{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260928-absolute-value-distance-0013",
  "pilot_number": "R0001-01063",
  "number": 1063,
  "family_id": "qf-absolute-value-distance",
  "title": {
    "zh-Hant": "第 1063 題：數線上的兩點距離",
    "en": "Question 1063: Distance on the Real Number Line"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260928-absolute-value-distance-0013",
    "batch_id": "batch-20260928-absolute-value-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-absolute-value"
    ],
    "title_zh": "數線上的兩點距離",
    "stem_zh": "實數線上兩點 a=0、b=7。用 |a-b| 精確計算兩點距離。",
    "answer": {
      "kind": "short_text",
      "value": "7",
      "explanation_zh": "|a-b|=|0-(7)|=|-7|=7；交換端點得到 |b-a| 仍為 7。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 2,
      "skills": [
        "數線距離",
        "差的絕對值"
      ]
    },
    "variant": {
      "family_id": "qf-absolute-value-distance",
      "seed": 20261141,
      "parameters": {
        "a": 0,
        "b": 7,
        "domain": "reals",
        "operation": "number_line_distance",
        "semantic_template": "qf-absolute-value-distance/{\"a\":0,\"b\":7,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "json_schema",
        "independent_answer_recomputation"
      ],
      "warning_zh": "本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "Codex GPT-5 (single-context degraded run)",
      "generated_at": "2026-09-28",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20260928-absolute-value-distance-0013",
    "batch_id": "batch-20260928-absolute-value-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "665d51ac2ec92740daa403ab5c445214759a0f2a055f825041baf87f36991e43",
      "family_id": "qf-absolute-value-distance",
      "seed": 20261141,
      "semantic_template": "qf-absolute-value-distance/{\"a\":0,\"b\":7,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"
    },
    "fields": {
      "title": "Distance on the Real Number Line",
      "stem": "On the real number line, a=0 and b=7. Compute the distance |a-b| exactly.",
      "answer": {
        "kind": "short_text",
        "value": "7",
        "explanation": "|a-b|=|0-(7)|=|-7|=7; exchanging the endpoints gives the same distance."
      },
      "skills": [
        "number-line distance",
        "absolute value of a difference"
      ],
      "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": "實數線上兩點 a=0、b=7。用 |a-b| 精確計算兩點距離。",
        "en": "On the real number line, a=0 and b=7. Compute the distance |a-b| exactly."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "x∈R",
      "after": "|x|=x if x≥0; |x|=−x if x<0",
      "relation": "implies",
      "rule_id": "absolute_definition",
      "conditions": [],
      "explanation": {
        "zh-Hant": "兩個符號分支覆蓋全部實數，且0歸非負分支。",
        "en": "The sign branches cover every real number, with0 in the nonnegative branch."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "確認使用≥0而不是>0，不能把0遺漏。",
          "en": "Use ≥0 rather than >0 so that0 is not omitted."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "a−b := sub(0, 7)",
      "after": "a−b = -7",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先計算帶符號的兩點差，不把它直接當距離。",
        "en": "Compute the signed difference first, not the distance itself."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 a−b，不以小數近似替代。",
          "en": "Recompute a−b with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "0",
          "7"
        ],
        "output": "-7",
        "label": "a−b"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "a−b=-7",
      "after": "distance=|a−b|=7",
      "relation": "implies",
      "rule_id": "number_line_metric",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依差的符號套用絕對值分支，所得距離必非負。",
        "en": "Use the sign branch for the difference; the resulting distance is nonnegative."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "b−a := sub(7, 0)",
      "after": "b−a = 7",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "交換點次序會反轉差的符號。",
        "en": "Swapping the points reverses the difference's sign."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 b−a，不以小數近似替代。",
          "en": "Recompute b−a with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "7",
          "0"
        ],
        "output": "7",
        "label": "b−a"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "|a−b|=7; |b−a|=7",
      "after": "swapping endpoints preserves distance",
      "relation": "implies",
      "rule_id": "distance_symmetry",
      "conditions": [],
      "explanation": {
        "zh-Hant": "兩點次序不同但絕對值相同，完成反向核對。",
        "en": "Endpoint order changes but the absolute values agree, completing the reverse audit."
      },
      "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": {
    "difference": "-7",
    "distance": "7"
  },
  "conclusion": {
    "canonical_value": "7",
    "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-20260928-absolute-value-foundations",
      "batch_path": "public/data/questions/batches/batch-20260928-absolute-value-foundations/questions.jsonl",
      "batch_sha256": "49b8ee3d45e2794c0becbb27af857e4727b0e8bb396a02f7a2366076a4788da8",
      "original_line": 63,
      "original_line_sha256": "688bc47678112538b38499d7e9e3b7f8a8a2398e673c2413cd954dfa4cf96116",
      "question_compact_sha256": "665d51ac2ec92740daa403ab5c445214759a0f2a055f825041baf87f36991e43",
      "english_row_compact_sha256": "50d43d6664b551e688bbcc09a2b313c589af6c0e3018042109e09868de347642",
      "english_manifest_path": "public/data/i18n/editions/batch-20260928-absolute-value-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20260928-absolute-value-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-absolute-value": {
        "sha256": "7df0aed9ca41a0e67b84a464f450422348753d1171802220b41a103488fb5f95",
        "english_sha256": "7f191b7dbbd24ac7ec2a252a08d3178f961ef31414f76098c51f5f01d63473f6",
        "original_path": "public/data/mko/absolute-value.json",
        "english_path": "public/data/i18n/editions/mko-absolute-value.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "b9fe70a7a264c90c20349be0449b2bd1a1b4d0e0a97092bc9fbcb7ca36ce0694",
    "original_candidate_sha256": "ee8ec40a3d2a734c0e8e779adbef6713b3dc0f374f8abcb2b9eb937993af766d",
    "original_candidate_line_sha256": "ee8ec40a3d2a734c0e8e779adbef6713b3dc0f374f8abcb2b9eb937993af766d"
  },
  "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-20261026-004-p2",
    "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": "c3b44ce8ed60ada6902fb206627537d5f90ba2a867eaba43a36f903280c496cc",
      "question_first_witness_sha256": "3e91602adc7f81a2671a2a3ffaf6a447028b56abc5853e8271673d76f30cd7ad"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 5,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "1197371b97601b7ba6de00762daf02eccf21e55d80ff30592bdb7569fe7061b0",
      "arithmetic_steps": 2
    },
    "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."
  }
}