{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261014-advance-20261030-r07-convergence-in-probability-0079",
  "pilot_number": "R0029-15054",
  "number": 15054,
  "family_id": "qf-mod30-convprob-eventual-equality",
  "title": {
    "zh-Hant": "第 15054 題：依機率收斂",
    "en": "Question 15054: Eventual Equality Supplies a Conditional Universal-Tail Certificate"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261014-advance-20261030-r07-convergence-in-probability-0079",
    "batch_id": "batch-20261014-advance-20261030-r07-convergence-in-probability-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-convergence-in-probability"
    ],
    "title_zh": "依機率收斂",
    "stem_zh": "共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":4,\"n\":4}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。",
    "answer": {
      "kind": "expression",
      "value": "(4, 4, 0, 是, eventual_equality_universal_tail_certificate)",
      "explanation_zh": "Wave4第四層核對=(4, 4, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 1,
      "skills": [
        "依機率收斂"
      ]
    },
    "variant": {
      "family_id": "qf-mod30-convprob-eventual-equality",
      "seed": 202610307079,
      "parameters": {
        "settling_index": 4,
        "n": 4,
        "domain": "Symbolic_deviation_probability_tail",
        "operation": "convprob-eventual-equality",
        "semantic_template": "qf-mod30-convprob-eventual-equality/{\"n\":4,\"settling_index\":4}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_finite_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、一般域／Hilbert／martingale／無限基數／一般收斂、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-20261030-r07-convergence-in-probability-0079",
    "batch_id": "batch-20261014-advance-20261030-r07-convergence-in-probability-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "9700366a38e1fb0f7433d1a57f481be0f7090cc928e4f07366c1c2937149b155",
      "family_id": "qf-mod30-convprob-eventual-equality",
      "seed": 202610307079,
      "semantic_template": "qf-mod30-convprob-eventual-equality/{\"n\":4,\"settling_index\":4}"
    },
    "fields": {
      "title": "Eventual Equality Supplies a Conditional Universal-Tail Certificate",
      "stem": "On the declared common probability space assume X_n=X almost surely for every n≥settling_index=4; inspect n=4. Give (settling_index,n,zero_probability_status,certificate?,eventual_equality_universal_tail_certificate).",
      "answer": {
        "kind": "expression",
        "value": "(4, 4, 0, Yes, eventual_equality_universal_tail_certificate)",
        "explanation": "At or beyond the settling index the deviation probability is0 for every positive epsilon. Earlier not_yet_zero means this certificate has not yet supplied a zero value; it does not independently establish a positive deviation probability. The final Yes is the conditional eventual-equality tail certificate, not a proof from this single inspected index. The exact result, retaining the requested order, is (4, 4, 0, Yes, eventual_equality_universal_tail_certificate)."
      },
      "skills": [
        "Eventual Equality Supplies a Conditional Universal-Tail Certificate"
      ],
      "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": "共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":4,\"n\":4}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。",
        "en": "On the declared common probability space assume X_n=X almost surely for every n≥settling_index=4; inspect n=4. Give (settling_index,n,zero_probability_status,certificate?,eventual_equality_universal_tail_certificate)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "declared common probability space;X_k=X almost surely for EVERY k>=4;inspected n=4",
      "after": "inspected deviation status=0;for EVERY positive epsilon,all k>=4 have deviation probability0",
      "relation": "implies",
      "rule_id": "eventual_equality_full_tail_not_one_index",
      "conditions": [],
      "explanation": {
        "zh-Hant": "用的是永遠尾段a.s.相等的明示前提，不是由這一個n猜規律。n較早的not_yet_zero只說此證書尚未給零，不是已知正機率；全尾段0對每個epsilon都給依機率收斂的條件證書。",
        "en": "Use the explicitly declared all-later almost-sure equality,not a pattern guessed from this index.Earlier not_yet_zero only means the certificate has not supplied0,not a known positive probability.The all-epsilon zero tail gives the conditional convergence-in-probability certificate."
      },
      "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": [
      4,
      4,
      "0",
      true,
      "eventual_equality_universal_tail_certificate"
    ]
  },
  "conclusion": {
    "canonical_value": "(4, 4, 0, 是, eventual_equality_universal_tail_certificate)",
    "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": {
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      "batch_path": "public/data/questions/revisions/ocme-parameter-revision-20261017/batch-20261014-advance-20261030-r07-convergence-in-probability-foundations/questions.jsonl",
      "batch_sha256": "d7c47d3e90c56e1c29fd84b1df706b21e2a32f6cb096069ad21f4d2c85515aa8",
      "original_line": 79,
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      "english_row_compact_sha256": "c52bcba1a8fde8e4c9713213eb3b4ea8e0745876f9eedab85a7eaee2c9429f58",
      "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261030-r07-convergence-in-probability-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261030-r07-convergence-in-probability-foundations.en.jsonl"
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        "english_sha256": "662ebc13877df7163257281afba7044949cf6e065b78a7bd62b854e3ad9fbbff",
        "original_path": "public/data/mko/convergence-in-probability.json",
        "english_path": "public/data/i18n/editions/mko-convergence-in-probability.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "54de60dca082018923bf089f2b1eb0a6666cc401916115af792056c8bae935db",
    "original_candidate_sha256": "9f2b1579dd6d26e4b141f258e1e4f4a6710f4bdbcb3361e9a86441d5c67769db",
    "original_candidate_line_sha256": "9f2b1579dd6d26e4b141f258e1e4f4a6710f4bdbcb3361e9a86441d5c67769db"
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      "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-20261026-007-p30",
    "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": {
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    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
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    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
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    "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."
  }
}