{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20260928-absolute-value-equation-class-0003",
  "pilot_number": "R0001-01078",
  "number": 1078,
  "family_id": "qf-absolute-value-equation-class",
  "title": {
    "zh-Hant": "第 1078 題：絕對值方程的解分類",
    "en": "Question 1078: Solution Classification of an Absolute-Value Equation"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20260928-absolute-value-equation-class-0003",
    "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|=-2 的解集。",
    "answer": {
      "kind": "short_text",
      "value": "無解",
      "explanation_zh": "絕對值永遠非負，不可能等於 -2，所以無解。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 1,
      "skills": [
        "絕對值方程",
        "解集合分類"
      ]
    },
    "variant": {
      "family_id": "qf-absolute-value-equation-class",
      "seed": 20261231,
      "parameters": {
        "c": -2,
        "domain": "reals",
        "operation": "absolute_equation_solution_class",
        "semantic_template": "qf-absolute-value-equation-class/{\"c\":-2,\"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-0003",
    "batch_id": "batch-20260928-absolute-value-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "3eed105fc0e647db81cb491549fc65ca78c9b8dec691037379d523566114e667",
      "family_id": "qf-absolute-value-equation-class",
      "seed": 20261231,
      "semantic_template": "qf-absolute-value-equation-class/{\"c\":-2,\"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|=-2.",
      "answer": {
        "kind": "short_text",
        "value": "no solution",
        "explanation": "Absolute value is nonnegative and cannot equal -2, so there is no solution."
      },
      "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|=-2 的解集。",
        "en": "Over the real numbers, classify the solution set of |x|=-2."
      }
    }
  ],
  "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|=-2",
      "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": "c=-2<0",
      "after": "nonnegative left side cannot equal this right side",
      "relation": "implies",
      "rule_id": "negative_rhs_obstruction",
      "conditions": [],
      "explanation": {
        "zh-Hant": "非負數不能等於負數，所以不存在任何實解，不需要逐點試猜。",
        "en": "A nonnegative number cannot equal a negative one, so no real solution exists; sampling guesses is unnecessary."
      },
      "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": "contradiction for every x∈R",
      "after": "無解",
      "relation": "implies",
      "rule_id": "empty_solution_set",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依解集定義，此矛盾得到空解集。",
        "en": "By the definition of solution set, this contradiction gives the empty set."
      },
      "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": -2,
    "roots": []
  },
  "conclusion": {
    "canonical_value": "無解",
    "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": 78,
      "original_line_sha256": "eb407372b5dc1c9d4d8eef71808e19035125166cb93259eba3231698c25e3000",
      "question_compact_sha256": "3eed105fc0e647db81cb491549fc65ca78c9b8dec691037379d523566114e667",
      "english_row_compact_sha256": "91ffc92565d4cb35ddd5d2dfe9a389a0c3fb336ec93637af2bf8ca7c4f3feca6",
      "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": {
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        "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": "2731928cadecce6bd7ac41e1c590a162087e74d3a910379c97decc58479b6129",
    "original_candidate_line_sha256": "2731928cadecce6bd7ac41e1c590a162087e74d3a910379c97decc58479b6129"
  },
  "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": 4,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "afa2f509c9c8e2bad359772d12fe1628f21e34c9dbd7fa47114c31203221205a",
      "arithmetic_steps": 0
    },
    "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."
  }
}