{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261008-advance-20261012-r03-proposition-0079",
  "pilot_number": "R0010-05779",
  "number": 5779,
  "family_id": "qf-density12-proposition-report-defects",
  "title": {
    "zh-Hant": "第 5779 題：候選自報真假與實際核對",
    "en": "Question 5779: Candidate Truth Reports Checked Independently"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261008-advance-20261012-r03-proposition-0079",
    "batch_id": "batch-20261008-advance-20261012-r03-proposition-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-proposition"
    ],
    "title_zh": "候選自報真假與實際核對",
    "stem_zh": "古典整數語境；pairs=[[-9, 0], [-2, 2], [-1, 0]]，P_i為a_i≤b_i；候選自報reported=[1, 1, 0]，1自報真、0自報假。依序答 (實際真假, 自報是否匹配, 有號a_i−b_i)。",
    "answer": {
      "kind": "expression",
      "value": "([真, 真, 真], [是, 是, 否], [-9, -4, -1])",
      "explanation_zh": "候選自報與真假核對=([真, 真, 真], [是, 是, 否], [-9, -4, -1])。由整數比較另算真假再核各報告；候選自報非證據，真假不等於已有證明。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 1,
      "skills": [
        "候選自報真假與實際核對"
      ]
    },
    "variant": {
      "family_id": "qf-density12-proposition-report-defects",
      "seed": 202610123079,
      "parameters": {
        "pairs": [
          [
            -9,
            0
          ],
          [
            -2,
            2
          ],
          [
            -1,
            0
          ]
        ],
        "reported": [
          1,
          1,
          0
        ],
        "operation": "density12_proposition_report_defects",
        "domain": "closed_classical_integer_statements",
        "semantic_template": "qf-density12-proposition-report-defects/[[\"-9\",\"-4\",\"-1\"],[1,1,0]]"
      }
    },
    "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": "2026-10-08",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261008-advance-20261012-r03-proposition-0079",
    "batch_id": "batch-20261008-advance-20261012-r03-proposition-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "1aebad644b1f7336cc54e3d9e8432586554de44f037934e03aa1de7957a9d4e9",
      "family_id": "qf-density12-proposition-report-defects",
      "seed": 202610123079,
      "semantic_template": "qf-density12-proposition-report-defects/[[\"-9\",\"-4\",\"-1\"],[1,1,0]]"
    },
    "fields": {
      "title": "Candidate Truth Reports Checked Independently",
      "stem": "In a classical integer context, ordered pairs=[[-9, 0], [-2, 2], [-1, 0]]. P_i means a_i≤b_i. Candidate reported=[1, 1, 0], with 1 reporting True and 0 False. Give (actual truth values, report-match Yes/No values, signed a_i−b_i values).",
      "answer": {
        "kind": "expression",
        "value": "([True, True, True], [Yes, Yes, No], [-9, -4, -1])",
        "explanation": "Recompute comparisons before checking reports; a candidate self-report is not Evidence, and truth is not a formal proof receipt. The exact result, retaining the requested order, is ([True, True, True], [Yes, Yes, No], [-9, -4, -1])."
      },
      "skills": [
        "Candidate Truth Reports Checked Independently"
      ],
      "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": "古典整數語境；pairs=[[-9, 0], [-2, 2], [-1, 0]]，P_i為a_i≤b_i；候選自報reported=[1, 1, 0]，1自報真、0自報假。依序答 (實際真假, 自報是否匹配, 有號a_i−b_i)。",
        "en": "In a classical integer context, ordered pairs=[[-9, 0], [-2, 2], [-1, 0]]. P_i means a_i≤b_i. Candidate reported=[1, 1, 0], with 1 reporting True and 0 False. Give (actual truth values, report-match Yes/No values, signed a_i−b_i values)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "classical integer formulas with explicit binding/data",
      "after": "a truth verdict is not a delivered general proof object",
      "relation": "implies",
      "rule_id": "proposition_truth_and_proof_scope",
      "conditions": [],
      "explanation": {
        "zh-Hant": "假陳述仍是命題；這裡提供有限代入與比較見證，不把真值標記升格為一般形式證明或任意推理規則的完備性。",
        "en": "A false closed statement is still a proposition.These finite substitutions and comparison witnesses do not promote a truth label to a general formal proof or completeness of arbitrary inference rules."
      },
      "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": "integer comparison difference0 := sub(-9, 0)",
      "after": "integer comparison difference0 = -9",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按有序對求a−b；零差與正負差都保留。",
        "en": "Compute a−b from the ordered pair,retaining zero and either sign."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 integer comparison difference0，不以小數近似替代。",
          "en": "Recompute integer comparison difference0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "-9",
          "0"
        ],
        "output": "-9",
        "label": "integer comparison difference0"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "row=0;a=-9;b=0;a−b=-9",
      "after": "statement=a≤b;truth=真",
      "relation": "implies",
      "rule_id": "closed_integer_statement_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "相等要差0，≤要差非正；差的符號提供精確比較見證，不是讀取候選自報。",
        "en": "Equality requires difference0 and ≤ requires a nonpositive difference;the signed difference supplies the exact comparison witness,not a candidate report."
      },
      "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": "integer comparison difference1 := sub(-2, 2)",
      "after": "integer comparison difference1 = -4",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按有序對求a−b；零差與正負差都保留。",
        "en": "Compute a−b from the ordered pair,retaining zero and either sign."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 integer comparison difference1，不以小數近似替代。",
          "en": "Recompute integer comparison difference1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "-2",
          "2"
        ],
        "output": "-4",
        "label": "integer comparison difference1"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "row=1;a=-2;b=2;a−b=-4",
      "after": "statement=a≤b;truth=真",
      "relation": "implies",
      "rule_id": "closed_integer_statement_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "相等要差0，≤要差非正；差的符號提供精確比較見證，不是讀取候選自報。",
        "en": "Equality requires difference0 and ≤ requires a nonpositive difference;the signed difference supplies the exact comparison witness,not a candidate report."
      },
      "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": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "integer comparison difference2 := sub(-1, 0)",
      "after": "integer comparison difference2 = -1",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按有序對求a−b；零差與正負差都保留。",
        "en": "Compute a−b from the ordered pair,retaining zero and either sign."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 integer comparison difference2，不以小數近似替代。",
          "en": "Recompute integer comparison difference2 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "-1",
          "0"
        ],
        "output": "-1",
        "label": "integer comparison difference2"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "row=2;a=-1;b=0;a−b=-1",
      "after": "statement=a≤b;truth=真",
      "relation": "implies",
      "rule_id": "closed_integer_statement_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "相等要差0，≤要差非正；差的符號提供精確比較見證，不是讀取候選自報。",
        "en": "Equality requires difference0 and ≤ requires a nonpositive difference;the signed difference supplies the exact comparison witness,not a candidate report."
      },
      "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": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "row=0;reported bit=1;independently computed truth=真",
      "after": "report matches=是",
      "relation": "implies",
      "rule_id": "report_vs_integer_witness",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先由給定整數另算真假，再核自報；自報1或0本身不是比較證據。",
        "en": "Compute truth from the given integers first,then audit the report;reported1 or0 is not itself comparison evidence."
      },
      "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": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "row=1;reported bit=1;independently computed truth=真",
      "after": "report matches=是",
      "relation": "implies",
      "rule_id": "report_vs_integer_witness",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先由給定整數另算真假，再核自報；自報1或0本身不是比較證據。",
        "en": "Compute truth from the given integers first,then audit the report;reported1 or0 is not itself comparison evidence."
      },
      "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": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "row=2;reported bit=0;independently computed truth=真",
      "after": "report matches=否",
      "relation": "implies",
      "rule_id": "report_vs_integer_witness",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先由給定整數另算真假，再核自報；自報1或0本身不是比較證據。",
        "en": "Compute truth from the given integers first,then audit the report;reported1 or0 is not itself comparison evidence."
      },
      "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": {
    "result": [
      [
        true,
        true,
        true
      ],
      [
        true,
        true,
        false
      ],
      [
        "-9",
        "-4",
        "-1"
      ]
    ]
  },
  "conclusion": {
    "canonical_value": "([真, 真, 真], [是, 是, 否], [-9, -4, -1])",
    "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-20261008-advance-20261012-r03-proposition-foundations",
      "batch_path": "public/data/questions/batches/batch-20261008-advance-20261012-r03-proposition-foundations/questions.jsonl",
      "batch_sha256": "5b0a0faf5bf6b380d452a972543ab58c4753045b86dd5aa697810565dc73b8e9",
      "original_line": 79,
      "original_line_sha256": "bd17a575ac50857c40c87b4cbeffe3fd89e9db844196dda24da8fa0d5d24e20a",
      "question_compact_sha256": "1aebad644b1f7336cc54e3d9e8432586554de44f037934e03aa1de7957a9d4e9",
      "english_row_compact_sha256": "efa63e7f6e7bb51ab097646bff6cd5b8d96163197f424dc726cff82b3002025b",
      "english_manifest_path": "public/data/i18n/editions/batch-20261008-advance-20261012-r03-proposition-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261008-advance-20261012-r03-proposition-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-proposition": {
        "sha256": "77a5e0d8403fa47d1ee57431b11f6fc52bfdde80a575db9dac3589fb0b9e8510",
        "english_sha256": "3d649ce5ebed9f16e8aea38557e60c43c771430b81bdc1be7533001a956f0608",
        "original_path": "public/data/mko/proposition.json",
        "english_path": "public/data/i18n/editions/mko-proposition.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "aeab777a3897ae2c01315b86b5e9b9a43ffb59b075efae44fd95d447123d32f1",
    "original_candidate_sha256": "c181967f3339d52115f821df0f279de486622097940f673b1ba0b21949c93093",
    "original_candidate_line_sha256": "c181967f3339d52115f821df0f279de486622097940f673b1ba0b21949c93093"
  },
  "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-p11",
    "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": "0328166a2e335aac7a5fb34556e68c80ba7d16612e822b3999c8ac348a9ca06f",
      "question_first_witness_sha256": "0da18e4e6cf71ece5ec5f00dd0cd161217b6d251672bc0b46d79fe7e6253f5fc"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 10,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "1bf43e368b43df046dff64afb2f1d2d2ef525e0534fe48e8782ac1cb833b774d",
      "arithmetic_steps": 3
    },
    "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."
  }
}