{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261013-advance-20261024-r01-linear-independence-basis-0045",
  "pilot_number": "R0021-11220",
  "number": 11220,
  "family_id": "qf-mod24-linbasis-basis-r2-audit",
  "title": {
    "zh-Hant": "第 11220 題：線性獨立與基底",
    "en": "Question 11220: Independence and Spanning Are Separate Plane-Basis Obligations"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261013-advance-20261024-r01-linear-independence-basis-0045",
    "batch_id": "batch-20261013-advance-20261024-r01-linear-independence-basis-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-linear-independence-basis"
    ],
    "title_zh": "線性獨立與基底",
    "stem_zh": "明示有限座標向量族。操作=linbasis-basis-r2-audit；資料={\"vectors\":[[1,7],[0,1]]}。請依 [vectors,rank,independent,spans_R2,basis_R2] 欄序回答。",
    "answer": {
      "kind": "expression",
      "value": "([[1, 7], [0, 1]], 2, 是, 是, 是)",
      "explanation_zh": "依賴結構核對=([[1, 7], [0, 1]], 2, 是, 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；基底必須同時線性獨立並生成宣告空間；行列式與座標唯一性只用於方形R2基底。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 3,
      "skills": [
        "線性獨立與基底"
      ]
    },
    "variant": {
      "family_id": "qf-mod24-linbasis-basis-r2-audit",
      "seed": 202610241045,
      "parameters": {
        "vectors": [
          [
            1,
            7
          ],
          [
            0,
            1
          ]
        ],
        "domain": "Exact_finite_coordinate_basis",
        "operation": "linbasis-basis-r2-audit",
        "semantic_template": "qf-mod24-linbasis-basis-r2-audit/{\"vectors\":[[1,7],[0,1]]}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_finite_model",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication",
        "producer_json_schema"
      ],
      "warning_zh": "產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "model_unknown",
      "generated_at": "2026-10-13",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261013-advance-20261024-r01-linear-independence-basis-0045",
    "batch_id": "batch-20261013-advance-20261024-r01-linear-independence-basis-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "fd1ba8fd5c08cd8577e81d4cd8561a798d9a8f1ddd033e938ac9330be8dfeec8",
      "family_id": "qf-mod24-linbasis-basis-r2-audit",
      "seed": 202610241045,
      "semantic_template": "qf-mod24-linbasis-basis-r2-audit/{\"vectors\":[[1,7],[0,1]]}"
    },
    "fields": {
      "title": "Independence and Spanning Are Separate Plane-Basis Obligations",
      "stem": "Use the explicitly supplied finite integer-coordinate vector family in a real coordinate space. Preserve vector order and coefficient pairing. Rank is computed by exact rational elimination; a basis requires both independence and spanning the declared space, not just one condition. vectors=[[1, 7], [0, 1]] must all have dimension 2. Give (vectors,rank,independent?,spans R²?,is an R² basis?). Spanning requires rank 2; a basis additionally requires exactly two independent vectors.",
      "answer": {
        "kind": "expression",
        "value": "([[1, 7], [0, 1]], 2, Yes, Yes, Yes)",
        "explanation": "An independent singleton need not span R², and a redundant spanning family is not a basis. Keep all three flags distinct. This exact finite slice is not automatically a general infinite conclusion. The exact result, retaining the requested order, is ([[1, 7], [0, 1]], 2, Yes, Yes, Yes)."
      },
      "skills": [
        "Independence and Spanning Are Separate Plane-Basis Obligations"
      ],
      "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": "明示有限座標向量族。操作=linbasis-basis-r2-audit；資料={\"vectors\":[[1,7],[0,1]]}。請依 [vectors,rank,independent,spans_R2,basis_R2] 欄序回答。",
        "en": "Use the explicitly supplied finite integer-coordinate vector family in a real coordinate space. Preserve vector order and coefficient pairing. Rank is computed by exact rational elimination; a basis requires both independence and spanning the declared space, not just one condition. vectors=[[1, 7], [0, 1]] must all have dimension 2. Give (vectors,rank,independent?,spans R²?,is an R² basis?). Spanning requires rank 2; a basis additionally requires exactly two independent vectors."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "ordered column vectors=[[1, 7], [0, 1]]",
      "after": "homogeneous coefficient matrix=[[1, 0], [7, 1]];unknown count=2",
      "relation": "implies",
      "rule_id": "column_matrix_homogeneous_equations",
      "conditions": [],
      "explanation": {
        "zh-Hant": "向量依原序作直欄，線性獨立等價於此齊次系統只有零係數解；實際列運算須保留整組方程的解。",
        "en": "Use vectors as columns in original order.Independence means this homogeneous system has only the zero coefficient solution;row operations must preserve its solution 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
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "matrix=[[1, 0], [7, 1]];next pivot column=0;swap rows 0,0",
      "after": "matrix=[[1, 0], [7, 1]]",
      "relation": "implies",
      "rule_id": "invertible_row_swap",
      "conditions": [],
      "explanation": {
        "zh-Hant": "交換兩列只交換方程次序，反向再交換即可回復，不交換原向量欄序。",
        "en": "Swapping rows only reorders equations;the same swap reverses it.It does not exchange the original vector columns."
      },
      "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": "pivot0 normalized column0 := div(1, 1)",
      "after": "pivot0 normalized column0 = 1",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本步已指定的角色逐項精確運算；保留符號、分母與原始配對。",
        "en": "Compute exactly with this step's specified roles,retaining signs,denominators and original pairings."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 pivot0 normalized column0，不以小數近似替代。",
          "en": "Recompute pivot0 normalized column0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "1",
          "1"
        ],
        "output": "1",
        "label": "pivot0 normalized column0"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "pivot0 normalized column1 := div(0, 1)",
      "after": "pivot0 normalized column1 = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本步已指定的角色逐項精確運算；保留符號、分母與原始配對。",
        "en": "Compute exactly with this step's specified roles,retaining signs,denominators and original pairings."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 pivot0 normalized column1，不以小數近似替代。",
          "en": "Recompute pivot0 normalized column1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "0",
          "1"
        ],
        "output": "0",
        "label": "pivot0 normalized column1"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "row=0;old row=[1, 0];nonzero divisor=1",
      "after": "new row=[1, 0]",
      "relation": "implies",
      "rule_id": "nonzero_row_scaling_solution_equivalence",
      "conditions": [],
      "explanation": {
        "zh-Hant": "樞軸已證非零才可除整列；乘回同一數可反向，因此齊次解集不變。",
        "en": "The pivot is known nonzero before division of the whole row.Multiplication by it reverses the operation,so the homogeneous solution set is unchanged."
      },
      "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": "eliminate pivot0 row1 column0 scaled := mul(7, 1)",
      "after": "eliminate pivot0 row1 column0 scaled = 7",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本步已指定的角色逐項精確運算；保留符號、分母與原始配對。",
        "en": "Compute exactly with this step's specified roles,retaining signs,denominators and original pairings."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 eliminate pivot0 row1 column0 scaled，不以小數近似替代。",
          "en": "Recompute eliminate pivot0 row1 column0 scaled with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "7",
          "1"
        ],
        "output": "7",
        "label": "eliminate pivot0 row1 column0 scaled"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "eliminate pivot0 row1 column0 residual := sub(7, 7)",
      "after": "eliminate pivot0 row1 column0 residual = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本步已指定的角色逐項精確運算；保留符號、分母與原始配對。",
        "en": "Compute exactly with this step's specified roles,retaining signs,denominators and original pairings."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 eliminate pivot0 row1 column0 residual，不以小數近似替代。",
          "en": "Recompute eliminate pivot0 row1 column0 residual with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "7",
          "7"
        ],
        "output": "0",
        "label": "eliminate pivot0 row1 column0 residual"
      }
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "eliminate pivot0 row1 column1 scaled := mul(7, 0)",
      "after": "eliminate pivot0 row1 column1 scaled = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本步已指定的角色逐項精確運算；保留符號、分母與原始配對。",
        "en": "Compute exactly with this step's specified roles,retaining signs,denominators and original pairings."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 eliminate pivot0 row1 column1 scaled，不以小數近似替代。",
          "en": "Recompute eliminate pivot0 row1 column1 scaled with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "7",
          "0"
        ],
        "output": "0",
        "label": "eliminate pivot0 row1 column1 scaled"
      }
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "eliminate pivot0 row1 column1 residual := sub(1, 0)",
      "after": "eliminate pivot0 row1 column1 residual = 1",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本步已指定的角色逐項精確運算；保留符號、分母與原始配對。",
        "en": "Compute exactly with this step's specified roles,retaining signs,denominators and original pairings."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 eliminate pivot0 row1 column1 residual，不以小數近似替代。",
          "en": "Recompute eliminate pivot0 row1 column1 residual with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "1",
          "0"
        ],
        "output": "1",
        "label": "eliminate pivot0 row1 column1 residual"
      }
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "target row=1;old=[7, 1];pivot row=[1, 0];factor=7",
      "after": "new row=[0, 1];matrix=[[1, 0], [0, 1]]",
      "relation": "implies",
      "rule_id": "invertible_pivot_row_subtraction",
      "conditions": [],
      "explanation": {
        "zh-Hant": "用目標列減factor倍的樞軸列消去此欄；加回同一倍數便回原式，故不會創造或刪掉解。",
        "en": "Subtract factor times the pivot row to eliminate this entry.Adding it back recovers the original equation;no solutions are created or lost."
      },
      "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": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "matrix=[[1, 0], [0, 1]];next pivot column=1;swap rows 1,1",
      "after": "matrix=[[1, 0], [0, 1]]",
      "relation": "implies",
      "rule_id": "invertible_row_swap",
      "conditions": [],
      "explanation": {
        "zh-Hant": "交換兩列只交換方程次序，反向再交換即可回復，不交換原向量欄序。",
        "en": "Swapping rows only reorders equations;the same swap reverses it.It does not exchange the original vector columns."
      },
      "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": "S012",
      "uses": [
        "G001",
        "S011"
      ],
      "before": "pivot1 normalized column0 := div(0, 1)",
      "after": "pivot1 normalized column0 = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本步已指定的角色逐項精確運算；保留符號、分母與原始配對。",
        "en": "Compute exactly with this step's specified roles,retaining signs,denominators and original pairings."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 pivot1 normalized column0，不以小數近似替代。",
          "en": "Recompute pivot1 normalized column0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "0",
          "1"
        ],
        "output": "0",
        "label": "pivot1 normalized column0"
      }
    },
    {
      "id": "S013",
      "uses": [
        "G001",
        "S012"
      ],
      "before": "pivot1 normalized column1 := div(1, 1)",
      "after": "pivot1 normalized column1 = 1",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本步已指定的角色逐項精確運算；保留符號、分母與原始配對。",
        "en": "Compute exactly with this step's specified roles,retaining signs,denominators and original pairings."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 pivot1 normalized column1，不以小數近似替代。",
          "en": "Recompute pivot1 normalized column1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "1",
          "1"
        ],
        "output": "1",
        "label": "pivot1 normalized column1"
      }
    },
    {
      "id": "S014",
      "uses": [
        "G001",
        "S013"
      ],
      "before": "row=1;old row=[0, 1];nonzero divisor=1",
      "after": "new row=[0, 1]",
      "relation": "implies",
      "rule_id": "nonzero_row_scaling_solution_equivalence",
      "conditions": [],
      "explanation": {
        "zh-Hant": "樞軸已證非零才可除整列；乘回同一數可反向，因此齊次解集不變。",
        "en": "The pivot is known nonzero before division of the whole row.Multiplication by it reverses the operation,so the homogeneous solution set is unchanged."
      },
      "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": "S015",
      "uses": [
        "G001",
        "S014"
      ],
      "before": "reduced matrix=[[1, 0], [0, 1]];pivot columns=[0, 1];unknown count=2",
      "after": "rank=2;free variables=0;independent=是",
      "relation": "implies",
      "rule_id": "rank_free_variables_and_independence",
      "conditions": [],
      "explanation": {
        "zh-Hant": "樞軸數是秩；每欄都有樞軸時齊次解只能全零。否則選一個自由變數為1、其餘自由變數0，再回代樞軸變數得到非平凡零組合。",
        "en": "Rank is the pivot count.If every column pivots,the homogeneous solution is zero only.Otherwise set one free variable to1,the other free variables to0,and back-substitute pivot variables to obtain a nontrivial zero combination."
      },
      "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": "S016",
      "uses": [
        "G001",
        "S015"
      ],
      "before": "ambient space=R2;rank=2;family size=2",
      "after": "independent=是;spans_R2=是;basis_R2=是",
      "relation": "implies",
      "rule_id": "basis_independence_and_spanning_separate",
      "conditions": [],
      "explanation": {
        "zh-Hant": "列運算可逆且主元直欄保持像空間維數，秩2才張成整個R²。獨立單向量不張成平面，多餘向量雖張成也不是基底。",
        "en": "Invertible row operations preserve image dimension;rank2 is required to span R².An independent singleton does not span the plane,and redundant spanning vectors are not a basis."
      },
      "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": [
      [
        [
          1,
          7
        ],
        [
          0,
          1
        ]
      ],
      2,
      true,
      true,
      true
    ]
  },
  "conclusion": {
    "canonical_value": "([[1, 7], [0, 1]], 2, 是, 是, 是)",
    "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-20261013-advance-20261024-r01-linear-independence-basis-foundations",
      "batch_path": "public/data/questions/batches/batch-20261013-advance-20261024-r01-linear-independence-basis-foundations/questions.jsonl",
      "batch_sha256": "9c09bb587cfb555cea8fbb6e53978a87ed1a994c6c16dd9c77a76f0a37571632",
      "original_line": 45,
      "original_line_sha256": "7ec62824cf4e9671f2808f24fde44fcc01602459524360e0e5f3e51791d52cdb",
      "question_compact_sha256": "fd1ba8fd5c08cd8577e81d4cd8561a798d9a8f1ddd033e938ac9330be8dfeec8",
      "english_row_compact_sha256": "c273d2899c28559293f3ec93940f326dd8e6a256e3b84d1f30575b1636645dd1",
      "english_manifest_path": "public/data/i18n/editions/batch-20261013-advance-20261024-r01-linear-independence-basis-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261013-advance-20261024-r01-linear-independence-basis-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-linear-independence-basis": {
        "sha256": "78c45988a718f6a7ca4acf2aba00ea4df794c8f141cefe822bf72206fa2b2f62",
        "english_sha256": "48c43771b8f6734ece79626851e05a5dca9bb984732eb3f69cffe2c6e364a912",
        "original_path": "public/data/mko/linear-independence-basis.json",
        "english_path": "public/data/i18n/editions/mko-linear-independence-basis.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "18bbb89127e14ce3466c1a8730f1c3c6e22a8f59a9148433b2abc7f6ea274ee5",
    "original_candidate_sha256": "327a1058f77e941c5f5705b9abec987bc8f4996c5d3bfb78e933750f195b88a1",
    "original_candidate_line_sha256": "327a1058f77e941c5f5705b9abec987bc8f4996c5d3bfb78e933750f195b88a1"
  },
  "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-20261026-006-p22",
    "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": "47d23d3735987d68e27733b051bdfa80a3616d44fb223b82bf2e6c8e46d49258",
      "question_first_witness_sha256": "a857db558000724020d2d5e815cb6bc3e2c9e2933df295bf33eb478d3c695139"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 16,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "ad1d548387c97477602fbdc4b53bd02d08f56b29fc826d914a3993c3e8c94156",
      "arithmetic_steps": 8
    },
    "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."
  }
}