "after": "first quotient difference = -3",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步原始操作數及指定次序精確計算，不用近似值或替換候選。",
        "en": "Calculate exactly in the specified source-operand order without approximation or substituting a different candidate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 first quotient difference，不以小數近似替代。",
          "en": "Recompute first quotient difference with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "3",
          "6"
        ],
        "output": "-3",
        "label": "first quotient difference"
      }
    },
    {
      "id": "S012",
      "uses": [
        "G001",
        "S011"
      ],
      "before": "second quotient difference := sub(6, 7)",
      "after": "second quotient difference = -1",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步原始操作數及指定次序精確計算，不用近似值或替換候選。",
        "en": "Calculate exactly in the specified source-operand order without approximation or substituting a different candidate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 second quotient difference，不以小數近似替代。",
          "en": "Recompute second quotient difference with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "6",
          "7"
        ],
        "output": "-1",
        "label": "second quotient difference"
      }
    },
    {
      "id": "S013",
      "uses": [
        "G001",
        "S012"
      ],
      "before": "sum difference multiplier := sum(-3, -1)",
      "after": "sum difference multiplier = -4",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步原始操作數及指定次序精確計算，不用近似值或替換候選。",
        "en": "Calculate exactly in the specified source-operand order without approximation or substituting a different candidate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 sum difference multiplier，不以小數近似替代。",
          "en": "Recompute sum difference multiplier with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "-3",
          "-1"
        ],
        "output": "-4",
        "label": "sum difference multiplier"
      }
    },
    {
      "id": "S014",
      "uses": [
        "G001",
        "S013"
      ],
      "before": "combined difference := sub(37, 53)",
      "after": "combined difference = -16",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步原始操作數及指定次序精確計算，不用近似值或替換候選。",
        "en": "Calculate exactly in the specified source-operand order without approximation or substituting a different candidate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 combined difference，不以小數近似替代。",
          "en": "Recompute combined difference with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "37",
          "53"
        ],
        "output": "-16",
        "label": "combined difference"
      }
    },
    {
      "id": "S015",
      "uses": [
        "G001",
        "S014"
      ],
      "before": "modulus times difference multiplier := mul(4, -4)",
      "after": "modulus times difference multiplier = -16",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本步原始操作數及指定次序精確計算，不用近似值或替換候選。",
        "en": "Calculate exactly in the specified source-operand order without approximation or substituting a different candidate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 modulus times difference multiplier，不以小數近似替代。",
          "en": "Recompute modulus times difference multiplier with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "4",
          "-4"
        ],
        "output": "-16",
        "label": "modulus times difference multiplier"
      }
    },
    {
      "id": "S016",
      "uses": [
        "G001",
        "S015"
      ],
      "before": "combined difference=-16;integer multiplier=-4;modulus=4",
      "after": "difference=n*multiplier=-16",
      "relation": "implies",
      "rule_id": "applicable_modular_preservation_witness",
      "conditions": [],
      "explanation": {
        "zh-Hant": "相同餘數相減後，a−b=n(qa−qb)、c−d=n(qc−qd)。加法直接相加；乘法用ac−bd=a(c−d)+d(a−b)。乘數可為負整數，不需取消共同因子。",
        "en": "Equal remainders give a−b=n(qa−qb) and c−d=n(qc−qd).Add directly,or use ac−bd=a(c−d)+d(a−b).The multiplier may be a negative integer;no factor cancellation is needed."
      },
      "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": "S017",
      "uses": [
        "G001",
        "S016"
      ],
      "before": "premises=是;conclusion=是",
      "after": "material implication=是",
      "relation": "implies",
      "rule_id": "modular_implication_not_applicable_premise",
      "conditions": [],
      "explanation": {
        "zh-Hant": "前提為假時材料蘊涵為真只是其真值定義，不是取得可套用的保持定理前提。",
        "en": "A false premise makes the material implication true by its truth definition,not by supplying applicable preservation premises."
      },
      "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": [
      4,
      [
        12,
        24
      ],
      [
        25,
        29
      ],
      true,
      [
        1,
        1
      ],
      true,
      true
    ]
  },
  "conclusion": {
    "canonical_value": "(4, [12, 24], [25, 29], 是, [1, 1], 是, 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-20261018-r05-modular-congruence-foundations",
      "batch_path": "public/data/questions/batches/batch-20261013-advance-20261018-r05-modular-congruence-foundations/questions.jsonl",
      "batch_sha256": "11ab2f76ce5fc3b4ea3ee6beb1fac6bbbec928d3634a3cf0d7d08dbbe78db498",
      "original_line": 62,
      "original_line_sha256": "d12802e102a1586681fb4713c045102fd2afbc989488334d59c0c0896ee6204b",
      "question_compact_sha256": "dccb7d729d5f6f61c0af0a86fb0e1c8c01394f85a109d6cd95053f58c7a16b45",
      "english_row_compact_sha256": "dcb59f3f209149efeb4cdc09dfd97d6a114e2e2a1ace74f98aa989d2b0c3c6a9",
      "english_manifest_path": "public/data/i18n/editions/batch-20261013-advance-20261018-r05-modular-congruence-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261013-advance-20261018-r05-modular-congruence-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-modular-congruence": {
        "sha256": "f2701dae3fc0037b15acf2146bea327e803c9f727d640db0a85d02de29f3f635",
        "english_sha256": "b1c4c24d7715216387b6c6d80d0393707e999f09f844c40b624b56ec79f8ec35",
        "original_path": "public/data/mko/modular-congruence.json",
        "english_path": "public/data/i18n/editions/mko-modular-congruence.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "20e59f30c0b6218e6d9614c16170d770e56a2f1e4ae5ce39d0a8a3db206afa61",
    "original_candidate_sha256": "873e7e76c097033f649ae0364b0ee77363ea1389b7a7bc884cc63d3564edcaac",
    "original_candidate_line_sha256": "873e7e76c097033f649ae0364b0ee77363ea1389b7a7bc884cc63d3564edcaac"
  },
  "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-p18",
    "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": "abad28564830bb9b6ef069ca5a1aa128ce7b1a67a5cb8fe6d868a06db73bcfb8",
      "question_first_witness_sha256": "43126988479968837abe086263dac1b24c37463ad80e00d2e280a7b8e9036a04"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 17,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "05708ce3907be1f40f2f0cff9eb13b10a2227d100b1e4be990c9551582bb8a97",
      "arithmetic_steps": 13
    },
    "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."
  }
}