{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261013-advance-20261020-r06-discrete-exponential-growth-0094", "pilot_number": "R0002-01744", "number": 1744, "family_id": "qf-app20-growth-factor-regime", "title": { "zh-Hant": "第 1744 題：離散固定因子模型", "en": "Question 1744: Classify the Nonnegative Factor, Not Every Orbit’s Monotonicity" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261013-advance-20261020-r06-discrete-exponential-growth-0094", "batch_id": "batch-20261013-advance-20261020-r06-discrete-exponential-growth-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-discrete-exponential-growth" ], "title_zh": "離散固定因子模型", "stem_zh": "固定時間步與精確固定因子。操作=growth-factor-regime；資料={\"factor\":[0,5]}。請依 [factor,regime] 欄序回答。", "answer": { "kind": "expression", "value": "(0, 因子介於0與1)", "explanation_zh": "應用基礎核對=(0, 因子介於0與1)；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；不是連續時間模型；不是經驗預測。" }, "difficulty": { "band": "upper_secondary", "level": 3, "skills": [ "離散固定因子模型" ] }, "variant": { "family_id": "qf-app20-growth-factor-regime", "seed": 202610206094, "parameters": { "factor": [ 0, 5 ], "domain": "Exact_discrete_exponential_model", "operation": "growth-factor-regime", "semantic_template": "qf-app20-growth-factor-regime/{\"factor\":[0,5]}" } }, "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-r06-discrete-exponential-growth-0094", "batch_id": "batch-20261013-advance-20261020-r06-discrete-exponential-growth-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "a1bb52bad857d2244f34673a160cec60dff6d2ef0d1f7b8a583b8c3e39e9aa8a", "family_id": "qf-app20-growth-factor-regime", "seed": 202610206094, "semantic_template": "qf-app20-growth-factor-regime/{\"factor\":[0,5]}" }, "fields": { "title": "Classify the Nonnegative Factor, Not Every Orbit’s Monotonicity", "stem": "Use fixed discrete time steps and one exact nonnegative rational factor throughout. This is not a continuous-time model or an empirical population prediction; signed initial quantities and the zero case must retain their specified values. factor=0/5. Give (normalized factor, one label: factor greater than 1 / factor equals 1 / factor at least 0 and below 1). The last case includes factor 0. A zero initial value remains zero, and signed initial data do not all increase when the factor exceeds 1.", "answer": { "kind": "expression", "value": "(0, factor at least 0 and below 1)", "explanation": "Compare the given factor with 1; this regime label does not certify observed growth, empirical fit or continuous-time behavior. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (0, factor at least 0 and below 1)." }, "skills": [ "Classify the Nonnegative Factor, Not Every Orbit’s Monotonicity" ], "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": "固定時間步與精確固定因子。操作=growth-factor-regime；資料={\"factor\":[0,5]}。請依 [factor,regime] 欄序回答。", "en": "Use fixed discrete time steps and one exact nonnegative rational factor throughout. This is not a continuous-time model or an empirical population prediction; signed initial quantities and the zero case must retain their specified values. factor=0/5. Give (normalized factor, one label: factor greater than 1 / factor equals 1 / factor at least 0 and below 1). The last case includes factor 0. A zero initial value remains zero, and signed initial data do not all increase when the factor exceeds 1." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "factor q=0≥0", "after": "X_(k+1)=q·X_k", "relation": "implies", "rule_id": "fixed_factor_recurrence", "conditions": [], "explanation": { "zh-Hant": "固定同一因子；這是題目明示的離散模型，不從少量數值猜測一般規律。", "en": "Use the same factor in the declared discrete model,rather than infer a general law from a few values." }, "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": "q=0", "after": "compare q with1: q−1=-1", "relation": "implies", "rule_id": "factor_threshold", "conditions": [], "explanation": { "zh-Hant": "用精確有理數比較1，不能只看名稱推斷一定增長。", "en": "Compare exactly with1;the name alone does not imply growth." }, "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": "qualified interval: 0≤q<1", "after": "preserved source label=因子介於0與1", "relation": "implies", "rule_id": "qualified_factor_label", "conditions": [], "explanation": { "zh-Hant": "保留原始中文標籤，但明確寫出本合約的低因子分支含q=0；不是偷偷改成嚴格01 need not increase a negative initial value", "relation": "implies", "rule_id": "factor_not_signed_monotonicity", "conditions": [], "explanation": { "zh-Hant": "因子分類不等於所有初值的數值都同向增加；零初值、負初值與零因子需分清。", "en": "Factor classification is not a claim that every initial value increases;distinguish zero or negative initial values and a zero factor." }, "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": [ "0", "因子介於0與1" ], "recurrence_values": [], "qualified_interval": "0≤q<1" }, "conclusion": { "canonical_value": "(0, 因子介於0與1)", "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-r06-discrete-exponential-growth-foundations", "batch_path": "public/data/questions/batches/batch-20261013-advance-20261020-r06-discrete-exponential-growth-foundations/questions.jsonl", "batch_sha256": "c2e2d6e56d2e17262678fe2d2a402a35aab9b8fbdd2c94544b16fe6f43d25a81", "original_line": 94, "original_line_sha256": "a294bd3cb744d023916dfdfa3d9f11578e28873fcdc6d60927b992b64f0a98bb", "question_compact_sha256": "a1bb52bad857d2244f34673a160cec60dff6d2ef0d1f7b8a583b8c3e39e9aa8a", "english_row_compact_sha256": "0ff5afa0895342fc2a029ccdc0dd95c5d4e48469a07e0d13435bdbd77bd6be35", "english_manifest_path": "public/data/i18n/editions/batch-20261013-advance-20261020-r06-discrete-exponential-growth-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261013-advance-20261020-r06-discrete-exponential-growth-foundations.en.jsonl" }, "mko_bindings": { "mko-discrete-exponential-growth": { "sha256": "81d7d953b56dc3b4f26d1051ae74ae30b298a2c6085c59c5f06439b68ea8e780", "english_sha256": "e3b7db219c9df5e1a4a5757566489aba9a73916a7d659377948d93c20b4c77b0", "original_path": "public/data/mko/discrete-exponential-growth.json", "english_path": "public/data/i18n/editions/mko-discrete-exponential-growth.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "e476360038ede38e6f70fbe8c039b14a4f4bd45937ee88050de8370944911f19", "original_candidate_sha256": "add2eb4ebb50ebc1329097f84e86605402dade1dcf1edd7c5c915cf10ddc9651", "original_candidate_line_sha256": "add2eb4ebb50ebc1329097f84e86605402dade1dcf1edd7c5c915cf10ddc9651" }, "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": "28e934c406b1d39341997e354344cc8d6df0f5f32086d684baf9c3366d3e5123", "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." } }