{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0076", "pilot_number": "R0054-27676", "number": 27676, "family_id": "qf-mod49-slln-scope-boundary", "title": { "zh-Hant": "第 27676 題：有限值IID強大數律", "en": "Question 27676: Outside-Scope Inputs Are Not General Strong-Law Counterexamples" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0076", "batch_id": "batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-strong-law-large-numbers-finite-valued-iid" ], "title_zh": "有限值IID強大數律", "stem_zh": "無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"nonfinite_support\",\"model\":{\"support_kind\":\"countably_infinite\",\"moment_status\":\"integrable\"}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "answer": { "kind": "expression", "value": "(nonfinite_support, countably_infinite, integrable, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)", "explanation_zh": "Wave6第十二層核對=(nonfinite_support, countably_infinite, integrable, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。" }, "difficulty": { "band": "undergraduate_core", "level": 1, "skills": [ "有限值IID強大數律" ] }, "variant": { "family_id": "qf-mod49-slln-scope-boundary", "seed": 202611182076, "parameters": { "mode": "nonfinite_support", "model": { "support_kind": "countably_infinite", "moment_status": "integrable" }, "domain": "Exact_finite_valued_SLLN_boundary", "operation": "slln-scope-boundary", "semantic_template": "slln-scope-boundary|{mode:\"nonfinite_support\",model:{moment_status:\"integrable\",support_kind:\"countably_infinite\"}}" } }, "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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-15", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0076", "batch_id": "batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "d82890ee53a8284a7bb7cd7b02d7e799c7af841e10afc765e93be7e5ee290f1e", "family_id": "qf-mod49-slln-scope-boundary", "seed": 202611182076, "semantic_template": "slln-scope-boundary|{mode:\"nonfinite_support\",model:{moment_status:\"integrable\",support_kind:\"countably_infinite\"}}" }, "fields": { "title": "Outside-Scope Inputs Are Not General Strong-Law Counterexamples", "stem": "Use mode=nonfinite_support, complete model={\"support_kind\":\"countably_infinite\",\"moment_status\":\"integrable\"}. Give (mode, support_kind, moment_status, this_finite_valued_theorem_applicable, scope).", "answer": { "kind": "expression", "value": "(nonfinite_support, countably_infinite, integrable, No, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)", "explanation": "Different marginals or nonfinite support do not meet this finite-valued IID theorem scope; this is not a claim that every general SLLN fails. A finite prefix does not establish an infinite process or limit. A proposed target different from the common expectation is not the theorem target. The exact result, retaining the requested order, is (nonfinite_support, countably_infinite, integrable, No, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)." }, "skills": [ "Outside-Scope Inputs Are Not General Strong-Law Counterexamples" ], "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": "無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={\"mode\":\"nonfinite_support\",\"model\":{\"support_kind\":\"countably_infinite\",\"moment_status\":\"integrable\"}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "en": "Use mode=nonfinite_support, complete model={\"support_kind\":\"countably_infinite\",\"moment_status\":\"integrable\"}. Give (mode, support_kind, moment_status, this_finite_valued_theorem_applicable, scope)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [slln-scope-boundary]", "after": "derived = [[mode, support_kind, moment_status, this_finite_valued_theorem_applicable, scope]]", "relation": "implies", "rule_id": "source_ordered_fields_without_JS", "conditions": [], "explanation": { "zh-Hant": "直接明列此操作與mode完整欄序，不依JavaScript、不由答案形狀猜角色；布林、字串、null與未作聲稱保持不同。", "en": "List the complete operation/mode field order without JavaScript or answer-shape inference;Boolean,string,null and an unclaimed result remain distinct." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。", "en": "Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [countably_infinite, integrable]", "after": "derived = [否]", "relation": "implies", "rule_id": "SLLN_outside_FINITE_valued_scope_NOT_general_counterexample", "conditions": [], "explanation": { "zh-Hant": "本節只處理finite-valued IID；非有限support不符合本節範圍，不表示一般SLLN失敗，integrable字串也不自動補齊其餘前提。", "en": "This section handles finite-valued IID only.Nonfinite support is outside this scope,not a general SLLN counterexample;an integrable label does not supply missing hypotheses." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。", "en": "Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct." } }, "arithmetic": null } ], "math_model": { "result": [ "nonfinite_support", "countably_infinite", "integrable", false, "outside_finite_valued_scope_not_a_counterexample_to_general_SLLN" ] }, "conclusion": { "canonical_value": "(nonfinite_support, countably_infinite, integrable, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)", "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-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations", "batch_path": "public/data/questions/batches/batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations/questions.jsonl", "batch_sha256": "ddb49de712a058f17353bffb58a7d023ec4a62dc04e72fd2aa4d83570a11cec2", "original_line": 76, "original_line_sha256": "f5488750eebd33495b349e246a560783ca202fce3638b48ffb659efec79cd13e", "question_compact_sha256": "d82890ee53a8284a7bb7cd7b02d7e799c7af841e10afc765e93be7e5ee290f1e", "english_row_compact_sha256": "3ea917748d3db388af5067a7a5727b0d47330d4e80a4e79612205c5fd17ed20c", "english_manifest_path": "public/data/i18n/editions/batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations.en.jsonl" }, "mko_bindings": { "mko-strong-law-large-numbers-finite-valued-iid": { "sha256": "14ad2e3637b7d7efdbf46bd6d640bf2637a5ab65b1f9ceafa6ff1a08565e9037", "english_sha256": "d7006cf0173ce35dcb02c4b0f80110b0124038bb778c5edc2903ca25a2569553", "original_path": "public/data/mko/strong-law-large-numbers-finite-valued-iid.json", "english_path": "public/data/i18n/editions/mko-strong-law-large-numbers-finite-valued-iid.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "ad40cc18f9292c43924a7679f3af46574a5284aa5447f5f7f78a0de98840acb8", "original_candidate_sha256": "c0a95cbff0596f36ea9c438a6170809496d0cdc7004b292f6cc3702f108e0e5d", "original_candidate_line_sha256": "c0a95cbff0596f36ea9c438a6170809496d0cdc7004b292f6cc3702f108e0e5d" }, "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-p55", "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": "0a76d8e93c08bb16998a0483f3dfc0504f269fc3e1982e6cd868cab0a2856d54", "question_first_witness_sha256": "09127b736c225714dfa0b7ceb0e6a6e66df27438b480cad8217d3c2f99ce9437" }, "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": "b318c7ae7d907615a247fb596ec8f18b505de7daa608723e9b174f59e4339cd2", "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." } }