{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261009-advance-20261013-r02-integer-0069",
  "pilot_number": "R0011-06144",
  "number": 6144,
  "family_id": "qf-density13-integer-opposite-difference",
  "title": {
    "zh-Hant": "第 6144 題：相反數與兩個方向的差",
    "en": "Question 6144: Ordered Opposites and Two Difference Directions"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261009-advance-20261013-r02-integer-0069",
    "batch_id": "batch-20261009-advance-20261013-r02-integer-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-integer"
    ],
    "title_zh": "相反數與兩個方向的差",
    "stem_zh": "有限整數協議；a=6、b=-17。依序求 (−a, −b, a−b, b−a)，保留方向與符號。",
    "answer": {
      "kind": "expression",
      "value": "(-6, 17, 23, -23)",
      "explanation_zh": "相反數與雙向差=(-6, 17, 23, -23)。相反數逐項換號，差按指定方向計算；有限運算非整數環公理證明。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 3,
      "skills": [
        "相反數與兩個方向的差"
      ]
    },
    "variant": {
      "family_id": "qf-density13-integer-opposite-difference",
      "seed": 202610132069,
      "parameters": {
        "a": 6,
        "b": -17,
        "operation": "density13_integer_opposite_difference",
        "domain": "finite_integer_arithmetic_protocol",
        "semantic_template": "qf-density13-integer-opposite-difference/[6,-17]"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_integer_rational_arithmetic",
        "producer_finite_enumeration",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication",
        "producer_json_schema"
      ],
      "warning_zh": "僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "model_unknown",
      "generated_at": "2026-10-09",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261009-advance-20261013-r02-integer-0069",
    "batch_id": "batch-20261009-advance-20261013-r02-integer-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "b46120c837a25088628a34de941c34bdf033b83a655c90232eaabe3af002de7a",
      "family_id": "qf-density13-integer-opposite-difference",
      "seed": 202610132069,
      "semantic_template": "qf-density13-integer-opposite-difference/[6,-17]"
    },
    "fields": {
      "title": "Ordered Opposites and Two Difference Directions",
      "stem": "Integers a=6, b=-17. Give (−a, −b, a−b, b−a), retaining signs and direction.",
      "answer": {
        "kind": "expression",
        "value": "(-6, 17, 23, -23)",
        "explanation": "Negate each operand separately and subtract in the requested order; this finite computation does not prove all integer algebra laws. The exact result, retaining the requested order, is (-6, 17, 23, -23)."
      },
      "skills": [
        "Ordered Opposites and Two Difference Directions"
      ],
      "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": "有限整數協議；a=6、b=-17。依序求 (−a, −b, a−b, b−a)，保留方向與符號。",
        "en": "Integers a=6, b=-17. Give (−a, −b, a−b, b−a), retaining signs and direction."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "declared exact integer or rational-representation protocol",
      "after": "retain signs,ordered operands and original index order",
      "relation": "implies",
      "rule_id": "integer_arithmetic_scope",
      "conditions": [],
      "explanation": {
        "zh-Hant": "用精確整數運算核對此有限資料，不取浮點近似，也不把有限計算升為全部整數環公理證明。",
        "en": "Check these finite data with exact integer arithmetic,without floating approximations or a claim to prove all integer-ring axioms."
      },
      "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": "opposite of a := mul(-1, 6)",
      "after": "opposite of a = -6",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "相反數乘−1，0仍為0。",
        "en": "Multiply by−1 for the additive opposite;0 stays0."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 opposite of a，不以小數近似替代。",
          "en": "Recompute opposite of a with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "-1",
          "6"
        ],
        "output": "-6",
        "label": "opposite of a"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "opposite of b := mul(-1, -17)",
      "after": "opposite of b = 17",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "對b獨立換號，不改原始b。",
        "en": "Negate b separately without changing its original value."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 opposite of b，不以小數近似替代。",
          "en": "Recompute opposite of b with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "-1",
          "-17"
        ],
        "output": "17",
        "label": "opposite of b"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "a minus b := sub(6, -17)",
      "after": "a minus b = 23",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按a−b順序計算有號差。",
        "en": "Compute the signed difference in the order a−b."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 a minus b，不以小數近似替代。",
          "en": "Recompute a minus b with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "6",
          "-17"
        ],
        "output": "23",
        "label": "a minus b"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "b minus a := sub(-17, 6)",
      "after": "b minus a = -23",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "反方向差須另算，等於前差的相反數。",
        "en": "Compute the reverse difference separately;it is the opposite of the first."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 b minus a，不以小數近似替代。",
          "en": "Recompute b minus a with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "-17",
          "6"
        ],
        "output": "-23",
        "label": "b minus a"
      }
    }
  ],
  "math_model": {
    "result": [
      "-6",
      "17",
      "23",
      "-23"
    ]
  },
  "conclusion": {
    "canonical_value": "(-6, 17, 23, -23)",
    "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": {
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    "question_binding": {
      "batch_id": "batch-20261009-advance-20261013-r02-integer-foundations",
      "batch_path": "public/data/questions/batches/batch-20261009-advance-20261013-r02-integer-foundations/questions.jsonl",
      "batch_sha256": "fe7ab53bd896704506979e7b4bde27359c6a58a2382c94c9e728ab4500a3982d",
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      "original_line_sha256": "1bde9bad5984e3521ebb28e730e3ffbf3c7aadca6e95945dc18d109bc7cde89c",
      "question_compact_sha256": "b46120c837a25088628a34de941c34bdf033b83a655c90232eaabe3af002de7a",
      "english_row_compact_sha256": "8e47c304783788367b31f2e59e1a84fc377604102d0639851e162d8063babced",
      "english_manifest_path": "public/data/i18n/editions/batch-20261009-advance-20261013-r02-integer-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261009-advance-20261013-r02-integer-foundations.en.jsonl"
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        "original_path": "public/data/mko/integer.json",
        "english_path": "public/data/i18n/editions/mko-integer.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "5b2ce631281eb24b279908f47c6de66fa60d326520852879d324c4f3ac653970",
    "original_candidate_sha256": "da0370261bf810180bf3b20a45cee153711a0cf66b3ae67c73513d63c0d46b3f",
    "original_candidate_line_sha256": "da0370261bf810180bf3b20a45cee153711a0cf66b3ae67c73513d63c0d46b3f"
  },
  "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-20261026-005-p12",
    "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": {
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      "question_first_witness_sha256": "93f720df3ab3af13a792a3e6b443728e3c2a56276df839911f36569333236c55"
    },
    "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": {
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    "formalization": "not_formalized",
    "Lean": "NOT_RUN",
    "Canonical_truth_promotion": false,
    "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged."
  }
}