{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261014-advance-20261105-r07-weak-law-large-numbers-0091", "pilot_number": "R0037-19266", "number": 19266, "family_id": "qf-mod36-wlln-finite-simulation-boundary", "title": { "zh-Hant": "第 19266 題：弱大數律", "en": "Question 19266: A Finite Simulation Does Not Certify the Whole IID Sequence" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261014-advance-20261105-r07-weak-law-large-numbers-0091", "batch_id": "batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-weak-law-large-numbers" ], "title_zh": "弱大數律", "stem_zh": "IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[15,16],\"variance\":[16,17],\"epsilon\":[1,17],\"prefix_sample_means\":[[16,17],[17,18],[18,19]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "answer": { "kind": "expression", "value": "(15/16, 1/17, [16/17, 17/18, 18/19], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)", "explanation_zh": "Wave5第五層核對=(15/16, 1/17, [16/17, 17/18, 18/19], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。" }, "difficulty": { "band": "undergraduate_core", "level": 2, "skills": [ "弱大數律" ] }, "variant": { "family_id": "qf-mod36-wlln-finite-simulation-boundary", "seed": 202611057091, "parameters": { "mean": [ 15, 16 ], "variance": [ 16, 17 ], "epsilon": [ 1, 17 ], "prefix_sample_means": [ [ 16, 17 ], [ 17, 18 ], [ 18, 19 ] ], "iid_certificate": "finite_simulation_only", "domain": "Symbolic_iid_Chebyshev_WLLN", "operation": "wlln-finite-simulation-boundary", "semantic_template": "qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,17],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[15,16],\"prefix_sample_means\":[[16,17],[17,18],[18,19]],\"variance\":[16,17]}" } }, "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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、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-20261105-r07-weak-law-large-numbers-0091", "batch_id": "batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "b8deac9566b721573a936e449c5b8660f655ae068a7dfe94c54eef7cedc938be", "family_id": "qf-mod36-wlln-finite-simulation-boundary", "seed": 202611057091, "semantic_template": "qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,17],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[15,16],\"prefix_sample_means\":[[16,17],[17,18],[18,19]],\"variance\":[16,17]}" }, "fields": { "title": "A Finite Simulation Does Not Certify the Whole IID Sequence", "stem": "Use declared mean=15/16, positive finite variance=16/17, and iid_certificate=finite_simulation_only. In the symbolic theorem families this marker supplies the premise of common mean/variance and IID for every finite subfamily of the whole sequence; a token or finite simulation is not independent proof of that premise. Independence then gives Var(sample mean_n)=variance/n and Chebyshev controls P(|sample mean_n−mean|≥epsilon). This finite-variance WLLN slice claims convergence in probability, not the strong law, CLT or finite-n equality with a limit. Positive epsilon=1/17, finite prefix of sample means=[16/17, 17/18, 18/19]. The supplied marker is finite_simulation_only, not the symbolic whole-sequence premise. Give (mean, epsilon, prefix_sample_means, sufficient, boundary).", "answer": { "kind": "expression", "value": "(15/16, 1/17, [16/17, 17/18, 18/19], No, finite_simulation_not_IID_certificate_or_WLLN_proof)", "explanation": "Retain the exact observed prefix and No for sufficiency. No finite prefix alone proves IID for arbitrary finite subfamilies, the WLLN tail or a stronger convergence mode. The exact result, retaining the requested order, is (15/16, 1/17, [16/17, 17/18, 18/19], No, finite_simulation_not_IID_certificate_or_WLLN_proof)." }, "skills": [ "A Finite Simulation Does Not Certify the Whole IID Sequence" ], "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": "IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[15,16],\"variance\":[16,17],\"epsilon\":[1,17],\"prefix_sample_means\":[[16,17],[17,18],[18,19]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "en": "Use declared mean=15/16, positive finite variance=16/17, and iid_certificate=finite_simulation_only. In the symbolic theorem families this marker supplies the premise of common mean/variance and IID for every finite subfamily of the whole sequence; a token or finite simulation is not independent proof of that premise. Independence then gives Var(sample mean_n)=variance/n and Chebyshev controls P(|sample mean_n−mean|≥epsilon). This finite-variance WLLN slice claims convergence in probability, not the strong law, CLT or finite-n equality with a limit. Positive epsilon=1/17, finite prefix of sample means=[16/17, 17/18, 18/19]. The supplied marker is finite_simulation_only, not the symbolic whole-sequence premise. Give (mean, epsilon, prefix_sample_means, sufficient, boundary)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source operation=wlln-finite-simulation-boundary;original snapshot and mathematics retained", "after": "explicit ordered source output fields=[mean, epsilon, prefix_sample_means, sufficient, boundary]", "relation": "implies", "rule_id": "source_ordered_interface_explicit_without_javascript", "conditions": [], "explanation": { "zh-Hant": "原題快照保留歷史介面標記；本頁直接列原始欄位順序，不需JavaScript或查外部表。欄位名字本身不自動是數學證據，No依各題的聲稱範圍解讀。", "en": "Retain the historical interface marker in the original snapshot while listing ordered source fields here,without JavaScript or external lookup.Field names are not mathematical evidence,and No retains the operation's specific 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 declared mean=15/16;positive variance=16/17;epsilon=1/17;original finite prefix=[16/17, 17/18, 18/19];certificate=finite_simulation_only", "after": "finite simulation alone supplies NO whole-sequence IID premise or all-n probability tail;finite_simulation_not_IID_certificate_or_WLLN_proof", "relation": "implies", "rule_id": "wlln_finite_data_No_not_theorem_or_convergence_negation", "conditions": [], "explanation": { "zh-Hant": "連空prefix也可保留。有限列數值或接近mean不證任意有限子族的IID、共同moments或全部後續n的機率界；No不宣稱未指定序列必不收斂，也不否定WLLN定理。", "en": "Retain even an empty prefix.Finite values or proximity to a mean do not certify IID for arbitrary finite subfamilies,common moments or all-later probability bounds.The No does not prove an unspecified sequence divergent or refute the WLLN." }, "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": [ "15/16", "1/17", [ "16/17", "17/18", "18/19" ], false, "finite_simulation_not_IID_certificate_or_WLLN_proof" ] }, "conclusion": { "canonical_value": "(15/16, 1/17, [16/17, 17/18, 18/19], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)", "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-20261105-r07-weak-law-large-numbers-foundations", "batch_path": "public/data/questions/batches/batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations/questions.jsonl", "batch_sha256": "cb37c1b02120639bde918f12fac038639408d2229daab60e5de8ed9750046d5b", "original_line": 91, "original_line_sha256": "b35ee240ffac3ea8897791778ae0480c4c58931fd7079cb5d47646f21c73ead9", "question_compact_sha256": "b8deac9566b721573a936e449c5b8660f655ae068a7dfe94c54eef7cedc938be", "english_row_compact_sha256": "4edacc709e881cde30128c6dad81a1eb3c61eb9316d0c17d6abff85be8df1add", "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations.en.jsonl" }, "mko_bindings": { "mko-weak-law-large-numbers": { "sha256": "7eb5ea7326a95ec1926f661b129d1f6ed74f95c53574aea5f3878111f80bb55c", "english_sha256": "cbabd753c9362d2298518ae3dd4332e7dc4007f7b436746fdb53dd41565de8a3", "original_path": "public/data/mko/source13-20261018-weak-law-large-numbers.json", "english_path": "public/data/i18n/editions/mko-weak-law-large-numbers.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "7be57d88eceb13736454f82dd18bb3c4ec9d30c0367f974dcefdf8990dc4e3cb", "original_candidate_sha256": "c3d5c7cda67df668e3f371391894c0e67754f72b582ec95148bc0651974f4898", "original_candidate_line_sha256": "c3d5c7cda67df668e3f371391894c0e67754f72b582ec95148bc0651974f4898" }, "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-20261026-008-p38", "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": "065507b602ceee60cf47a700d387a51940e0c6724c35a3336a7a7948a199ed80", "question_first_witness_sha256": "7203f33b030792559673b0fee520a8c0e70903c4dd970b35293aa40852f333d6" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 2, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "d26a63e0d2dc86cfdeb7b8095419e65d3bdc43916aaf00282de5e6116d3f6f5c", "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." } }