{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261008-advance-20261011-r06-sample-space-0096", "pilot_number": "R0008-04971", "number": 4971, "family_id": "qf-density11-sample-outcome-event-masks", "title": { "zh-Hant": "第 4971 題：基本結果與事件的有序資格", "en": "Question 4971: Outcome and Event Membership Masks" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261008-advance-20261011-r06-sample-space-0096", "batch_id": "batch-20261008-advance-20261011-r06-sample-space-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-sample-space" ], "title_zh": "基本結果與事件的有序資格", "stem_zh": "基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[0, 4, 3]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。", "answer": { "kind": "expression", "value": "([是, 是, 是], [否, 否, 是])", "explanation_zh": "可能結果與事件資格=([是, 是, 是], [否, 否, 是])。先按固定S檢查結果，再按事件查隸屬；事件不是單一結果，域外候選只供待查，不指定概率。" }, "difficulty": { "band": "lower_secondary", "level": 3, "skills": [ "基本結果與事件的有序資格" ] }, "variant": { "family_id": "qf-density11-sample-outcome-event-masks", "seed": 202610116096, "parameters": { "n": 6, "E": [ 1, 2, 3 ], "candidates": [ 0, 4, 3 ], "operation": "density11_sample_outcome_event_masks", "domain": "finite_possible_outcome_protocol", "semantic_template": "qf-density11-sample-outcome-event-masks/[\"outside_event\",\"outside_event\",\"in_event\"]" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_integer_rational_arithmetic", "producer_finite_enumeration", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-08", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261008-advance-20261011-r06-sample-space-0096", "batch_id": "batch-20261008-advance-20261011-r06-sample-space-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "eb69826b3c8bbcc136d260b100aba30331212f32306f73a751e8fbd2cdd86f14", "family_id": "qf-density11-sample-outcome-event-masks", "seed": 202610116096, "semantic_template": "qf-density11-sample-outcome-event-masks/[\"outside_event\",\"outside_event\",\"in_event\"]" }, "fields": { "title": "Outcome and Event Membership Masks", "stem": "Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[0, 4, 3]. Give (membership-in-space mask, membership-in-E mask) using Yes/No.", "answer": { "kind": "expression", "value": "([Yes, Yes, Yes], [No, No, Yes])", "explanation": "Check the fixed sample space and the event separately; an event is not a single outcome, outside candidates are only inputs to be checked, and no probabilities are assigned. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [No, No, Yes])." }, "skills": [ "Outcome and Event Membership Masks" ], "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": "基本可能結果S={0,…,5}，事件E=[1, 2, 3]⊆S；有序候選=[0, 4, 3]。依序答 (各候選是否屬S, 各候選是否屬E) 的兩個是／否列表。", "en": "Elementary outcomes are Fin(6)={0,…,5}, event E=[1, 2, 3] is a subset of the space, and ordered candidates=[0, 4, 3]. Give (membership-in-space mask, membership-in-E mask) using Yes/No." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "explicit finite possible-outcome protocol", "after": "no probability law,equiprobability or independence inferred", "relation": "implies", "rule_id": "possible_outcomes_not_probabilities", "conditions": [], "explanation": { "zh-Hant": "這裡列可能基本結果、記錄或事件資格，不指定概率；所有組合可發生不等於等可能或兩階段獨立。", "en": "These tasks list possible outcomes,recordings or event membership without assigning probabilities.All combinations being possible does not imply equiprobability or independence." }, "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": "candidate=0;S=[0, 1, 2, 3, 4, 5];E=[1, 2, 3]", "after": "in S=是;in E=否", "relation": "implies", "rule_id": "possible_outcome_and_event_membership", "conditions": [], "explanation": { "zh-Hant": "事件E是S的子集合，不是一個單獨的結果；域外候選不在E中，並保留原候選列序。", "en": "Event E is a subset of S,not a single outcome.An outside candidate is not in E;retain the original candidate order." }, "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": "candidate=4;S=[0, 1, 2, 3, 4, 5];E=[1, 2, 3]", "after": "in S=是;in E=否", "relation": "implies", "rule_id": "possible_outcome_and_event_membership", "conditions": [], "explanation": { "zh-Hant": "事件E是S的子集合，不是一個單獨的結果；域外候選不在E中，並保留原候選列序。", "en": "Event E is a subset of S,not a single outcome.An outside candidate is not in E;retain the original candidate order." }, "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": "candidate=3;S=[0, 1, 2, 3, 4, 5];E=[1, 2, 3]", "after": "in S=是;in E=是", "relation": "implies", "rule_id": "possible_outcome_and_event_membership", "conditions": [], "explanation": { "zh-Hant": "事件E是S的子集合，不是一個單獨的結果；域外候選不在E中，並保留原候選列序。", "en": "Event E is a subset of S,not a single outcome.An outside candidate is not in E;retain the original candidate order." }, "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": [ [ true, true, true ], [ false, false, true ] ] }, "conclusion": { "canonical_value": "([是, 是, 是], [否, 否, 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-20261008-advance-20261011-r06-sample-space-foundations", "batch_path": "public/data/questions/batches/batch-20261008-advance-20261011-r06-sample-space-foundations/questions.jsonl", "batch_sha256": "a3c5671d763c26ec164aeff524d6308ad28eb3415359ccb057a20ba767acdcc9", "original_line": 96, "original_line_sha256": "9ec8c81868bba8b4dfcf3dc913677f6c525d4f410e7c9cc83de2bf25722cd174", "question_compact_sha256": "eb69826b3c8bbcc136d260b100aba30331212f32306f73a751e8fbd2cdd86f14", "english_row_compact_sha256": "cb7992395e54b11499404bfcb3d017c8127cacfedb704e9e062fad43aeda453d", "english_manifest_path": "public/data/i18n/editions/batch-20261008-advance-20261011-r06-sample-space-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261008-advance-20261011-r06-sample-space-foundations.en.jsonl" }, "mko_bindings": { "mko-sample-space": { "sha256": "c58b0d07252ece257a4143fd10f0f25b249023f4ed50bc6d393f4752a91267f7", "english_sha256": "ba452c266ef8c6ab4b549a3ccb6bc04a19fc7fafef1934d17f821c9ef4c04756", "original_path": "public/data/mko/sample-space.json", "english_path": "public/data/i18n/editions/mko-sample-space.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "6dc34e24b0f43c50e49365ca1a1153175f8661d5290c9236df5527bb047157eb", "original_candidate_sha256": "21fff67de829f1df72ae4ce88354f96a3729c2ccf5effe9455094b67b2c464dc", "original_candidate_line_sha256": "21fff67de829f1df72ae4ce88354f96a3729c2ccf5effe9455094b67b2c464dc" }, "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-20261026-004-p9", "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": "b6e05a3e8193a93db505dbf337528fca72e2e41528b1e92b698a3f0683d74289", "question_first_witness_sha256": "caa8693baf0b91acd09a20215d1aa6954ae513fc0b0814f26ac1c8c834b60d67" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 4, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "6601e6a6c8911a86d601cb7a0611a810fcc53b4a528ff0333fb6b92c4798ac70", "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." } }