{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20260913-finite-set-membership-0022", "pilot_number": "R0063-32072", "number": 32072, "family_id": "qf-finite-set-membership", "title": { "zh-Hant": "第 32072 題：有限集合隸屬判定", "en": "Question 32072: Finite Set Membership" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20260913-finite-set-membership-0022", "batch_id": "batch-20260913-foundational-language", "language": "zh-Hant", "source_mko_ids": [ "mko-set-membership" ], "title_zh": "有限集合隸屬判定", "stem_zh": "令 A={211、212} 為明示列舉的有限集合。217 是否滿足 217∈A？", "answer": { "kind": "choice", "value": "否", "choices": [ "是", "否" ], "explanation_zh": "217 未出現在 A 的明示列舉中，因此 217∉A；本題只判定這個有限列舉。" }, "difficulty": { "band": "upper_secondary", "level": 1, "skills": [ "集合隸屬", "有限列舉" ] }, "variant": { "family_id": "qf-finite-set-membership", "seed": 20260954, "parameters": { "elements": [ 211, 212 ], "query": 217, "scenario": "unlisted_element", "semantic_template": "finite-set/unlisted_element/elements-211,212/query-217" } }, "verification": { "status": "candidate", "checks": [ "schema_pending", "independent_recomputation_pending" ], "warning_zh": "本題僅依明示的有限參數作分類或重算；不構成普遍證明，且尚未人工審查或發布。" }, "provenance": { "generator_role": "question_producer", "generator_model": "GPT-5.6 Terra", "generated_at": "2026-09-13", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20260913-finite-set-membership-0022", "batch_id": "batch-20260913-foundational-language", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "74c4ab1fcfb693a7d5c4f8b9a83d95b26889c61cbc9e2be905f9c0b3cf1bc8b2", "family_id": "qf-finite-set-membership", "seed": 20260954, "semantic_template": "finite-set/unlisted_element/elements-211,212/query-217" }, "fields": { "title": "Finite Set Membership", "stem": "Let A={211, 212} be an explicitly enumerated finite set. Does 217 satisfy 217∈A?", "answer": { "kind": "choice", "value": "No", "choices": [ "Yes", "No" ], "explanation": "217 does not occur in the explicit enumeration of A, so 217∉A." }, "skills": [ "set membership", "finite enumeration" ], "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": "令 A={211、212} 為明示列舉的有限集合。217 是否滿足 217∈A？", "en": "Let A={211, 212} be an explicitly enumerated finite set. Does 217 satisfy 217∈A?" } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-finite-set-membership, no-required-operation, no-required-domain, [scenario]]", "after": "derived = [[typed_atom_membership_YesNo_STRING]]", "relation": "implies", "rule_id": "R63_SOURCE_bank_keys_operation_domain_output_roles_metadata_not_oracle", "conditions": [], "explanation": { "zh-Hant": "BASE來源沒有本輪legacy的通用operation/domain/額外欄位禁令；保metadata而不當答案。PULSE與legacy則核來源精確欄位、operation及domain。不要把tuple、/1或輸入界強套全部題族。", "en": "BASE sources do not acquire a generic legacy operation/domain or unknown-metadata ban.Retain metadata WITHOUT using it as an answer oracle.PULSE/legacy enforce their exact source keys,operation/domain.Do not impose universal tuples,/1 or input bounds." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "依原始輸入、型別、論域及明示前提反向代回核對；不是由結論唯一還原前提。來源綁定候選、獨立審查、形式證明與發布各自分開。", "en": "Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [0, [Number, 211], [Number, 217]]", "after": "derived = [否]", "relation": "implies", "rule_id": "Membership_EACH_original_enumerated_atom_TYPE_aware_equality", "conditions": [], "explanation": { "zh-Hant": "逐原列舉元素與query比型別及值；不把False當0，不把字串數字強轉，也不因重複列舉先拒絕。JSON不同reference節點不以deep equality冒充同一JS物件。", "en": "Compare EVERY ORIGINAL enumerated atom with the query by type/value.Do not identify False with0 or coerce numeric strings,and do not reject repeated enumeration.Distinct JSON reference nodes do not become the same JS object by deep equality." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "依原始輸入、型別、論域及明示前提反向代回核對；不是由結論唯一還原前提。來源綁定候選、獨立審查、形式證明與發布各自分開。", "en": "Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "source roles = [1, [Number, 212], [Number, 217]]", "after": "derived = [否]", "relation": "implies", "rule_id": "Membership_EACH_original_enumerated_atom_TYPE_aware_equality", "conditions": [], "explanation": { "zh-Hant": "逐原列舉元素與query比型別及值；不把False當0，不把字串數字強轉，也不因重複列舉先拒絕。JSON不同reference節點不以deep equality冒充同一JS物件。", "en": "Compare EVERY ORIGINAL enumerated atom with the query by type/value.Do not identify False with0 or coerce numeric strings,and do not reject repeated enumeration.Distinct JSON reference nodes do not become the same JS object by deep equality." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "依原始輸入、型別、論域及明示前提反向代回核對；不是由結論唯一還原前提。來源綁定候選、獨立審查、形式證明與發布各自分開。", "en": "Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "source roles = [[[Number, 211], [Number, 212]], [Number, 217], [scenario]]", "after": "derived = [[否, 否], 否]", "relation": "implies", "rule_id": "Membership_COMPLETE_any_match_ignores_scenario_metadata", "conditions": [], "explanation": { "zh-Hant": "任何一項真正吻合才Yes，全部不吻合則No。scenario等欄位保留但不當truth oracle；不套另一集合題的unique／SAFE／整數限制。本輪凍結例皆小整數，不宣稱任意unsafe JS數值已認證。", "en": "Yes requires an ACTUAL match;No requires all comparisons false.Retain scenario/other metadata WITHOUT treating it as a truth oracle.Do not import another set bank uniqueness/SAFE/integer restriction.This frozen slice uses small integers,not universal unsafe-JS certification." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "依原始輸入、型別、論域及明示前提反向代回核對；不是由結論唯一還原前提。來源綁定候選、獨立審查、形式證明與發布各自分開。", "en": "Reverse-check ORIGINAL inputs,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate." } }, "arithmetic": null } ], "math_model": { "result": "否" }, "conclusion": { "canonical_value": "否", "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-20260913-foundational-language", "batch_path": "public/data/questions/batches/batch-20260913-foundational-language/questions.jsonl", "batch_sha256": "f9197588b4d22a517e5a50d721638afb80a8f8f03cc65234ee357d2ba1823172", "original_line": 42, "original_line_sha256": "099071ca30f05e4fcb2874b2458dce86b133341532c2e8742852218532b485cf", "question_compact_sha256": "74c4ab1fcfb693a7d5c4f8b9a83d95b26889c61cbc9e2be905f9c0b3cf1bc8b2", "english_row_compact_sha256": "2a85a06d5d7d9e7d94c34616ead8f3424a8397a32e1917dd5b8bf12050d1bc24", "english_manifest_path": "public/data/i18n/editions/batch-20260913-foundational-language.en.json", "english_rows_path": "public/data/i18n/questions/batch-20260913-foundational-language.en.jsonl" }, "mko_bindings": { "mko-set-membership": { "sha256": "2a438aa79c23e6d37869e1e63eb48420bcf2f114f44b58fe5bea386076b4f0db", "english_sha256": "3c93982fdf37b764e4dcea079fba39532642656286a8cfbae67470b6274a4e38", "original_path": "public/data/mko/set-membership.json", "english_path": "public/data/i18n/editions/mko-set-membership.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "f3271d6047df957dbf3d61120bd3dd374784c828b17849887e14caf59d93f745", "original_candidate_sha256": "73dee49b899d1fe3dbae62cfff92d251ed2e012643db2d2a8d2bcc710611eda2", "original_candidate_line_sha256": "73dee49b899d1fe3dbae62cfff92d251ed2e012643db2d2a8d2bcc710611eda2" }, "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-20261026-011-p64", "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": "acf03b776f4855e3869810bcbecf1116e3a2b11dfb1e2a5dfbcf8135ad24a7d0", "question_first_witness_sha256": "eadbbac3220988b52754f32450fb536d627217306d1ce28a49134f56c21bfa88" }, "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": "bca71e82a3b603522a7c8b63fcbc81f6ac763288e5b122c1663da40e54865d65", "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." } }