{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261005-advance-20261006-r03-rate-of-change-0036", "pilot_number": "R0056-28636", "number": 28636, "family_id": "qf-rate-denominator-validity", "title": { "zh-Hant": "第 28636 題：平均變化率的非零分母資格", "en": "Question 28636: Nonzero-Denominator Eligibility for an Average Rate" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261005-advance-20261006-r03-rate-of-change-0036", "batch_id": "batch-20261005-advance-20261006-r03-rate-of-change-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-rate-of-change" ], "title_zh": "平均變化率的非零分母資格", "stem_zh": "平均變化率使用輸入差作分母。給兩個輸入 x0=-10、x1=0，是否滿足本題差商的非零分母資格？", "answer": { "kind": "short_text", "value": "是", "explanation_zh": "輸入差=10。只有輸入差非零才具此資格；相同輸入不把商填零或 0/0，且本題不是導數判定。" }, "difficulty": { "band": "upper_secondary", "level": 2, "skills": [ "平均變化率的非零分母資格" ] }, "variant": { "family_id": "qf-rate-denominator-validity", "seed": 202610063036, "parameters": { "x0": -10, "x1": 0, "operation": "denominator_validity", "semantic_template": "qf-rate-denominator-validity/{\"inputs\":[\"10\"],\"operation\":\"denominator_validity\"}" } }, "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": "2026-10-05", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261005-advance-20261006-r03-rate-of-change-0036", "batch_id": "batch-20261005-advance-20261006-r03-rate-of-change-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "1756c01980e8c7a2ea655c3819f9f3a4b51b5c8d1261461c31404259cdf390ba", "family_id": "qf-rate-denominator-validity", "seed": 202610063036, "semantic_template": "qf-rate-denominator-validity/{\"inputs\":[\"10\"],\"operation\":\"denominator_validity\"}" }, "fields": { "title": "Nonzero-Denominator Eligibility for an Average Rate", "stem": "The proposed permitted endpoint inputs are x0=-10 and x1=0. Is their difference a valid nonzero denominator for an average rate of change?", "answer": { "kind": "short_text", "value": "Yes", "explanation": "The input difference is 10, so the eligibility answer is Yes. Equal inputs fail this teaching condition; no value is assigned to their quotient here. This is an endpoint average rate, not a derivative." }, "skills": [ "Nonzero-Denominator Eligibility for an Average Rate" ], "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": "平均變化率使用輸入差作分母。給兩個輸入 x0=-10、x1=0，是否滿足本題差商的非零分母資格？", "en": "The proposed permitted endpoint inputs are x0=-10 and x1=0. Is their difference a valid nonzero denominator for an average rate of change?" } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-rate-denominator-validity, denominator_validity]", "after": "derived = [distinct_endpoint_eligibility]", "relation": "implies", "rule_id": "R56_source_answer_role_and_EXACT_family_interface", "conditions": [], "explanation": { "zh-Hant": "本題輸出依原scalar／set／是非／fraction角色；有理數整數保留/1。不加未宣告domain，不改中英來源、公式或題目。", "en": "Use the declared scalar/set/Yes-No/fraction answer role;integer fractions retain/1.Do not add an undeclared domain or change original bilingual data,formulas or questions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向逐項代回原始資料與本步條件；保持索引、符號、嚴格／非嚴格邊界，不能用正確答案代替推導責任。這是候選教學與精確核對，非形式證明或發布資格。", "en": "Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "Rate ORIGINAL x1 minus x0 := sub(0, -10)", "after": "Rate ORIGINAL x1 minus x0 = 10", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按本題原始角色作精確有理運算；SAFE只約束原輸入，衍生整數不截斷，不作浮點近似。", "en": "Perform exact rational arithmetic on the ORIGINAL roles.SAFE bounds raw inputs only;derived integers are unbounded and never approximated by floats." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Rate ORIGINAL x1 minus x0，不以小數近似替代。", "en": "Recompute Rate ORIGINAL x1 minus x0 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "0", "-10" ], "output": "10", "label": "Rate ORIGINAL x1 minus x0" } }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "source roles = [-10, 0, 10]", "after": "derived = [是, 是]", "relation": "implies", "rule_id": "Rate_equal_endpoints_legal_eligibility_NO_division", "conditions": [], "explanation": { "zh-Hant": "分母x1-x0非零才可定平均率；相等是合法的No題，不計0/0，也不移動端點修復。", "en": "The average rate requires x1-x0 nonzero.Equal endpoints are a legal No eligibility case;do not compute0/0 or repair the endpoints." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向逐項代回原始資料與本步條件；保持索引、符號、嚴格／非嚴格邊界，不能用正確答案代替推導責任。這是候選教學與精確核對，非形式證明或發布資格。", "en": "Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance." } }, "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-20261005-advance-20261006-r03-rate-of-change-foundations", "batch_path": "public/data/questions/batches/batch-20261005-advance-20261006-r03-rate-of-change-foundations/questions.jsonl", "batch_sha256": "f7f2bbd6cbef58468a160367d229b21789cc36fdb8bdd1e96573aa6af31dfae1", "original_line": 36, "original_line_sha256": "78e07ccf747fbe20c33957524e579f6572cac4a1c4c86babdb78642204d21a87", "question_compact_sha256": "1756c01980e8c7a2ea655c3819f9f3a4b51b5c8d1261461c31404259cdf390ba", "english_row_compact_sha256": "3f923e3d7de4a833760bc3bc09370e5d403bdf82dc7040dcbd07133bcdefe3d9", "english_manifest_path": "public/data/i18n/editions/batch-20261005-advance-20261006-r03-rate-of-change-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261005-advance-20261006-r03-rate-of-change-foundations.en.jsonl" }, "mko_bindings": { "mko-rate-of-change": { "sha256": "8c12a896998e745bbd3743c80ae005d1ffbc28d69ea33072b8e08d03c3837416", "english_sha256": "da425c268629ac1b5344a831974cfbf2e90a380deb76eb9cf2eab84d01f97ec2", "original_path": "public/data/mko/rate-of-change.json", "english_path": "public/data/i18n/editions/mko-rate-of-change.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "e340023047850507ee3fe2ae1466d606cfcbd26849aa3bb168d53248f38097e5", "original_candidate_sha256": "79c38dbe8e8e18518a6f0ebf43aa88c27cb4f40a8c6efc95765ebb4ab027cb70", "original_candidate_line_sha256": "79c38dbe8e8e18518a6f0ebf43aa88c27cb4f40a8c6efc95765ebb4ab027cb70" }, "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-20261026-010-p57", "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": "8bbda4edbed7078634ae88342998c79bcfb95de96187fac119c3b08e0adb0bc8", "question_first_witness_sha256": "3edafa72d63d16a22414892b55806430e0a25b15b926d04f312550179607759f" }, "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": 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." } }