{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260912-distance-coordinate-0030",
  "pilot_number": "R0070-35545",
  "number": 35545,
  "family_id": "qf-distance-coordinate",
  "title": {
    "zh-Hant": "第 35545 題：座標平面距離計算",
    "en": "Question 35545: Coordinate-Plane Distance"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260912-distance-coordinate-0030",
    "batch_id": "batch-20260912-geometry-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-euclidean-length"
    ],
    "title_zh": "座標平面距離計算",
    "stem_zh": "在歐幾里得平面上，點 P=(-8, -25) 與 Q=(-74, 87)。求距離 d(P,Q)。",
    "answer": {
      "kind": "numeric",
      "value": 130,
      "explanation_zh": "座標差為 (-66, 112)，所以 d=√((-66)²+112²)=130。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 3,
      "skills": [
        "座標差",
        "距離公式"
      ]
    },
    "variant": {
      "family_id": "qf-distance-coordinate",
      "seed": 20260941,
      "parameters": {
        "p": [
          -8,
          -25
        ],
        "q": [
          -74,
          87
        ],
        "expected_distance": 130
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "schema_pending",
        "independent_recomputation_pending"
      ],
      "warning_zh": "本題僅對列出的有限參數重算；不構成相關定義或定理的普遍證明，且尚未人工審查。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "GPT-5.6 Terra",
      "generated_at": "2026-09-12",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20260912-distance-coordinate-0030",
    "batch_id": "batch-20260912-geometry-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "07c0416627cbc34bc595ae6911139695a17bade3aec3dc3a88404c03cc9646bb",
      "family_id": "qf-distance-coordinate",
      "seed": 20260941,
      "semantic_template": "qf-distance-coordinate/20260941"
    },
    "fields": {
      "title": "Coordinate-Plane Distance",
      "stem": "In the Euclidean plane, P=(-8, -25) and Q=(-74, 87). Find the distance d(P,Q).",
      "answer": {
        "kind": "numeric",
        "value": 130,
        "explanation": "The coordinate difference is (-66, 112), so d=√((-66)²+(112)²)=130."
      },
      "skills": [
        "coordinate differences",
        "distance formula"
      ],
      "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": "在歐幾里得平面上，點 P=(-8, -25) 與 Q=(-74, 87)。求距離 d(P,Q)。",
        "en": "In the Euclidean plane, P=(-8, -25) and Q=(-74, 87). Find the distance d(P,Q)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-distance-coordinate, [expected_distance, p, q]]",
      "after": "derived = [distance, null, null]",
      "relation": "implies",
      "rule_id": "R70_SOURCE_bank_specific_interface",
      "conditions": [],
      "explanation": {
        "zh-Hant": "只使用此bank真正明示的欄位、operation/domain與型別；BASE容許保留額外metadata，不把LDL SAFE/集合上限或其他bank的去重規則搬來。",
        "en": "Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。",
          "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "source roles = [[-8, -25], [-74, 87]]",
      "after": "derived = [orthonormal common coordinate frame]",
      "relation": "implies",
      "rule_id": "Distance_GIVEN_same_Euclidean_frame_integral_last5",
      "conditions": [],
      "explanation": {
        "zh-Hant": "這五題的給定座標皆為整數且在同一歐氏座標架構；距離不是座標差的和或Manhattan距離，expected_distance只是不用的metadata。",
        "en": "These LAST FIVE questions give integral coordinates in ONE Euclidean frame.Distance is neither the sum of coordinate differences nor Manhattan distance;expected_distance metadata is NOT an oracle."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。",
          "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "Distance ORIGINAL coordinate difference i=0 := sub(-74, -8)",
      "after": "Distance ORIGINAL coordinate difference i=0 = -66",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "本步精確列出原操作數與運算；乘、減、除恰兩項。分數保持精確，衍生BigInt不重套raw SAFE，不用近似值湊答案。",
        "en": "This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Distance ORIGINAL coordinate difference i=0，不以小數近似替代。",
          "en": "Recompute Distance ORIGINAL coordinate difference i=0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "-74",
          "-8"
        ],
        "output": "-66",
        "label": "Distance ORIGINAL coordinate difference i=0"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "Distance square signed difference i=0 := mul(-66, -66)",
      "after": "Distance square signed difference i=0 = 4356",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "本步精確列出原操作數與運算；乘、減、除恰兩項。分數保持精確，衍生BigInt不重套raw SAFE，不用近似值湊答案。",
        "en": "This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Distance square signed difference i=0，不以小數近似替代。",
          "en": "Recompute Distance square signed difference i=0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "-66",
          "-66"
        ],
        "output": "4356",
        "label": "Distance square signed difference i=0"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "Distance ORIGINAL coordinate difference i=1 := sub(87, -25)",
      "after": "Distance ORIGINAL coordinate difference i=1 = 112",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "本步精確列出原操作數與運算；乘、減、除恰兩項。分數保持精確，衍生BigInt不重套raw SAFE，不用近似值湊答案。",
        "en": "This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Distance ORIGINAL coordinate difference i=1，不以小數近似替代。",
          "en": "Recompute Distance ORIGINAL coordinate difference i=1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "87",
          "-25"
        ],
        "output": "112",
        "label": "Distance ORIGINAL coordinate difference i=1"
      }
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "Distance square signed difference i=1 := mul(112, 112)",
      "after": "Distance square signed difference i=1 = 12544",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "本步精確列出原操作數與運算；乘、減、除恰兩項。分數保持精確，衍生BigInt不重套raw SAFE，不用近似值湊答案。",
        "en": "This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Distance square signed difference i=1，不以小數近似替代。",
          "en": "Recompute Distance square signed difference i=1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "112",
          "112"
        ],
        "output": "12544",
        "label": "Distance square signed difference i=1"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "Distance sum BOTH coordinate squares := sum(4356, 12544)",
      "after": "Distance sum BOTH coordinate squares = 16900",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "本步精確列出原操作數與運算；乘、減、除恰兩項。分數保持精確，衍生BigInt不重套raw SAFE，不用近似值湊答案。",
        "en": "This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Distance sum BOTH coordinate squares，不以小數近似替代。",
          "en": "Recompute Distance sum BOTH coordinate squares with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "4356",
          "12544"
        ],
        "output": "16900",
        "label": "Distance sum BOTH coordinate squares"
      }
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "Distance principal nonnegative root squared back := mul(130, 130)",
      "after": "Distance principal nonnegative root squared back = 16900",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "本步精確列出原操作數與運算；乘、減、除恰兩項。分數保持精確，衍生BigInt不重套raw SAFE，不用近似值湊答案。",
        "en": "This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Distance principal nonnegative root squared back，不以小數近似替代。",
          "en": "Recompute Distance principal nonnegative root squared back with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "130",
          "130"
        ],
        "output": "16900",
        "label": "Distance principal nonnegative root squared back"
      }
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "source roles = [[-66, 112], 16900]",
      "after": "derived = [130]",
      "relation": "implies",
      "rule_id": "Distance_PRINCIPAL_root_not_negative_or_approximate",
      "conditions": [],
      "explanation": {
        "zh-Hant": "d²為兩分量平方和，距離定義非負，故取已精確平方回驗的主平方根；不能選負根或用預期答案反推。",
        "en": "The sum of BOTH squared components is d².Distance is nonnegative,so choose the principal root and square it back EXACTLY.Neither a negative root nor expected-answer backsolving is allowed."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。",
          "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": 130
  },
  "conclusion": {
    "canonical_value": "130",
    "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-20260912-geometry-foundations",
      "batch_path": "public/data/questions/batches/batch-20260912-geometry-foundations/questions.jsonl",
      "batch_sha256": "818fc9bd154b15a97199c437c5345260e55307eada85586bf547e52c4ae518dc",
      "original_line": 30,
      "original_line_sha256": "2c29b31b51881fc472b20c6bbaa5ab593c1762187fe6378c28b4db12d452f847",
      "question_compact_sha256": "07c0416627cbc34bc595ae6911139695a17bade3aec3dc3a88404c03cc9646bb",
      "english_row_compact_sha256": "c33ae0b477f5419e66c4ec66ba4fe1a3568bc4c144a15a77426ed7db02f823a5",
      "english_manifest_path": "public/data/i18n/editions/batch-20260912-geometry-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20260912-geometry-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-euclidean-length": {
        "sha256": "485948172a6b39e7ec2cf3170ab03489fed98190d0c868161fbbd037f7151e91",
        "english_sha256": "b3ddf0a703643ec48198e001b53296e8991e8855e011f8b9ac9462cd47d53435",
        "original_path": "public/data/mko/euclidean-length.json",
        "english_path": "public/data/i18n/editions/mko-euclidean-length.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "20c37a7e64ee5969e7606c5cc3a00e575002ebebdfe82873521cc3d7c608caff",
    "original_candidate_sha256": "f9f768e936724f3f221899c97cde7fc5f700ab0617e7a73130af024d4ad6f740",
    "original_candidate_line_sha256": "f9f768e936724f3f221899c97cde7fc5f700ab0617e7a73130af024d4ad6f740"
  },
  "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-20261026-012-p71",
    "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": "9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80",
      "question_first_witness_sha256": "c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dab"
    },
    "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": "a2b2f468e262a289fca74b5e70ece5180d6c9673bf80d4344c71f19d941e56c1",
      "arithmetic_steps": 6
    },
    "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."
  }
}