{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261013-advance-20261020-r02-ordinary-differential-equation-0024", "pilot_number": "R0002-01974", "number": 1974, "family_id": "qf-app20-ode-order-classification", "title": { "zh-Hant": "第 1974 題：多項式 ODE 候選核對", "en": "Question 1974: Highest Explicit Derivative Order, Not Candidate Polynomial Degree" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261013-advance-20261020-r02-ordinary-differential-equation-0024", "batch_id": "batch-20261013-advance-20261020-r02-ordinary-differential-equation-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-ordinary-differential-equation" ], "title_zh": "多項式 ODE 候選核對", "stem_zh": "整係數多項式候選。操作=ode-order-classification；資料={\"derivative_orders\":[3,4]}。請依 [derivative_orders,order,includes_y] 欄序回答。", "answer": { "kind": "expression", "value": "([3, 4], 4, 否)", "explanation_zh": "應用基礎核對=([3, 4], 4, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；殘差核對不證解存在唯一；只核對明示點或初值。" }, "difficulty": { "band": "undergraduate_core", "level": 3, "skills": [ "多項式 ODE 候選核對" ] }, "variant": { "family_id": "qf-app20-ode-order-classification", "seed": 202610202024, "parameters": { "derivative_orders": [ 3, 4 ], "domain": "Polynomial_candidate_ODE", "operation": "ode-order-classification", "semantic_template": "qf-app20-ode-order-classification/{\"derivative_orders\":[3,4]}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_finite_model", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-13", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261013-advance-20261020-r02-ordinary-differential-equation-0024", "batch_id": "batch-20261013-advance-20261020-r02-ordinary-differential-equation-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "46e70dd4302fd81b6f13df7045cc9b59453f924d0d000f272515ee16a9f147da", "family_id": "qf-app20-ode-order-classification", "seed": 202610202024, "semantic_template": "qf-app20-ode-order-classification/{\"derivative_orders\":[3,4]}" }, "fields": { "title": "Highest Explicit Derivative Order, Not Candidate Polynomial Degree", "stem": "Derivative orders occurring in the specified relation are [3, 4], with 0 denoting y itself. Give (sorted distinct orders, highest order, does y occur?). A [0]-only list records the algebraic order-zero boundary, not evidence of a positive-order ODE.", "answer": { "kind": "expression", "value": "([3, 4], 4, No)", "explanation": "Use the derivatives actually declared in the relation, not the polynomial degree or number of terms. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 4], 4, No)." }, "skills": [ "Highest Explicit Derivative Order, Not Candidate Polynomial Degree" ], "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": "整係數多項式候選。操作=ode-order-classification；資料={\"derivative_orders\":[3,4]}。請依 [derivative_orders,order,includes_y] 欄序回答。", "en": "Derivative orders occurring in the specified relation are [3, 4], with 0 denoting y itself. Give (sorted distinct orders, highest order, does y occur?). A [0]-only list records the algebraic order-zero boundary, not evidence of a positive-order ODE." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "[3, 4]", "after": "distinct actual derivative orders=[3, 4]", "relation": "implies", "rule_id": "derivative_order_list", "conditions": [], "explanation": { "zh-Hant": "以題目明示實際出現的導數階數分類；排序與去重不增加導數項。", "en": "Classify using the explicitly present derivative orders;sorting and deduplication add no derivative terms." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "[3, 4]", "after": "highest listed order=4", "relation": "implies", "rule_id": "highest_derivative_order", "conditions": [], "explanation": { "zh-Hant": "取最高階數，而不是把清單項數當方程階數。", "en": "Take the highest order,not the number of entries in the list." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "0 in orders: 否", "after": "order0 denotes the undifferentiated y term", "relation": "implies", "rule_id": "includes_y_flag", "conditions": [], "explanation": { "zh-Hant": "第三個旗標問的是是否含y本身；含y不表示方程整體是零階。", "en": "The third flag asks whether y itself occurs;its presence does not make the whole equation order0." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "highest=4; includes_y=否", "after": "classification assumes the listed terms survive simplification", "relation": "implies", "rule_id": "order_not_existence_theorem", "conditions": [], "explanation": { "zh-Hant": "若只列0就是代數關係的邊界；這個讀表分類不證解的存在、唯一性或某候選為解。", "en": "A list containing only0 is the algebraic boundary;this classification proves no existence,uniqueness or candidate-solution claim." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。", "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence." } }, "arithmetic": null } ], "math_model": { "result": [ [ 3, 4 ], 4, false ] }, "conclusion": { "canonical_value": "([3, 4], 4, 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-20261013-advance-20261020-r02-ordinary-differential-equation-foundations", "batch_path": "public/data/questions/batches/batch-20261013-advance-20261020-r02-ordinary-differential-equation-foundations/questions.jsonl", "batch_sha256": "620a8e01a0625c037f17a83bb6bd43f79f250f9c0ffb67239fe74b16286ca2e5", "original_line": 24, "original_line_sha256": "76a8265efbfe0d40dbcf19cd54548ae6d8305b220e1440062f1d4905f71e965d", "question_compact_sha256": "46e70dd4302fd81b6f13df7045cc9b59453f924d0d000f272515ee16a9f147da", "english_row_compact_sha256": "d361ad90737da3f0465b8fabad97bbf124c78315e73776593f4338121d339de1", "english_manifest_path": "public/data/i18n/editions/batch-20261013-advance-20261020-r02-ordinary-differential-equation-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261013-advance-20261020-r02-ordinary-differential-equation-foundations.en.jsonl" }, "mko_bindings": { "mko-ordinary-differential-equation": { "sha256": "78a220ac6f5f781865fa9d3cdc17fd9d5f931ff83cfdd5890bfaae2b91641a13", "english_sha256": "435d009ee6ad859f9ac02c4a0cb32c615d035b5925c196f2f27b8e4f2ced3f71", "original_path": "public/data/mko/ordinary-differential-equation.json", "english_path": "public/data/i18n/editions/mko-ordinary-differential-equation.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "e476360038ede38e6f70fbe8c039b14a4f4bd45937ee88050de8370944911f19", "original_candidate_sha256": "9e745b92e909fc8e18aac9d1d4eb4351d0b472fee33cfb2cd4026eea2a9b7716", "original_candidate_line_sha256": "9e745b92e909fc8e18aac9d1d4eb4351d0b472fee33cfb2cd4026eea2a9b7716" }, "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-20261026-004-p3", "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": "340d74dcc6e37df6249594a0b79a9ee2af804337b7847478b3c1342af9722861", "question_first_witness_sha256": "9a06233d190d31a16f13fb03b6c3ceba4cbb748fff6c997941f66ab1888dcca8" }, "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": "ac3927e9a98f064194941272efde810536709d1dafce92aef254a40ff82975f2", "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." } }