{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260928-absolute-value-equation-class-0022",
  "pilot_number": "R0001-01097",
  "number": 1097,
  "family_id": "qf-absolute-value-equation-class",
  "title": {
    "zh-Hant": "第 1097 題：絕對值方程的解分類",
    "en": "Question 1097: Solution Classification of an Absolute-Value Equation"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260928-absolute-value-equation-class-0022",
    "batch_id": "batch-20260928-absolute-value-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-absolute-value"
    ],
    "title_zh": "絕對值方程的解分類",
    "stem_zh": "在實數論域，分類方程 |x|=17 的解集。",
    "answer": {
      "kind": "short_text",
      "value": "兩解 x=-17, 17",
      "explanation_zh": "到 0 的距離為 17 的實數位於兩側，因此 x=-17 或 x=17。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 2,
      "skills": [
        "絕對值方程",
        "解集合分類"
      ]
    },
    "variant": {
      "family_id": "qf-absolute-value-equation-class",
      "seed": 20261250,
      "parameters": {
        "c": 17,
        "domain": "reals",
        "operation": "absolute_equation_solution_class",
        "semantic_template": "qf-absolute-value-equation-class/{\"c\":17,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"
      }
    },
    "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-equation-class-0022",
    "batch_id": "batch-20260928-absolute-value-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "c45f9f974c8c5cb1b455a431664b6644e53aeef07214706c0e6f5732667166dd",
      "family_id": "qf-absolute-value-equation-class",
      "seed": 20261250,
      "semantic_template": "qf-absolute-value-equation-class/{\"c\":17,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"
    },
    "fields": {
      "title": "Solution Classification of an Absolute-Value Equation",
      "stem": "Over the real numbers, classify the solution set of |x|=17.",
      "answer": {
        "kind": "short_text",
        "value": "two solutions x=-17, 17",
        "explanation": "The real numbers at distance 17 from 0 are x=-17 and x=17."
      },
      "skills": [
        "absolute-value equations",
        "solution-set classification"
      ],
      "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": "在實數論域，分類方程 |x|=17 的解集。",
        "en": "Over the real numbers, classify the solution set of |x|=17."
      }
    }
  ],
  "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": "|x|=17",
      "after": "|x|≥0 for every real x",
      "relation": "implies",
      "rule_id": "absolute_nonnegativity",
      "conditions": [],
      "explanation": {
        "zh-Hant": "由分段定義，x與−x在各自分支都非負。",
        "en": "From the piecewise definition, x or −x is nonnegative on its respective branch."
      },
      "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": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "negative candidate := mul(-1, 17)",
      "after": "negative candidate = -17",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "在負分支從−x=c得到x=−c。",
        "en": "In the negative branch, −x=c gives x=−c."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 negative candidate，不以小數近似替代。",
          "en": "Recompute negative candidate with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "-1",
          "17"
        ],
        "output": "-17",
        "label": "negative candidate"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "x≥0 gives x=17; x<0 would give x=-17",
      "after": "distinct permitted roots=[-17, 17]",
      "relation": "implies",
      "rule_id": "exhaustive_sign_cases",
      "conditions": [],
      "explanation": {
        "zh-Hant": "非負與負分支已窮盡；c=0時兩個形式候選重合，負分支不另給負根。",
        "en": "The sign branches are exhaustive; for c=0 the formal candidates coincide and the negative branch adds no negative root."
      },
      "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": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "[-17, 17]",
      "after": "each displayed root has |x|=17",
      "relation": "implies",
      "rule_id": "substitution_and_exhaustion",
      "conditions": [],
      "explanation": {
        "zh-Hant": "把每個候選代回並核對分支符號，得到全部且僅有的解。",
        "en": "Substitute every candidate and check its branch sign to obtain every and only solution."
      },
      "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": {
    "rhs": 17,
    "roots": [
      -17,
      17
    ]
  },
  "conclusion": {
    "canonical_value": "兩解 x=-17, 17",
    "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": 97,
      "original_line_sha256": "849be7b33ae310d2e1d813681a7406b9f0057b0a638cbd5aa580c940480d90ef",
      "question_compact_sha256": "c45f9f974c8c5cb1b455a431664b6644e53aeef07214706c0e6f5732667166dd",
      "english_row_compact_sha256": "df53b30e66731ef63c628b15d81e8a969c9ff05477d5be3a3e8823f1c126ec68",
      "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": "bff7a8ee5a426227f5f65bcf776bd3ba6182e2386952958e3b510bf714d4195b",
    "original_candidate_line_sha256": "bff7a8ee5a426227f5f65bcf776bd3ba6182e2386952958e3b510bf714d4195b"
  },
  "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": "0e39f816d2f2d44e134b8b3e36f99b1172910b3646cbb56c1eb12eab2c6e7c37",
      "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."
  }
}