{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260919-signed-context-integer-0010",
  "pilot_number": "R0069-35185",
  "number": 35185,
  "family_id": "qf-signed-context-integer",
  "title": {
    "zh-Hant": "第 35185 題：qf-signed-context-integer",
    "en": "Question 35185: Integer in a Signed Context"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260919-signed-context-integer-0010",
    "batch_id": "batch-20260919-integer-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-integer"
    ],
    "title_zh": "qf-signed-context-integer",
    "stem_zh": "零點為入口，向上為正方向，單位為層。位置 -9 代表相對零點的哪個整數位移？",
    "answer": {
      "kind": "numeric",
      "value": -9,
      "explanation_zh": "零點與正方向已明示，-9層 直接表示帶符號位移；沒有加入單位換算。"
    },
    "difficulty": {
      "band": "upper_secondary",
      "level": 2,
      "skills": [
        "帶符號情境"
      ]
    },
    "variant": {
      "family_id": "qf-signed-context-integer",
      "seed": 20261229,
      "parameters": {
        "zero": "入口",
        "positive_direction": "向上",
        "unit": "層",
        "value": -9,
        "semantic_template": "qf-signed-context-integer/{\"positive_direction\":\"向上\",\"unit\":\"層\",\"value\":-9,\"zero\":\"入口\"}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "schema_pending",
        "independent_recomputation_pending"
      ],
      "warning_zh": "本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "GPT-5.6 Terra",
      "generated_at": "2026-09-19",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20260919-signed-context-integer-0010",
    "batch_id": "batch-20260919-integer-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "3b94b7e31ce1f8ee3932b376efc57212c00ee0399abf4b36ceed3cf903b0fc1d",
      "family_id": "qf-signed-context-integer",
      "seed": 20261229,
      "semantic_template": "qf-signed-context-integer/{\"positive_direction\":\"向上\",\"unit\":\"層\",\"value\":-9,\"zero\":\"入口\"}"
    },
    "fields": {
      "title": "Integer in a Signed Context",
      "stem": "The zero point is the entrance, the positive direction is upward, and the unit is floors. What signed integer displacement from zero is represented by position -9?",
      "answer": {
        "kind": "numeric",
        "value": -9,
        "explanation": "The zero point and positive direction are explicit, so -9 floors directly represents the signed displacement. No unit conversion is introduced."
      },
      "skills": [
        "signed contexts"
      ],
      "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": "零點為入口，向上為正方向，單位為層。位置 -9 代表相對零點的哪個整數位移？",
        "en": "The zero point is the entrance, the positive direction is upward, and the unit is floors. What signed integer displacement from zero is represented by position -9?"
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-signed-context-integer, [positive_direction, unit, value, zero]]",
      "after": "derived = [BASE-no-required-operation, no-invented-domain]",
      "relation": "implies",
      "rule_id": "R69_SOURCE_specific_keys_operation_domain_AND_binary_contract",
      "conditions": [],
      "explanation": {
        "zh-Hant": "各bank的keys/operation/domain獨立：LDL/PULSE/function legacy為表內underscore，TREE是完整tree_*與明定domain，BASE signed較寬不偷加op/domain。所有算術保持binary primitive契約。",
        "en": "Keep EACH bank’s keys/operation/domain distinct:LDL/PULSE/function legacy table underscores,TREE full tree_* with its declared domain,and permissive BASE signed without invented op/domain.All arithmetic respects the binary-primitive contract."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "source roles = [-9, zero/direction/unit are GIVEN in G001]",
      "after": "derived = [-1, 9, opposite_declared_positive_direction]",
      "relation": "implies",
      "rule_id": "Signed_GIVEN_frame_and_position_not_an_inferred_measurement",
      "conditions": [],
      "explanation": {
        "zh-Hant": "已給零點/正方向/單位與位置value；0在零點，正值沿指定正向，負值沿其反向，abs(value)為距離大小。本25題中英frame已逐份核對，不另作量測或單位換算。",
        "en": "The zero point,positive direction,unit and position value are GIVEN in G001.Zero is at the origin;positive is along the declared direction,negative opposite,and abs(value)is magnitude.The25 ACTUAL bilingual frames were checked;do not invent a measurement or unit conversion."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "Signed ORIGINAL sign times displacement magnitude := mul(-1, 9)",
      "after": "Signed ORIGINAL sign times displacement magnitude = -9",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "精確使用原操作數；乘/減/除每步明示兩項，避免舊binary primitive忽略第三項。raw SAFE與無界BigInt衍生量分開，不以浮點近似湊答案。",
        "en": "Use ORIGINAL operands exactly;mul/sub/div have EXPLICITLY TWO operands so the old binary primitive cannot ignore a third.Keep RAW SAFE bounds separate from unbounded derived BigInts;do not approximate to force answers."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Signed ORIGINAL sign times displacement magnitude，不以小數近似替代。",
          "en": "Recompute Signed ORIGINAL sign times displacement magnitude with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "-1",
          "9"
        ],
        "output": "-9",
        "label": "Signed ORIGINAL sign times displacement magnitude"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "source roles = [-1, 9]",
      "after": "derived = [-9]",
      "relation": "implies",
      "rule_id": "Signed_RECONSTRUCT_integer_value_from_sign_and_magnitude",
      "conditions": [],
      "explanation": {
        "zh-Hant": "sign*大小重建原帶號整數位移，不把負位移誤改為正距離，也不取倒數。數字是題給位置，不由文字旗標猜答案。",
        "en": "Reconstruct the ORIGINAL signed displacement as sign*magnitude.Do not replace a negative displacement by a positive distance or reciprocal.The position is GIVEN,not guessed from a metadata flag."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": -9
  },
  "conclusion": {
    "canonical_value": "-9",
    "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-20260919-integer-foundations",
      "batch_path": "public/data/questions/batches/batch-20260919-integer-foundations/questions.jsonl",
      "batch_sha256": "529bee0e669d336089b9b84409bed458d54dfcb02b3696e430887c1ed49bb6c4",
      "original_line": 85,
      "original_line_sha256": "01843141cd17b58fa564901e234a00a141e51aed516a1e0241d43de52922e0ca",
      "question_compact_sha256": "3b94b7e31ce1f8ee3932b376efc57212c00ee0399abf4b36ceed3cf903b0fc1d",
      "english_row_compact_sha256": "73ff39a86e84b548ae662727c3554b263e0b509f8f407d3b2ec4de8d37fe7732",
      "english_manifest_path": "public/data/i18n/editions/batch-20260919-integer-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20260919-integer-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-integer": {
        "sha256": "e1e3776eaf56e003f2eb07a66a39c7e221d26759df8fbc4db2652a2733318d66",
        "english_sha256": "24d4c8918b430c9dea2f942bb60a89a295d2386bf3bd9c14731ad56e0fb49034",
        "original_path": "public/data/mko/integer.json",
        "english_path": "public/data/i18n/editions/mko-integer.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "63155b87d4994521b4a60f8f179750f57cbbd094e66cc42652608d1bbab47a9f",
    "original_candidate_sha256": "1ccc1ac11491b4057238ef71f4a61e818e3e1791c2f9243e75602035a0317168",
    "original_candidate_line_sha256": "1ccc1ac11491b4057238ef71f4a61e818e3e1791c2f9243e75602035a0317168"
  },
  "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-p70",
    "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": "ccf93c72638d6abf6a412514da5838d55ecb09b71d0e4fdec2b559dc9fdee14b",
      "question_first_witness_sha256": "11af9a338b5a610342b2cfb2ee295683131b3139ac402dd19b1ba1725976d518"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 4,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "fe0c5d6517bcca2d32288b43c9186aab6e34eb76d1f3e74de93e09c535775309",
      "arithmetic_steps": 1
    },
    "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."
  }
}