{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261009-advance-20261013-r06-event-0093", "pilot_number": "R0011-06068", "number": 6068, "family_id": "qf-density13-event-occurrence-first-hit", "title": { "zh-Hant": "第 6068 題：觀測候選資格與第一個合法發生", "en": "Question 6068: Typed Observations, Event Occurrence, and First Hit" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261009-advance-20261013-r06-event-0093", "batch_id": "batch-20261009-advance-20261013-r06-event-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-event" ], "title_zh": "觀測候選資格與第一個合法發生", "stem_zh": "S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[100, 1, 0]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。", "answer": { "kind": "expression", "value": "([否, 是, 是], [不合樣本, 真, 假], 1)", "explanation_zh": "觀測資格與首發生=([否, 是, 是], [不合樣本, 真, 假], 1)。只把S內且屬E者列為發生，域外候選不合樣本；有限S不自動等於F=P(S)，集合資料不給概率或獨立性。" }, "difficulty": { "band": "upper_secondary", "level": 3, "skills": [ "觀測候選資格與第一個合法發生" ] }, "variant": { "family_id": "qf-density13-event-occurrence-first-hit", "seed": 202610136093, "parameters": { "n": 3, "E": [ 1 ], "outcomes": [ 100, 1, 0 ], "event_model": "full_powerset", "operation": "density13_event_occurrence_first_hit", "domain": "finite_declared_event_family", "semantic_template": "qf-density13-event-occurrence-first-hit/[\"outside\",\"member\",\"nonmember\"]" } }, "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": "2026-10-09", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261009-advance-20261013-r06-event-0093", "batch_id": "batch-20261009-advance-20261013-r06-event-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "a98812156039939cab559f120648f4fa87ee4afcd2edea5823c123898fdcf841", "family_id": "qf-density13-event-occurrence-first-hit", "seed": 202610136093, "semantic_template": "qf-density13-event-occurrence-first-hit/[\"outside\",\"member\",\"nonmember\"]" }, "fields": { "title": "Typed Observations, Event Occurrence, and First Hit", "stem": "S=Fin(3)={0,…,2}; the event family is explicitly F=P(S). E=[1], ordered outcomes=[100, 1, 0]. Give (sample-eligibility mask, True/False/invalid-outcome occurrence list, first legal E hit’s zero-based index or none).", "answer": { "kind": "expression", "value": "([No, Yes, Yes], [invalid-outcome, True, False], 1)", "explanation": "Only a legal sample-space value belonging to E is an occurrence; an outside candidate is invalid-outcome, not False. A finite S alone does not declare F=P(S); these set data assign neither probabilities nor independence. The exact result, retaining the requested order, is ([No, Yes, Yes], [invalid-outcome, True, False], 1)." }, "skills": [ "Typed Observations, Event Occurrence, and First Hit" ], "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": "S=Fin(n)，n=3；F=P(S)；E=[1]，有序outcomes=[100, 1, 0]。依序答 (樣本資格列表, 事件發生真／假／不合樣本列表, 首個合法E命中的0起索引或無)。", "en": "S=Fin(3)={0,…,2}; the event family is explicitly F=P(S). E=[1], ordered outcomes=[100, 1, 0]. Give (sample-eligibility mask, True/False/invalid-outcome occurrence list, first legal E hit’s zero-based index or none)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "S=Fin(3)=[0, 1, 2];declared event model=full_powerset", "after": "finite S alone does not specify its event family or a probability law", "relation": "implies", "rule_id": "declared_finite_event_family", "conditions": [], "explanation": { "zh-Hant": "有限樣本空間不自動指定F=P(S)；此處依題目宣告的事件族運算，集合資料不給概率、等可能性或獨立性。", "en": "A finite sample space does not automatically choose F=P(S).Use the declared event family;set data alone give no probabilities,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": "observation position=0;candidate outcome=100;inside S=否", "after": "event occurrence=不合樣本", "relation": "implies", "rule_id": "typed_event_occurrence_row", "conditions": [], "explanation": { "zh-Hant": "先檢基本結果是否在S，再判事件隸屬；域外不填成事件為假，位置索引與結果值不混同。", "en": "First check whether the outcome lies in S,then event membership.An outside candidate is not assigned False occurrence;observation position and outcome value differ." }, "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": "observation position=1;candidate outcome=1;inside S=是", "after": "event occurrence=真", "relation": "implies", "rule_id": "typed_event_occurrence_row", "conditions": [], "explanation": { "zh-Hant": "先檢基本結果是否在S，再判事件隸屬；域外不填成事件為假，位置索引與結果值不混同。", "en": "First check whether the outcome lies in S,then event membership.An outside candidate is not assigned False occurrence;observation position and outcome value differ." }, "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": "observation position=2;candidate outcome=0;inside S=是", "after": "event occurrence=假", "relation": "implies", "rule_id": "typed_event_occurrence_row", "conditions": [], "explanation": { "zh-Hant": "先檢基本結果是否在S，再判事件隸屬；域外不填成事件為假，位置索引與結果值不混同。", "en": "First check whether the outcome lies in S,then event membership.An outside candidate is not assigned False occurrence;observation position and outcome value differ." }, "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": "S005", "uses": [ "G001", "S004" ], "before": "legal event hits among ordered candidates;E=[1]", "after": "first hit position=1", "relation": "implies", "rule_id": "first_legal_event_hit_position", "conditions": [], "explanation": { "zh-Hant": "取有序觀測列中首個合法E命中的0起位置；空列或沒有命中答無，不補造觀測。", "en": "Return the first0-based position of a legal E-hit in the ordered list;an empty list or no hit gives none,without invented observations." }, "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": [ [ false, true, true ], [ "不合樣本", true, false ], "1" ] }, "conclusion": { "canonical_value": "([否, 是, 是], [不合樣本, 真, 假], 1)", "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-20261009-advance-20261013-r06-event-foundations", "batch_path": "public/data/questions/batches/batch-20261009-advance-20261013-r06-event-foundations/questions.jsonl", "batch_sha256": "2ed3cc2f0adb9a12f8e2c4de29b320306a65fe7af8296a1f1c5d0b14bc7776d9", "original_line": 93, "original_line_sha256": "60f7e2aecbeb3340dd47059501679454a6b8b9a33f309960d41237d5c57d090f", "question_compact_sha256": "a98812156039939cab559f120648f4fa87ee4afcd2edea5823c123898fdcf841", "english_row_compact_sha256": "b8be002f2efaaa1005e3c9d22e1cf652dc50b2eadc5a8238680813d6a58cbd5d", "english_manifest_path": "public/data/i18n/editions/batch-20261009-advance-20261013-r06-event-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261009-advance-20261013-r06-event-foundations.en.jsonl" }, "mko_bindings": { "mko-event": { "sha256": "5962ae6672cb79c34888bdda4ac66de557a4f9b21243f2445414d7dd326b9c74", "english_sha256": "12d8199c90226e08b52a3f9cf27ce44053dc8473e8bab4280145aea146a4c261", "original_path": "public/data/mko/event.json", "english_path": "public/data/i18n/editions/mko-event.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "5b2ce631281eb24b279908f47c6de66fa60d326520852879d324c4f3ac653970", "original_candidate_sha256": "5c597648d65c41cccc8f4c65cbd5a6337ff5a7728fd01ec38532199375bffcc6", "original_candidate_line_sha256": "5c597648d65c41cccc8f4c65cbd5a6337ff5a7728fd01ec38532199375bffcc6" }, "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-20261026-005-p12", "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": "b9bbc1c947f477a9c4bb5a579368ac5265f2da4572ce612c30f3633ecaf4ae80", "question_first_witness_sha256": "93f720df3ab3af13a792a3e6b443728e3c2a56276df839911f36569333236c55" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 5, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "b88e6f19367bb131c6788444c347092277de185393f8d5ac1167b83993092b58", "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." } }