{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20260919-integer-membership-0008", "pilot_number": "R0064-32533", "number": 32533, "family_id": "qf-integer-membership", "title": { "zh-Hant": "第 32533 題：qf-integer-membership", "en": "Question 32533: Integer Membership" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20260919-integer-membership-0008", "batch_id": "batch-20260919-integer-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-integer" ], "title_zh": "qf-integer-membership", "stem_zh": "-7 是否屬於整數集合 Z？", "answer": { "kind": "choice", "value": "是", "choices": [ "是", "否" ], "explanation_zh": "-7 沒有小數或分母表示，且是正整數、零或負整數。" }, "difficulty": { "band": "upper_secondary", "level": 3, "skills": [ "整數成員" ] }, "variant": { "family_id": "qf-integer-membership", "seed": 20260927, "parameters": { "raw": "-7", "integer": true, "semantic_template": "qf-integer-membership/{\"integer\":true,\"raw\":\"-7\"}" } }, "verification": { "status": "candidate", "checks": [ "schema_pending", "independent_recomputation_pending" ], "warning_zh": "本題是有限候選重算；不構成普遍證明、形式 Evidence 或人工審查。" }, "provenance": { "generator_role": "question_producer", "generator_model": "GPT-5.6 Terra", "generated_at": "2026-09-19", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20260919-integer-membership-0008", "batch_id": "batch-20260919-integer-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "261d660959003db265e1c9c425bad73587ceded06f724b03e39fcf33310de002", "family_id": "qf-integer-membership", "seed": 20260927, "semantic_template": "qf-integer-membership/{\"integer\":true,\"raw\":\"-7\"}" }, "fields": { "title": "Integer Membership", "stem": "Does -7 belong to the integer set Z?", "answer": { "kind": "choice", "value": "Yes", "choices": [ "Yes", "No" ], "explanation": "-7 is a positive integer, zero, or a negative integer, so it belongs to Z." }, "skills": [ "integer membership" ], "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": "-7 是否屬於整數集合 Z？", "en": "Does -7 belong to the integer set Z?" } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-integer-membership, no-required-operation, no-required-domain, []]", "after": "derived = [[mathematical_membership_YesNo_STRING]]", "relation": "implies", "rule_id": "R64_SOURCE_exact_legacy_interface_BASE_metadata_AND_output_roles", "conditions": [], "explanation": { "zh-Hant": "legacy核來源精確欄位及operation/domain；BASE整數保metadata但不當oracle。先分NUMBER、字串、fractionpair或vector等式，不強套同一格式；原中英／AST／status不變。", "en": "Legacy banks enforce their exact source keys/operation/domain.BASE integers retain metadata without treating it as an oracle.Distinguish NUMBER,string,fraction pair and vector equality formats;retain original bilingual data/AST/status." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。", "en": "Reverse-check ORIGINAL data,field roles,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 = [-7, 是]", "after": "derived = [是, -7/1, 是]", "relation": "implies", "rule_id": "Integer_RAW_ASCII_syntax_flag_verified_SEPARATE_exact_numeric_value", "conditions": [], "explanation": { "zh-Hant": "先驗raw字串與原Boolean旗標符合明示ASCII記法，再以精確值判整數。本輪No都是真正半整數；字串1.0的parser拒絕不能推成實數1.0不在Z。超出本凍結語義的歧義例不冒充數學No。", "en": "FIRST verify the raw string and Boolean flag against the declared ASCII syntax,THEN classify the exact value.The frozen No cases are genuine half-integers.A parser rejecting string1.0 does NOT prove real1.0 is outside Z.Ambiguous out-of-slice cases are not false mathematical No answers." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。", "en": "Reverse-check ORIGINAL data,field roles,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 = [-7, -7/1]", "after": "derived = [-7, 是]", "relation": "implies", "rule_id": "Integer_EXACT_value_has_denominator1_signed_integer_definition", "conditions": [], "explanation": { "zh-Hant": "最簡分母1表示值就是整數n，正整數、0及負整數都屬Z；不是從字面長相猜，也沒有把原raw改成別的資料。", "en": "A reduced denominator1 means the value IS the integer n.Positive integers,zero and negative integers all belong to Z.This is not an appearance guess or a rewrite of original raw data." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。", "en": "Reverse-check ORIGINAL data,field roles,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": "是" }, "conclusion": { "canonical_value": "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-20260919-integer-foundations", "batch_path": "public/data/questions/batches/batch-20260919-integer-foundations/questions.jsonl", "batch_sha256": "529bee0e669d336089b9b84409bed458d54dfcb02b3696e430887c1ed49bb6c4", "original_line": 8, "original_line_sha256": "23a696249cc6b76503dc2558ce88f8cd9a0c74b80e02d6204b5a9c6019032f56", "question_compact_sha256": "261d660959003db265e1c9c425bad73587ceded06f724b03e39fcf33310de002", "english_row_compact_sha256": "177a00c621c853652c4c85b83a574a3c1488e9dca55039b67132343bdb8cc204", "english_manifest_path": "public/data/i18n/editions/batch-20260919-integer-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20260919-integer-foundations.en.jsonl" }, "mko_bindings": { "mko-integer": { "sha256": "e1e3776eaf56e003f2eb07a66a39c7e221d26759df8fbc4db2652a2733318d66", "english_sha256": "24d4c8918b430c9dea2f942bb60a89a295d2386bf3bd9c14731ad56e0fb49034", "original_path": "public/data/mko/integer.json", "english_path": "public/data/i18n/editions/mko-integer.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "528186aa825c3054db15f4ce0a03ad58f72be7e7eb5bb236c4cc7ef34ff5a470", "original_candidate_sha256": "f1068e2acff71612f1f92418a6c71d482d86ee1e43ee30129be9665e64ae5e05", "original_candidate_line_sha256": "f1068e2acff71612f1f92418a6c71d482d86ee1e43ee30129be9665e64ae5e05" }, "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-p65", "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": "8b9ea3ddfab468e9e3f0a0fc0f7682987d5e030be0d7c8860fd85df19cbe183b", "question_first_witness_sha256": "066bfeab8fc279706861faade71b9a18a61a25235fc48700092f0488d2a6da6a" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 3, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "04d3f7b1b53a2175e0fd8707acf3c0dbdc2b84c660bca89bf8f716e25f5ad050", "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." } }