{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20260920-rational-reduced-form-0020", "pilot_number": "R0068-34820", "number": 34820, "family_id": "qf-rational-reduced-form", "title": { "zh-Hant": "第 34820 題：qf-rational-reduced-form", "en": "Question 34820: Reduced Rational Form" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20260920-rational-reduced-form-0020", "batch_id": "batch-20260920-rational-number-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-rational-number" ], "title_zh": "qf-rational-reduced-form", "stem_zh": "將 -120/8 約為分母為正的最簡精確形式。", "answer": { "kind": "short_text", "value": "-15/1", "explanation_zh": "gcd(|-120|,|8|)=8，約分後為 -15/1。" }, "difficulty": { "band": "upper_secondary", "level": 3, "skills": [ "gcd 約分", "最簡形式" ] }, "variant": { "family_id": "qf-rational-reduced-form", "seed": 20261240, "parameters": { "p": -120, "q": 8, "semantic_template": "qf-rational-reduced-form/{\"p\":-120,\"q\":8}" } }, "verification": { "status": "candidate", "checks": [ "schema_pending", "independent_recomputation_pending" ], "warning_zh": "本題僅重算有限整數分數，不構成一般有理數定理、形式 Evidence 或人工審查。" }, "provenance": { "generator_role": "question_producer", "generator_model": "GPT-5.6 Terra", "generated_at": "2026-09-20", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20260920-rational-reduced-form-0020", "batch_id": "batch-20260920-rational-number-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "29d7161960b88acf2d6fd5cf2f83aab8a3570b426aea430940d80e040bcf7899", "family_id": "qf-rational-reduced-form", "seed": 20261240, "semantic_template": "qf-rational-reduced-form/{\"p\":-120,\"q\":8}" }, "fields": { "title": "Reduced Rational Form", "stem": "Reduce -120/8 to an exact lowest-terms form with a positive denominator.", "answer": { "kind": "short_text", "value": "-15/1", "explanation": "Divide numerator and denominator by their gcd and normalize the denominator sign; the result is -15/1." }, "skills": [ "gcd reduction", "reduced form" ], "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": "將 -120/8 約為分母為正的最簡精確形式。", "en": "Reduce -120/8 to an exact lowest-terms form with a positive denominator." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-rational-reduced-form, [p, q]]", "after": "derived = [BASE-no-required-operation, no-invented-domain]", "relation": "implies", "rule_id": "R68_BANK_specific_keys_operations_and_numeric_guards", "conditions": [], "explanation": { "zh-Hant": "按來源分bank：legacy raw SAFE/衍生BigInt無界，BASE Number.isInteger不偷加SAFE/百萬界。underscore operation、domain及寬/嚴keys各依本bank；原JSON完整保存。", "en": "Separate source banks:legacy RAW SAFE with unbounded derived BigInts versus BASE Number.isInteger without invented SAFE/million caps.Operations,domains and permissive/exact keys follow THIS bank.Keep ORIGINAL JSON intact." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。", "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [ORIGINAL rational reduction, 120, 8]", "after": "derived = [15, 0]", "relation": "implies", "rule_id": "Rational_EUCLID_exact_quotient_remainder_preserves_gcd", "conditions": [], "explanation": { "zh-Hant": "以a=b*q+r且0≤r