{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261005-advance-20261006-r02-quadratic-function-0086",
  "pilot_number": "R0055-28486",
  "number": 28486,
  "family_id": "qf-quadratic-function-axis-mirror",
  "title": {
    "zh-Hant": "第 28486 題：對稱軸另一側的圖形點",
    "en": "Question 28486: Graph Point Reflected across the Axis"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261005-advance-20261006-r02-quadratic-function-0086",
    "batch_id": "batch-20261005-advance-20261006-r02-quadratic-function-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-quadratic-function"
    ],
    "title_zh": "對稱軸另一側的圖形點",
    "stem_zh": "在全實數論域，指定 q:R→R，q(x)=11(x−(-2))²+(0)，a=11≠0。圖形點 (-1,q(-1)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。",
    "answer": {
      "kind": "expression",
      "value": "(-3, 11)",
      "explanation_zh": "對稱點=(-3, 11)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"
    },
    "difficulty": {
      "band": "upper_secondary",
      "level": 2,
      "skills": [
        "對稱軸另一側的圖形點"
      ]
    },
    "variant": {
      "family_id": "qf-quadratic-function-axis-mirror",
      "seed": 202610062086,
      "parameters": {
        "a": 11,
        "h": -2,
        "k": 0,
        "x": -1,
        "domain": "reals",
        "operation": "quadratic_mirror",
        "semantic_template": "qf-quadratic-function-axis-mirror/{\"inputs\":[\"11\",\"-2\",\"0\",\"-1\"],\"operation\":\"quadratic_mirror\"}"
      }
    },
    "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": "2026-10-05",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261005-advance-20261006-r02-quadratic-function-0086",
    "batch_id": "batch-20261005-advance-20261006-r02-quadratic-function-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "00ec9c3f0c3b4a15fcdf1c2181076a0c1038a69c31d4516654d1e373c50b81c8",
      "family_id": "qf-quadratic-function-axis-mirror",
      "seed": 202610062086,
      "semantic_template": "qf-quadratic-function-axis-mirror/{\"inputs\":[\"11\",\"-2\",\"0\",\"-1\"],\"operation\":\"quadratic_mirror\"}"
    },
    "fields": {
      "title": "Graph Point Reflected across the Axis",
      "stem": "On the full real domain, let q:R→R be q(x)=(11)(x−(-2))²+(0), with a≠0. Reflect the graph point (-1,q(-1)) across x=-2. Give the reflected (input,output) pair.",
      "answer": {
        "kind": "expression",
        "value": "(-3, 11)",
        "explanation": "The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (-3, 11); a point on the axis is its own reflection."
      },
      "skills": [
        "Graph Point Reflected across the Axis"
      ],
      "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": "在全實數論域，指定 q:R→R，q(x)=11(x−(-2))²+(0)，a=11≠0。圖形點 (-1,q(-1)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。",
        "en": "On the full real domain, let q:R→R be q(x)=(11)(x−(-2))²+(0), with a≠0. Reflect the graph point (-1,q(-1)) across x=-2. Give the reflected (input,output) pair."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-quadratic-function-axis-mirror, quadratic_mirror]",
      "after": "derived = [[reflected_input_unchanged_output_graph_POINT]]",
      "relation": "implies",
      "rule_id": "source_answer_roles_or_ordered_fields_without_JS",
      "conditions": [],
      "explanation": {
        "zh-Hant": "此頁明列本題scalar／label／set／point或mode欄序，不強套現代tuple。舊題domain與operation底線格式按原資料，分數整數亦保/1；原中英快照不改。",
        "en": "List this scalar/label/set/point answer role or mode-specific ordered fields,not an imposed universal tuple.Retain legacy domain/underscore operation and integer fractions with/1;original bilingual snapshots stay unchanged."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回查完整來源資料、原操作數及本步條件；有限核對、條件式理由、形式證明與發布資格分開。",
          "en": "Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "Legacy mirror ORIGINAL x minus h := sub(-1, -2)",
      "after": "Legacy mirror ORIGINAL x minus h = 1",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原始角色精確代值，不作浮點近似或換操作數；額外教學等式不另縮原題域。",
        "en": "Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Legacy mirror ORIGINAL x minus h，不以小數近似替代。",
          "en": "Recompute Legacy mirror ORIGINAL x minus h with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "-1",
          "-2"
        ],
        "output": "1",
        "label": "Legacy mirror ORIGINAL x minus h"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "Legacy mirror ORIGINAL squared displacement := mul(1, 1)",
      "after": "Legacy mirror ORIGINAL squared displacement = 1",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原始角色精確代值，不作浮點近似或換操作數；額外教學等式不另縮原題域。",
        "en": "Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Legacy mirror ORIGINAL squared displacement，不以小數近似替代。",
          "en": "Recompute Legacy mirror ORIGINAL squared displacement with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1",
          "1"
        ],
        "output": "1",
        "label": "Legacy mirror ORIGINAL squared displacement"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "Legacy mirror ORIGINAL a times displacement square := mul(11, 1)",
      "after": "Legacy mirror ORIGINAL a times displacement square = 11",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原始角色精確代值，不作浮點近似或換操作數；額外教學等式不另縮原題域。",
        "en": "Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Legacy mirror ORIGINAL a times displacement square，不以小數近似替代。",
          "en": "Recompute Legacy mirror ORIGINAL a times displacement square with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "11",
          "1"
        ],
        "output": "11",
        "label": "Legacy mirror ORIGINAL a times displacement square"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "Legacy mirror ORIGINAL graph output plus k := sum(11, 0)",
      "after": "Legacy mirror ORIGINAL graph output plus k = 11",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原始角色精確代值，不作浮點近似或換操作數；額外教學等式不另縮原題域。",
        "en": "Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Legacy mirror ORIGINAL graph output plus k，不以小數近似替代。",
          "en": "Recompute Legacy mirror ORIGINAL graph output plus k with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "11",
          "0"
        ],
        "output": "11",
        "label": "Legacy mirror ORIGINAL graph output plus k"
      }
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "Legacy mirror ORIGINAL twice h := mul(2, -2)",
      "after": "Legacy mirror ORIGINAL twice h = -4",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原始角色精確代值，不作浮點近似或換操作數；額外教學等式不另縮原題域。",
        "en": "Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Legacy mirror ORIGINAL twice h，不以小數近似替代。",
          "en": "Recompute Legacy mirror ORIGINAL twice h with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "2",
          "-2"
        ],
        "output": "-4",
        "label": "Legacy mirror ORIGINAL twice h"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "Legacy mirror ORIGINAL reflected input := sub(-4, -1)",
      "after": "Legacy mirror ORIGINAL reflected input = -3",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原始角色精確代值，不作浮點近似或換操作數；額外教學等式不另縮原題域。",
        "en": "Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Legacy mirror ORIGINAL reflected input，不以小數近似替代。",
          "en": "Recompute Legacy mirror ORIGINAL reflected input with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "-4",
          "-1"
        ],
        "output": "-3",
        "label": "Legacy mirror ORIGINAL reflected input"
      }
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "Legacy mirror reflected displacement := sub(-3, -2)",
      "after": "Legacy mirror reflected displacement = -1",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原始角色精確代值，不作浮點近似或換操作數；額外教學等式不另縮原題域。",
        "en": "Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 Legacy mirror reflected displacement，不以小數近似替代。",
          "en": "Recompute Legacy mirror reflected displacement with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "-3",
          "-2"
        ],
        "output": "-1",
        "label": "Legacy mirror reflected displacement"
      }
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "source roles = [11, -2, 0, -1, -3]",
      "after": "derived = [1, -1, 11, 2h-(2h-x)=x]",
      "relation": "implies",
      "rule_id": "Legacy_mirror_FULLreal_vertex_quadratic_involution_unchanged_output",
      "conditions": [],
      "explanation": {
        "zh-Hant": "x_prime=2h-x使x_prime-h=-(x-h)，平方不變，所以q(x_prime)=q(x)。輸出完整graph point，不是axis或vertex；x=h可自身反射，derived座標／值不截SAFE。",
        "en": "x_prime=2h-x gives x_prime-h=-(x-h),so the square and q value are unchanged.Return the FULL graph point,not the axis or vertex.A point at x=h reflects to itself;derived coordinates/values are not SAFE-clipped."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回查完整來源資料、原操作數及本步條件；有限核對、條件式理由、形式證明與發布資格分開。",
          "en": "Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": "(-3, 11)"
  },
  "conclusion": {
    "canonical_value": "(-3, 11)",
    "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-20261005-advance-20261006-r02-quadratic-function-foundations",
      "batch_path": "public/data/questions/batches/batch-20261005-advance-20261006-r02-quadratic-function-foundations/questions.jsonl",
      "batch_sha256": "32ddadfe8c46e9f3d07fce31517b78bd2cd661610eee7e0d814f91fecbc51be4",
      "original_line": 86,
      "original_line_sha256": "a656ab89978ed4334d7387ed39a4b3a69905bde21ad08312b00253a3debb2b6b",
      "question_compact_sha256": "00ec9c3f0c3b4a15fcdf1c2181076a0c1038a69c31d4516654d1e373c50b81c8",
      "english_row_compact_sha256": "8035c065bc7c403edd5e4a7e096a3743407910b33625f58dca508528c44111d6",
      "english_manifest_path": "public/data/i18n/editions/batch-20261005-advance-20261006-r02-quadratic-function-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261005-advance-20261006-r02-quadratic-function-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-quadratic-function": {
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        "english_sha256": "302ee0311ea4ba78b81f3c48951bf1dc495a2b158c4c0e46b3f8b3b0ff72bf67",
        "original_path": "public/data/mko/quadratic-function.json",
        "english_path": "public/data/i18n/editions/mko-quadratic-function.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "b5763df142e86ef7f9787b6ea86050afc60bd3c5c53538d4839606827cc44686",
    "original_candidate_sha256": "8365e595314c8c16507d28b40c8f98d71f0a6a9782cd0fdc1fbad968e0633d8b",
    "original_candidate_line_sha256": "8365e595314c8c16507d28b40c8f98d71f0a6a9782cd0fdc1fbad968e0633d8b"
  },
  "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-20261026-010-p56",
    "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": "6af367dae24a584f3596525c4953bbc2115343efd68cc9083693eb5c1ef2e683",
      "question_first_witness_sha256": "611eb69f3716404b968296a8b0d7d8c61b5ca18129d406f1ff9c7c11e10ffb4e"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 9,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "bc094f2dfb2ded117c46e5b6cf3b44396af8b86f000ab24f044197132c5d348f",
      "arithmetic_steps": 7
    },
    "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."
  }
}