{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0073",
  "pilot_number": "R0041-21048",
  "number": 21048,
  "family_id": "qf-mod39-monoseq-epsilon-witness",
  "title": {
    "zh-Hant": "第 21048 題：單調有界數列收斂定理",
    "en": "Question 21048: A Strict Epsilon Tail Needs the First Passing Index, Including Equality Boundaries"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0073",
    "batch_id": "batch-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-monotone-sequence-convergence-theorem"
    ],
    "title_zh": "單調有界數列收斂定理",
    "stem_zh": "實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={\"direction\":\"increasing\",\"limit\":[23,24],\"coefficient\":23,\"shift\":2,\"epsilon\":[1,32]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。",
    "answer": {
      "kind": "expression",
      "value": "(increasing, 23/24, 1/32, 735, 16399/17688, 是, forall_n_ge_N_by_monotone_symbolic_tail)",
      "explanation_zh": "Wave6第二層核對=(increasing, 23/24, 1/32, 735, 16399/17688, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 3,
      "skills": [
        "單調有界數列收斂定理"
      ]
    },
    "variant": {
      "family_id": "qf-mod39-monoseq-epsilon-witness",
      "seed": 202611082073,
      "parameters": {
        "limit": [
          23,
          24
        ],
        "coefficient": 23,
        "shift": 2,
        "direction": "increasing",
        "epsilon": [
          1,
          32
        ],
        "domain": "Symbolic_monotone_bounded_real_sequence",
        "operation": "monoseq-epsilon-witness",
        "semantic_template": "qf-mod39-monoseq-epsilon-witness/{\"coefficient\":23,\"direction\":\"increasing\",\"epsilon\":[1,32],\"limit\":[23,24],\"shift\":2}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_finite_or_symbolic_model",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication",
        "producer_json_schema"
      ],
      "warning_zh": "候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "model_unknown",
      "generated_at": "2026-10-14",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0073",
    "batch_id": "batch-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "9fd2eee9d310ba144101bd92bf095a7eab417228f931d25c81e4854e41e16a81",
      "family_id": "qf-mod39-monoseq-epsilon-witness",
      "seed": 202611082073,
      "semantic_template": "qf-mod39-monoseq-epsilon-witness/{\"coefficient\":23,\"direction\":\"increasing\",\"epsilon\":[1,32],\"limit\":[23,24],\"shift\":2}"
    },
    "fields": {
      "title": "A Strict Epsilon Tail Needs the First Passing Index, Including Equality Boundaries",
      "stem": "Use the whole real sequence a_n=L−c/(n+shift) for every n≥0, with L=23/24, positive c=23 and positive integer shift=2. The denominator shift is distinct from the theorem's supremum/infimum bound. The entire symbolic family, not a displayed finite prefix, supplies monotonicity and the corresponding bound. Direction=increasing, positive epsilon=1/32. Give (direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate).",
      "answer": {
        "kind": "expression",
        "value": "(increasing, 23/24, 1/32, 735, 16399/17688, Yes, forall_n_ge_N_by_monotone_symbolic_tail)",
        "explanation": "Find the least nonnegative N with c/(N+shift)<epsilon. A gap equal to epsilon still fails the strict criterion. Report a_N and retain the all-n≥N tail flag; increasing denominators preserve the strict bound. The exact result, retaining the requested order, is (increasing, 23/24, 1/32, 735, 16399/17688, Yes, forall_n_ge_N_by_monotone_symbolic_tail)."
      },
      "skills": [
        "A Strict Epsilon Tail Needs the First Passing Index, Including Equality Boundaries"
      ],
      "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": "實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={\"direction\":\"increasing\",\"limit\":[23,24],\"coefficient\":23,\"shift\":2,\"epsilon\":[1,32]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。",
        "en": "Use the whole real sequence a_n=L−c/(n+shift) for every n≥0, with L=23/24, positive c=23 and positive integer shift=2. The denominator shift is distinct from the theorem's supremum/infimum bound. The entire symbolic family, not a displayed finite prefix, supplies monotonicity and the corresponding bound. Direction=increasing, positive epsilon=1/32. Give (direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source operation=monoseq-epsilon-witness;original snapshot and mathematics retained",
      "after": "explicit ordered source output fields=[direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate]",
      "relation": "implies",
      "rule_id": "source_ordered_interface_explicit_without_javascript",
      "conditions": [],
      "explanation": {
        "zh-Hant": "原題歷史介面標記保留；此處直接列有序輸出欄位，不依賴JavaScript。欄位或tag不是額外數學證據，固定No保留原聲稱範圍。",
        "en": "Retain the historical interface marker while listing ordered output fields without JavaScript.Fields and tags are not extra mathematical evidence;fixed No markers retain their claim scope."
      },
      "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": "ORIGINAL direction=increasing,L=23/24,c=23>0,shift=2>=1;WHOLE a_n=L+(-1)c/(n+shift) for ALL n>=0",
      "after": "for EVERY n>=0,a_(n+1)-a_n=(1)*(23)/((n+2)*(n+1+2));positive denominator;all a_n strictly below L=23/24",
      "relation": "implies",
      "rule_id": "monoseq_whole_symbolic_monotonicity_and_matching_bound",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐次差由同分母相減得到；c正、分母正固定其符號，故遞增時L是上界，遞減時L是下界。這是全部n的公式，允許L為負且不把頭三項當證明。",
        "en": "Subtract adjacent symbolic terms using a common denominator.Positivity fixes the sign and gives upper bound L in the increasing case or lower bound L in the decreasing case.This holds for all n,allows negative L,and is not a three-term sample proof."
      },
      "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": "WHOLE increasing law with ORIGINAL L=23/24,c=23,shift=2",
      "after": "for ANY epsilon>0 choose natural N with N+2>23/epsilon;ALL n>=N have |a_n-L|<epsilon;L is supremum but NOT attained because c/(n+shift)>0",
      "relation": "implies",
      "rule_id": "monoseq_sup_inf_limit_proof_and_nonattainment",
      "conditions": [],
      "explanation": {
        "zh-Hant": "由Archimedean性選出N後控制所有後項；任何比L更小的上界（或更大的下界）會被足夠近L的項打破，故L是sup／inf。一般單調定理亦由sup−epsilon不是上界取得一項，再以單調性夾住尾部；遞減情況對偶。",
        "en": "The Archimedean choice controls every later term.Any smaller upper bound or larger lower bound is broken by a term sufficiently close to L,so L is the sup/inf.In the general monotone theorem,sup−epsilon is not an upper bound,which supplies a term;monotonicity then traps the tail.The decreasing proof is dual."
      },
      "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": "monoseq c over epsilon := div(23, 1/32)",
      "after": "monoseq c over epsilon = 736",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原題角色與已核中間量精確代值，保留原順序、正負號及量詞條件。",
        "en": "Substitute the original roles and established intermediates exactly,retaining order,signs and quantified conditions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 monoseq c over epsilon，不以小數近似替代。",
          "en": "Recompute monoseq c over epsilon with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "23",
          "1/32"
        ],
        "output": "736",
        "label": "monoseq c over epsilon"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "monoseq index multiple := mul(1, 735)",
      "after": "monoseq index multiple = 735",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原題角色與已核中間量精確代值，保留原順序、正負號及量詞條件。",
        "en": "Substitute the original roles and established intermediates exactly,retaining order,signs and quantified conditions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 monoseq index multiple，不以小數近似替代。",
          "en": "Recompute monoseq index multiple with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "1",
          "735"
        ],
        "output": "735",
        "label": "monoseq index multiple"
      }
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "monoseq actual source index := sum(0, 735)",
      "after": "monoseq actual source index = 735",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原題角色與已核中間量精確代值，保留原順序、正負號及量詞條件。",
        "en": "Substitute the original roles and established intermediates exactly,retaining order,signs and quantified conditions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 monoseq actual source index，不以小數近似替代。",
          "en": "Recompute monoseq actual source index with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "0",
          "735"
        ],
        "output": "735",
        "label": "monoseq actual source index"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "monoseq witness denominator := sum(735, 2)",
      "after": "monoseq witness denominator = 737",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原題角色與已核中間量精確代值，保留原順序、正負號及量詞條件。",
        "en": "Substitute the original roles and established intermediates exactly,retaining order,signs and quantified conditions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 monoseq witness denominator，不以小數近似替代。",
          "en": "Recompute monoseq witness denominator with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "735",
          "2"
        ],
        "output": "737",
        "label": "monoseq witness denominator"
      }
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "monoseq witness distance := div(23, 737)",
      "after": "monoseq witness distance = 23/737",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原題角色與已核中間量精確代值，保留原順序、正負號及量詞條件。",
        "en": "Substitute the original roles and established intermediates exactly,retaining order,signs and quantified conditions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 monoseq witness distance，不以小數近似替代。",
          "en": "Recompute monoseq witness distance with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "23",
          "737"
        ],
        "output": "23/737",
        "label": "monoseq witness distance"
      }
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "monoseq predecessor distance := div(23, 736)",
      "after": "monoseq predecessor distance = 1/32",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原題角色與已核中間量精確代值，保留原順序、正負號及量詞條件。",
        "en": "Substitute the original roles and established intermediates exactly,retaining order,signs and quantified conditions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 monoseq predecessor distance，不以小數近似替代。",
          "en": "Recompute monoseq predecessor distance with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "23",
          "736"
        ],
        "output": "1/32",
        "label": "monoseq predecessor distance"
      }
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "monoseq:c=23,shift=2,epsilon=1/32;index(q)=1q+0;c/epsilon=736;floor=736",
      "after": "least nonnegative witness=735;actual source index=735;distance=23/737<epsilon;predecessor distance=1/32;no predecessor evaluated when witness0",
      "relation": "implies",
      "rule_id": "tail_strict_least_index_not_equality_or_negative_predecessor",
      "conditions": [],
      "explanation": {
        "zh-Hant": "嚴格小於等價分母大於c/epsilon，整數分母需至少floor(c/epsilon)+1，再按stride向上取整且截到0。N>0才驗前一項仍≥epsilon；相等尚未通過。",
        "en": "Strict distance<epsilon means the denominator exceeds c/epsilon,so its integer threshold is floor(c/epsilon)+1.Round the affine index upward and clamp only the witness to0.Check the predecessor only when positive;equality still fails."
      },
      "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": "monoseq:positive c=23,epsilon=1/32,shift=2,stride=1,offset=0;least witness=735",
      "after": "for EVERY integer q>=735,denominator=1q+0+2>=witness denominator>0,so 0<distance<=(23/737)<epsilon",
      "relation": "implies",
      "rule_id": "tail_all_later_quantified_from_positive_denominator_growth",
      "conditions": [],
      "explanation": {
        "zh-Hant": "這一步是所有後續索引的代數不等式，不是只看一個數值猜收斂。分母正且遞增，固定正分子使誤差遞減；前一項檢查只證最小性。",
        "en": "This is an algebraic inequality for every later index,not convergence guessed from one evaluated term.Positive increasing denominators and a fixed positive numerator control the whole tail;the predecessor check proves minimality only."
      },
      "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": "monoseq at witness N denominator := sum(735, 2)",
      "after": "monoseq at witness N denominator = 737",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原題角色與已核中間量精確代值，保留原順序、正負號及量詞條件。",
        "en": "Substitute the original roles and established intermediates exactly,retaining order,signs and quantified conditions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 monoseq at witness N denominator，不以小數近似替代。",
          "en": "Recompute monoseq at witness N denominator with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "735",
          "2"
        ],
        "output": "737",
        "label": "monoseq at witness N denominator"
      }
    },
    {
      "id": "S013",
      "uses": [
        "G001",
        "S012"
      ],
      "before": "monoseq at witness N unsigned tail := div(23, 737)",
      "after": "monoseq at witness N unsigned tail = 23/737",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原題角色與已核中間量精確代值，保留原順序、正負號及量詞條件。",
        "en": "Substitute the original roles and established intermediates exactly,retaining order,signs and quantified conditions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 monoseq at witness N unsigned tail，不以小數近似替代。",
          "en": "Recompute monoseq at witness N unsigned tail with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "23",
          "737"
        ],
        "output": "23/737",
        "label": "monoseq at witness N unsigned tail"
      }
    },
    {
      "id": "S014",
      "uses": [
        "G001",
        "S013"
      ],
      "before": "monoseq at witness N signed value := sub(23/24, 23/737)",
      "after": "monoseq at witness N signed value = 16399/17688",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原題角色與已核中間量精確代值，保留原順序、正負號及量詞條件。",
        "en": "Substitute the original roles and established intermediates exactly,retaining order,signs and quantified conditions."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 monoseq at witness N signed value，不以小數近似替代。",
          "en": "Recompute monoseq at witness N signed value with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "23/24",
          "23/737"
        ],
        "output": "16399/17688",
        "label": "monoseq at witness N signed value"
      }
    }
  ],
  "math_model": {
    "result": [
      "increasing",
      "23/24",
      "1/32",
      735,
      "16399/17688",
      true,
      "forall_n_ge_N_by_monotone_symbolic_tail"
    ]
  },
  "conclusion": {
    "canonical_value": "(increasing, 23/24, 1/32, 735, 16399/17688, 是, forall_n_ge_N_by_monotone_symbolic_tail)",
    "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-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-foundations",
      "batch_path": "public/data/questions/batches/batch-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-foundations/questions.jsonl",
      "batch_sha256": "89dab9b3bab56cf32df54dfb1052a43027c5e475f1fe7279fd2a6f3e5b292774",
      "original_line": 73,
      "original_line_sha256": "ee7008fc077ecd4b6a941239e0bd89f7f3208234dac3a16b8ba5fad1d2fe077b",
      "question_compact_sha256": "9fd2eee9d310ba144101bd92bf095a7eab417228f931d25c81e4854e41e16a81",
      "english_row_compact_sha256": "a22cb2903d3b48dcb2d754cefed7b0b3f91e14317d981435c53adf1eb8825436",
      "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-monotone-sequence-convergence-theorem": {
        "sha256": "7347d54ee6a5bad0a10d31d2740a6f5af3d2539f9dd91cfc6e85d51ea7c966dc",
        "english_sha256": "04ac52a1866dfc205ff11c701b766a16b5e2bfa894396f50a16b4f6eb495d448",
        "original_path": "public/data/mko/monotone-sequence-convergence-theorem.json",
        "english_path": "public/data/i18n/editions/mko-monotone-sequence-convergence-theorem.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "2bda8f45e99ed8658b697be77ed3e5ec90ceff1b4f72fa7aa6a47d1a0c6254cf",
    "original_candidate_sha256": "4e517a226e90bfece8d96a15c38ea0abf494038de857b0b3be4de4cf3d3c9b84",
    "original_candidate_line_sha256": "4e517a226e90bfece8d96a15c38ea0abf494038de857b0b3be4de4cf3d3c9b84",
    "mko_binding_revision": {
      "id": "edition-symbol-bindings-20261101",
      "path": "content/edition-symbol-bindings-20261101/revision.json",
      "sha256": "e9b4c69f2c4732074c37abb624c8ab8a70afc3645c12bf9df2268ef650ad7b6c",
      "previous_english_sha256": {
        "mko-monotone-sequence-convergence-theorem": "c3634e802309cc74e6545f1ff6fbce10c51061adddafe94aa8151785626efdc9"
      }
    }
  },
  "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-20261026-009-p42",
    "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": "8f134403487694af4c70d2e00ec84bab542043ef4b3c54517c04f3c409c0262a",
      "question_first_witness_sha256": "ad772845088ed8e99f87f90d4264b05ea97be35775305a02011af5ee35f0f4ce"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 14,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "d2bf5cacfb5ea9b519f964f2d7f4720c0e625ebc8f998d7360d70251e528f9c5",
      "arithmetic_steps": 9
    },
    "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."
  }
}