{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261013-advance-20261020-r04-optimization-problem-0089",
  "pilot_number": "R0058-29889",
  "number": 29889,
  "family_id": "qf-app20-optimization-linear-constraint-audit",
  "title": {
    "zh-Hant": "第 29889 題：有限候選最佳化",
    "en": "Question 29889: A Linear Constraint on a Complete Ordered Finite Point List"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261013-advance-20261020-r04-optimization-problem-0089",
    "batch_id": "batch-20261013-advance-20261020-r04-optimization-problem-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-optimization-problem"
    ],
    "title_zh": "有限候選最佳化",
    "stem_zh": "完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,3],[2,5],[3,1]],\"constraint\":[2,1,10],\"objective\":[1,2],\"direction\":\"min\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。",
    "answer": {
      "kind": "expression",
      "value": "([2, 1, 10], [1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 3, 是, 7], [2, 2, 5, 是, 12], [3, 3, 1, 是, 5]], 0, [0])",
      "explanation_zh": "應用基礎核對=([2, 1, 10], [1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 3, 是, 7], [2, 2, 5, 是, 12], [3, 3, 1, 是, 5]], 0, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 2,
      "skills": [
        "有限候選最佳化"
      ]
    },
    "variant": {
      "family_id": "qf-app20-optimization-linear-constraint-audit",
      "seed": 202610204089,
      "parameters": {
        "points": [
          [
            0,
            0
          ],
          [
            1,
            3
          ],
          [
            2,
            5
          ],
          [
            3,
            1
          ]
        ],
        "constraint": [
          2,
          1,
          10
        ],
        "objective": [
          1,
          2
        ],
        "direction": "min",
        "domain": "Finite_declared_optimization",
        "operation": "optimization-linear-constraint-audit",
        "semantic_template": "qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,10],\"direction\":\"min\",\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,5],[3,1]]}"
      }
    },
    "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、一般定理、經驗預測、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-20261020-r04-optimization-problem-0089",
    "batch_id": "batch-20261013-advance-20261020-r04-optimization-problem-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "3780ab8ce270a589bb22dd888a7bd40d5130ffb5944a705d5ed9fffc60c9fb6d",
      "family_id": "qf-app20-optimization-linear-constraint-audit",
      "seed": 202610204089,
      "semantic_template": "qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,10],\"direction\":\"min\",\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,5],[3,1]]}"
    },
    "fields": {
      "title": "A Linear Constraint on a Complete Ordered Finite Point List",
      "stem": "Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 3], [2, 5], [3, 1]], constraint [A,B,c]=[2, 1, 10] means A*x+B*y≤c, objective [u,v]=[1, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.",
      "answer": {
        "kind": "expression",
        "value": "([2, 1, 10], [1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 5, Yes, 12], [3, 3, 1, Yes, 5]], 0, [0])",
        "explanation": "Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 10], [1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 5, Yes, 12], [3, 3, 1, Yes, 5]], 0, [0])."
      },
      "skills": [
        "A Linear Constraint on a Complete Ordered Finite Point List"
      ],
      "verification_warning": "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": "完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,3],[2,5],[3,1]],\"constraint\":[2,1,10],\"objective\":[1,2],\"direction\":\"min\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。",
        "en": "Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 3], [2, 5], [3, 1]], constraint [A,B,c]=[2, 1, 10] means A*x+B*y≤c, objective [u,v]=[1, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-app20-optimization-linear-constraint-audit, optimization-linear-constraint-audit]",
      "after": "derived = [[constraint, objective, direction, ALLrows, best, ALLarg_indices]]",
      "relation": "implies",
      "rule_id": "R58_EXACT_source_interface_and_answer_ROLE",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依本題銀行的keys、domain或frame、operation與輸出角色。STR22/App20 tuple與legacy scalar不同；分數是否保/1按原契約，不能用共同外觀改題。",
        "en": "Follow THIS bank exact keys,domain/frame,operation and answer role.STR22/App20 tuples differ from legacy scalars;retain or omit/1 by the ORIGINAL contract,not a generic visual convention."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。",
          "en": "Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "Optimization ORIGINAL row0 constraint A times x := mul(2, 0)",
      "after": "Optimization ORIGINAL row0 constraint A times x = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row0 constraint A times x，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row0 constraint A times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2",
          "0"
        ],
        "output": "0",
        "label": "Optimization ORIGINAL row0 constraint A times x"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "Optimization ORIGINAL row0 constraint B times y := mul(1, 0)",
      "after": "Optimization ORIGINAL row0 constraint B times y = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row0 constraint B times y，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row0 constraint B times y with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1",
          "0"
        ],
        "output": "0",
        "label": "Optimization ORIGINAL row0 constraint B times y"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "Optimization ORIGINAL row0 constraint sum := sum(0, 0)",
      "after": "Optimization ORIGINAL row0 constraint sum = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row0 constraint sum，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row0 constraint sum with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "0",
          "0"
        ],
        "output": "0",
        "label": "Optimization ORIGINAL row0 constraint sum"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "Optimization ORIGINAL row0 objective u times x := mul(1, 0)",
      "after": "Optimization ORIGINAL row0 objective u times x = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row0 objective u times x，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row0 objective u times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1",
          "0"
        ],
        "output": "0",
        "label": "Optimization ORIGINAL row0 objective u times x"
      }
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "Optimization ORIGINAL row0 objective v times y := mul(2, 0)",
      "after": "Optimization ORIGINAL row0 objective v times y = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row0 objective v times y，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row0 objective v times y with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2",
          "0"
        ],
        "output": "0",
        "label": "Optimization ORIGINAL row0 objective v times y"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "Optimization ORIGINAL row0 objective sum := sum(0, 0)",
      "after": "Optimization ORIGINAL row0 objective sum = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row0 objective sum，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row0 objective sum with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "0",
          "0"
        ],
        "output": "0",
        "label": "Optimization ORIGINAL row0 objective sum"
      }
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "source roles = [0, [0, 0], [2, 1, 10], [1, 2]]",
      "after": "derived = [0, 10, [0, 0, 0, 是, 0]]",
      "relation": "implies",
      "rule_id": "Optimization_EACH_original_point_INCLUSIVE_constraint_AND_objective",
      "conditions": [],
      "explanation": {
        "zh-Hant": "同一原row計A*x+B*y<=c（含等號）及u*x+v*y，保原index與重複point。不能把semantic identity排序／去重拿來改原題答案。",
        "en": "At the SAME original row calculate A*x+B*y<=c INCLUSIVELY and u*x+v*y.Preserve original index and repeated points.Semantic-identity sorting/deduplication cannot change this raw question or its answer."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。",
          "en": "Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "Optimization ORIGINAL row1 constraint A times x := mul(2, 1)",
      "after": "Optimization ORIGINAL row1 constraint A times x = 2",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row1 constraint A times x，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row1 constraint A times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2",
          "1"
        ],
        "output": "2",
        "label": "Optimization ORIGINAL row1 constraint A times x"
      }
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "Optimization ORIGINAL row1 constraint B times y := mul(1, 3)",
      "after": "Optimization ORIGINAL row1 constraint B times y = 3",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row1 constraint B times y，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row1 constraint B times y with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1",
          "3"
        ],
        "output": "3",
        "label": "Optimization ORIGINAL row1 constraint B times y"
      }
    },
    {
      "id": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "Optimization ORIGINAL row1 constraint sum := sum(2, 3)",
      "after": "Optimization ORIGINAL row1 constraint sum = 5",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row1 constraint sum，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row1 constraint sum with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "2",
          "3"
        ],
        "output": "5",
        "label": "Optimization ORIGINAL row1 constraint sum"
      }
    },
    {
      "id": "S012",
      "uses": [
        "G001",
        "S011"
      ],
      "before": "Optimization ORIGINAL row1 objective u times x := mul(1, 1)",
      "after": "Optimization ORIGINAL row1 objective u times x = 1",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row1 objective u times x，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row1 objective u times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1",
          "1"
        ],
        "output": "1",
        "label": "Optimization ORIGINAL row1 objective u times x"
      }
    },
    {
      "id": "S013",
      "uses": [
        "G001",
        "S012"
      ],
      "before": "Optimization ORIGINAL row1 objective v times y := mul(2, 3)",
      "after": "Optimization ORIGINAL row1 objective v times y = 6",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row1 objective v times y，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row1 objective v times y with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2",
          "3"
        ],
        "output": "6",
        "label": "Optimization ORIGINAL row1 objective v times y"
      }
    },
    {
      "id": "S014",
      "uses": [
        "G001",
        "S013"
      ],
      "before": "Optimization ORIGINAL row1 objective sum := sum(1, 6)",
      "after": "Optimization ORIGINAL row1 objective sum = 7",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row1 objective sum，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row1 objective sum with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "1",
          "6"
        ],
        "output": "7",
        "label": "Optimization ORIGINAL row1 objective sum"
      }
    },
    {
      "id": "S015",
      "uses": [
        "G001",
        "S014"
      ],
      "before": "source roles = [1, [1, 3], [2, 1, 10], [1, 2]]",
      "after": "derived = [5, 10, [1, 1, 3, 是, 7]]",
      "relation": "implies",
      "rule_id": "Optimization_EACH_original_point_INCLUSIVE_constraint_AND_objective",
      "conditions": [],
      "explanation": {
        "zh-Hant": "同一原row計A*x+B*y<=c（含等號）及u*x+v*y，保原index與重複point。不能把semantic identity排序／去重拿來改原題答案。",
        "en": "At the SAME original row calculate A*x+B*y<=c INCLUSIVELY and u*x+v*y.Preserve original index and repeated points.Semantic-identity sorting/deduplication cannot change this raw question or its answer."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。",
          "en": "Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S016",
      "uses": [
        "G001",
        "S015"
      ],
      "before": "Optimization ORIGINAL row2 constraint A times x := mul(2, 2)",
      "after": "Optimization ORIGINAL row2 constraint A times x = 4",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row2 constraint A times x，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row2 constraint A times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2",
          "2"
        ],
        "output": "4",
        "label": "Optimization ORIGINAL row2 constraint A times x"
      }
    },
    {
      "id": "S017",
      "uses": [
        "G001",
        "S016"
      ],
      "before": "Optimization ORIGINAL row2 constraint B times y := mul(1, 5)",
      "after": "Optimization ORIGINAL row2 constraint B times y = 5",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row2 constraint B times y，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row2 constraint B times y with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1",
          "5"
        ],
        "output": "5",
        "label": "Optimization ORIGINAL row2 constraint B times y"
      }
    },
    {
      "id": "S018",
      "uses": [
        "G001",
        "S017"
      ],
      "before": "Optimization ORIGINAL row2 constraint sum := sum(4, 5)",
      "after": "Optimization ORIGINAL row2 constraint sum = 9",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row2 constraint sum，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row2 constraint sum with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "4",
          "5"
        ],
        "output": "9",
        "label": "Optimization ORIGINAL row2 constraint sum"
      }
    },
    {
      "id": "S019",
      "uses": [
        "G001",
        "S018"
      ],
      "before": "Optimization ORIGINAL row2 objective u times x := mul(1, 2)",
      "after": "Optimization ORIGINAL row2 objective u times x = 2",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row2 objective u times x，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row2 objective u times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1",
          "2"
        ],
        "output": "2",
        "label": "Optimization ORIGINAL row2 objective u times x"
      }
    },
    {
      "id": "S020",
      "uses": [
        "G001",
        "S019"
      ],
      "before": "Optimization ORIGINAL row2 objective v times y := mul(2, 5)",
      "after": "Optimization ORIGINAL row2 objective v times y = 10",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row2 objective v times y，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row2 objective v times y with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2",
          "5"
        ],
        "output": "10",
        "label": "Optimization ORIGINAL row2 objective v times y"
      }
    },
    {
      "id": "S021",
      "uses": [
        "G001",
        "S020"
      ],
      "before": "Optimization ORIGINAL row2 objective sum := sum(2, 10)",
      "after": "Optimization ORIGINAL row2 objective sum = 12",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row2 objective sum，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row2 objective sum with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "2",
          "10"
        ],
        "output": "12",
        "label": "Optimization ORIGINAL row2 objective sum"
      }
    },
    {
      "id": "S022",
      "uses": [
        "G001",
        "S021"
      ],
      "before": "source roles = [2, [2, 5], [2, 1, 10], [1, 2]]",
      "after": "derived = [9, 10, [2, 2, 5, 是, 12]]",
      "relation": "implies",
      "rule_id": "Optimization_EACH_original_point_INCLUSIVE_constraint_AND_objective",
      "conditions": [],
      "explanation": {
        "zh-Hant": "同一原row計A*x+B*y<=c（含等號）及u*x+v*y，保原index與重複point。不能把semantic identity排序／去重拿來改原題答案。",
        "en": "At the SAME original row calculate A*x+B*y<=c INCLUSIVELY and u*x+v*y.Preserve original index and repeated points.Semantic-identity sorting/deduplication cannot change this raw question or its answer."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。",
          "en": "Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S023",
      "uses": [
        "G001",
        "S022"
      ],
      "before": "Optimization ORIGINAL row3 constraint A times x := mul(2, 3)",
      "after": "Optimization ORIGINAL row3 constraint A times x = 6",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row3 constraint A times x，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row3 constraint A times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2",
          "3"
        ],
        "output": "6",
        "label": "Optimization ORIGINAL row3 constraint A times x"
      }
    },
    {
      "id": "S024",
      "uses": [
        "G001",
        "S023"
      ],
      "before": "Optimization ORIGINAL row3 constraint B times y := mul(1, 1)",
      "after": "Optimization ORIGINAL row3 constraint B times y = 1",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row3 constraint B times y，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row3 constraint B times y with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1",
          "1"
        ],
        "output": "1",
        "label": "Optimization ORIGINAL row3 constraint B times y"
      }
    },
    {
      "id": "S025",
      "uses": [
        "G001",
        "S024"
      ],
      "before": "Optimization ORIGINAL row3 constraint sum := sum(6, 1)",
      "after": "Optimization ORIGINAL row3 constraint sum = 7",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row3 constraint sum，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row3 constraint sum with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "6",
          "1"
        ],
        "output": "7",
        "label": "Optimization ORIGINAL row3 constraint sum"
      }
    },
    {
      "id": "S026",
      "uses": [
        "G001",
        "S025"
      ],
      "before": "Optimization ORIGINAL row3 objective u times x := mul(1, 3)",
      "after": "Optimization ORIGINAL row3 objective u times x = 3",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row3 objective u times x，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row3 objective u times x with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1",
          "3"
        ],
        "output": "3",
        "label": "Optimization ORIGINAL row3 objective u times x"
      }
    },
    {
      "id": "S027",
      "uses": [
        "G001",
        "S026"
      ],
      "before": "Optimization ORIGINAL row3 objective v times y := mul(2, 1)",
      "after": "Optimization ORIGINAL row3 objective v times y = 2",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row3 objective v times y，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row3 objective v times y with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2",
          "1"
        ],
        "output": "2",
        "label": "Optimization ORIGINAL row3 objective v times y"
      }
    },
    {
      "id": "S028",
      "uses": [
        "G001",
        "S027"
      ],
      "before": "Optimization ORIGINAL row3 objective sum := sum(3, 2)",
      "after": "Optimization ORIGINAL row3 objective sum = 5",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確代值並保原操作數；額外教學運算不重套raw輸入界，只有明定的來源rational operation驗自己的profile。",
        "en": "Substitute exact ORIGINAL operands.Additional teaching algebra does not inherit raw-input caps;only declared SOURCE rational operations apply their own profile."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Optimization ORIGINAL row3 objective sum，不以小數近似替代。",
          "en": "Recompute Optimization ORIGINAL row3 objective sum with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "3",
          "2"
        ],
        "output": "5",
        "label": "Optimization ORIGINAL row3 objective sum"
      }
    },
    {
      "id": "S029",
      "uses": [
        "G001",
        "S028"
      ],
      "before": "source roles = [3, [3, 1], [2, 1, 10], [1, 2]]",
      "after": "derived = [7, 10, [3, 3, 1, 是, 5]]",
      "relation": "implies",
      "rule_id": "Optimization_EACH_original_point_INCLUSIVE_constraint_AND_objective",
      "conditions": [],
      "explanation": {
        "zh-Hant": "同一原row計A*x+B*y<=c（含等號）及u*x+v*y，保原index與重複point。不能把semantic identity排序／去重拿來改原題答案。",
        "en": "At the SAME original row calculate A*x+B*y<=c INCLUSIVELY and u*x+v*y.Preserve original index and repeated points.Semantic-identity sorting/deduplication cannot change this raw question or its answer."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。",
          "en": "Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S030",
      "uses": [
        "G001",
        "S029"
      ],
      "before": "source roles = [linear finite candidate list, [0, 7, 12, 5], [0, 1, 2, 3], min]",
      "after": "derived = [0, [0], [[0, 0, 是, 是], [1, 7, 是, 否], [2, 12, 是, 否], [3, 5, 是, 否]]]",
      "relation": "implies",
      "rule_id": "Optimization_ALL_feasible_objectives_bound_AND_every_tied_index",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部feasible原index核對best給相應上下界，且列出所有等號indices；最優value與arg集合不同，不選infeasible較佳值，不假設unique。結論僅限這個完整宣告有限集。",
        "en": "Check the corresponding bound for EVERY feasible ORIGINAL index and retain ALL equality indices.The optimal value differs from its arg set.Ignore better infeasible values and do not assume uniqueness.The conclusion is ONLY for this complete declared finite set."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。",
          "en": "Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S031",
      "uses": [
        "G001",
        "S030"
      ],
      "before": "source roles = [[[0, 0], [1, 3], [2, 5], [3, 1]], [2, 1, 10], [1, 2], min]",
      "after": "derived = [[[0, 0, 0, 是, 0], [1, 1, 3, 是, 7], [2, 2, 5, 是, 12], [3, 3, 1, 是, 5]], 0, [0]]",
      "relation": "implies",
      "rule_id": "Optimization_FINITE_list_not_continuous_halfplane",
      "conditions": [],
      "explanation": {
        "zh-Hant": "所有rows已算，但只對符合constraint的原候選最佳化；沒有宣告整個半平面全體點，不把有限best當連續問題的全域解。",
        "en": "All rows are evaluated,but optimize ONLY eligible ORIGINAL listed candidates.The whole half-plane was not declared as the candidate set;the finite best is not a continuous-domain global solution."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。",
          "en": "Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": [
      [
        2,
        1,
        10
      ],
      [
        1,
        2
      ],
      "min",
      [
        [
          0,
          0,
          0,
          true,
          0
        ],
        [
          1,
          1,
          3,
          true,
          7
        ],
        [
          2,
          2,
          5,
          true,
          12
        ],
        [
          3,
          3,
          1,
          true,
          5
        ]
      ],
      0,
      [
        0
      ]
    ]
  },
  "conclusion": {
    "canonical_value": "([2, 1, 10], [1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 3, 是, 7], [2, 2, 5, 是, 12], [3, 3, 1, 是, 5]], 0, [0])",
    "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-20261020-r04-optimization-problem-foundations",
      "batch_path": "public/data/questions/batches/batch-20261013-advance-20261020-r04-optimization-problem-foundations/questions.jsonl",
      "batch_sha256": "81535eb6e80198569e54d036aa76bc021ca6a29840d6f677dc163c2c3367a326",
      "original_line": 89,
      "original_line_sha256": "725dd8055c4d14609047b20f2b800c6e8f9bf6085ec53c9bf9787ecbd3473269",
      "question_compact_sha256": "3780ab8ce270a589bb22dd888a7bd40d5130ffb5944a705d5ed9fffc60c9fb6d",
      "english_row_compact_sha256": "e4fef9faedfcc08386a4caabc305d5d65ef47b4d1566e60806b230be50e21ed4",
      "english_manifest_path": "public/data/i18n/editions/batch-20261013-advance-20261020-r04-optimization-problem-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261013-advance-20261020-r04-optimization-problem-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-optimization-problem": {
        "sha256": "55c8accf83a0b3a16cb86f438bdc6575f8dcec45e670f324e863e79a1a233514",
        "english_sha256": "b6379fa21189b83b931814f4a2acdc266e8f73e8fa2fad6e9d2190456191279e",
        "original_path": "public/data/mko/optimization-problem.json",
        "english_path": "public/data/i18n/editions/mko-optimization-problem.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "623c23f45586b08629c5a347ffbc994cf8dbff2133c4f4cdb227b851d74ea6b6",
    "original_candidate_sha256": "9507d685661f2af4fcbfd63e675e2a3948358e8747e240d4ac765d1c790499ce",
    "original_candidate_line_sha256": "9507d685661f2af4fcbfd63e675e2a3948358e8747e240d4ac765d1c790499ce"
  },
  "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-20261026-011-p59",
    "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": "66bbb31c5fe644576dfd47ac71ca9e367fc23b948eac8e3eb648d96dadea05df",
      "question_first_witness_sha256": "b1e4fbdbca8d0ac3581e2f26466374d870f3c8498fab7cf6873feca5bbec44e7"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 31,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "31986043ead2cceeb1714539530810beae2f032e2129e8f583f7cb4689330c62",
      "arithmetic_steps": 24
    },
    "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."
  }
}