{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20260930-r02-proportion-fixed-factor-0018", "pilot_number": "R0067-34418", "number": 34418, "family_id": "qf-proportion-fixed-factor", "title": { "zh-Hant": "第 34418 題：固定比例因子檢查", "en": "Question 34418: Fixed-Factor Proportion Check" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20260930-r02-proportion-fixed-factor-0018", "batch_id": "batch-20260930-r02-ratio-proportion-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-ratio-proportion" ], "title_zh": "固定比例因子檢查", "stem_zh": "在有理數語境，固定因子 k=5。明示資料點 (x,y)=(0,1) 是否滿足 y=kx？只判定此點。", "answer": { "kind": "short_text", "value": "否", "explanation_zh": "kx 與給定 y 的精確值分別是 0, 1；比較後答案為否，不由此點推論其他輸入。" }, "difficulty": { "band": "lower_secondary", "level": 3, "skills": [ "固定因子", "逐點驗證" ] }, "variant": { "family_id": "qf-proportion-fixed-factor", "seed": 202609302318, "parameters": { "operation": "fixed_factor", "k": 5, "x": 0, "y": 1, "semantic_template": "qf-proportion-fixed-factor/{\"k\":5,\"operation\":\"fixed_factor\",\"x\":0,\"y\":1}" } }, "verification": { "status": "candidate", "checks": [ "json_schema", "producer_local_answer_invariants", "explanation_witness_accuracy" ], "warning_zh": "本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。" }, "provenance": { "generator_role": "question_producer", "generator_model": "Codex GPT-6 question producer", "generated_at": "2026-09-30", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20260930-r02-proportion-fixed-factor-0018", "batch_id": "batch-20260930-r02-ratio-proportion-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "c6480562bcae108cb91845ed83d131aad672e7f72b53957d588ab469dab3b4c3", "family_id": "qf-proportion-fixed-factor", "seed": 202609302318, "semantic_template": "qf-proportion-fixed-factor/{\"k\":5,\"operation\":\"fixed_factor\",\"x\":0,\"y\":1}" }, "fields": { "title": "Fixed-Factor Proportion Check", "stem": "In the rational setting, the fixed factor is k=5. Does the explicit point (x,y)=(0,1) satisfy y=kx? Check only this point.", "answer": { "kind": "short_text", "value": "No", "explanation": "kx=0 and the stated y is 1; comparison gives No and does not justify any claim about other inputs." }, "skills": [ "fixed proportionality factor", "pointwise verification" ], "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": "在有理數語境，固定因子 k=5。明示資料點 (x,y)=(0,1) 是否滿足 y=kx？只判定此點。", "en": "In the rational setting, the fixed factor is k=5. Does the explicit point (x,y)=(0,1) satisfy y=kx? Check only this point." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-proportion-fixed-factor, [k, operation, x, y]]", "after": "derived = [fixed_factor, no-invented-domain]", "relation": "implies", "rule_id": "R67_SOURCE_specific_keys_operation_domain_and_numeric_bank", "conditions": [], "explanation": { "zh-Hant": "按本bank核keys與operation/domain：legacy為各表underscore，MOD50用local hyphen；BASE參數較寬不加未知欄限制。Number.isInteger與SAFE兩種來源界分開，原JSON數字表示仍完整保存。", "en": "Check THIS bank’s keys/operation/domain:legacy table underscores,MOD50 local hyphens;permissive BASE data acquires no unknown-field restriction.Keep Number.isInteger and SAFE source guards distinct,while preserving ORIGINAL JSON number representations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以本題原始角色、完整前提及欄序反查本步；區分單向推論與等價，並保留原題與英文、MKO、AST及審查狀態。不把有限核對冒充獨立審查或一般形式證明。", "en": "Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "Proportion ORIGINAL fixed factor times point x := mul(5, 0)", "after": "Proportion ORIGINAL fixed factor times point x = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原操作數與原次序精確計算；legacy衍生整數不重套raw SAFE界，MOD50有理數則另保naive pre-reduction來源界。", "en": "Calculate exactly from ORIGINAL ordered operands.Legacy derived integers are not recapped at the RAW SAFE bound;MOD50 rationals separately retain the NAIVE pre-reduction source envelope." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Proportion ORIGINAL fixed factor times point x，不以小數近似替代。", "en": "Recompute Proportion ORIGINAL fixed factor times point x with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "5", "0" ], "output": "0", "label": "Proportion ORIGINAL fixed factor times point x" } }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "source roles = [5, 0, 1]", "after": "derived = [0, 否]", "relation": "implies", "rule_id": "Proportion_FIXED_factor_THIS_point_ONLY_zero_allowed", "conditions": [], "explanation": { "zh-Hant": "只核本點y=kx，k=0或x=0合法；一次吻合不推出其他輸入的比例關係，也不能從x=0倒推唯一k。", "en": "Check ONLY THIS point against y=kx.Zero k or x is allowed.One passing point does not establish proportionality for other inputs,nor does x=0 determine a unique factor." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以本題原始角色、完整前提及欄序反查本步；區分單向推論與等價，並保留原題與英文、MKO、AST及審查狀態。不把有限核對冒充獨立審查或一般形式證明。", "en": "Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof." } }, "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-20260930-r02-ratio-proportion-foundations", "batch_path": "public/data/questions/batches/batch-20260930-r02-ratio-proportion-foundations/questions.jsonl", "batch_sha256": "1f5eaf24316978d57a4c22a3f3aac6fd6dc95db9751a0100d628ac8d38366a55", "original_line": 93, "original_line_sha256": "6ffd4514ee8d2724aee29385f79e56fe61126e8b1b90b7612bcec797362bcb99", "question_compact_sha256": "c6480562bcae108cb91845ed83d131aad672e7f72b53957d588ab469dab3b4c3", "english_row_compact_sha256": "1fccbd8470797c60e2cd1a07f8cdb986dfc054e04fd34ed1234665df6e3f12e7", "english_manifest_path": "public/data/i18n/editions/batch-20260930-r02-ratio-proportion-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20260930-r02-ratio-proportion-foundations.en.jsonl" }, "mko_bindings": { "mko-ratio-proportion": { "sha256": "b0200b9dd1e1ceb4c2b34f37f0279a1abaf31c3021957de6cd9ea72919da47ec", "english_sha256": "f41a9985bd51a22f5108587c130e1ecaa9d44b5c929b8653cb23ff7ac3021771", "original_path": "public/data/mko/ratio-proportion.json", "english_path": "public/data/i18n/editions/mko-ratio-proportion.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "6bb156cec7bdb6baf2497762702fc01f94fd1db55a5926bc575b12ff9237a4de", "original_candidate_sha256": "899029f672c6fa20396f2bfcb661150cc4aae6de233d31c036362b433a9b6c89", "original_candidate_line_sha256": "899029f672c6fa20396f2bfcb661150cc4aae6de233d31c036362b433a9b6c89" }, "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-20261026-012-p68", "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": "c89efa383b67bb2cf25bcf16160b9f5f614bbe5e5e791f4d7f58234d17a3371c", "question_first_witness_sha256": "12766d451c5375842b4fc2843ae94807ec55f15763a916558026912a13873d57" }, "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": "bca71e82a3b603522a7c8b63fcbc81f6ac763288e5b122c1663da40e54865d65", "arithmetic_steps": 1 }, "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." } }