R0047-24040 · q-20261014-advance-20261112-r02-taylor-polynomial-0090
固定center、nonnegative order與完整zero-through-n derivative jet。操作=taylor-definition-boundary；資料={"mode":"missing_factorial","derivatives":[15,30,45],"center":2,"order":2,"alternate_center":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。
G001 — 固定center、nonnegative order與完整zero-through-n derivative jet。操作=taylor-definition-boundary；資料={"mode":"missing_factorial","derivatives":[15,30,45],"center":2,"order":2,"alternate_center":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。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。
操作前
source roles = [taylor-definition-boundary]
操作後
derived = [[mode, order, derivatives, center, alternate_center, unsupported_definition_or_remainder_claim, boundary]]
條件：無
本頁列完整來源欄序，不需JavaScript；gradient boundary依原mode選6／8／7欄，不補欄也不由答案猜mode。
規則：source_ordered_fields_without_JS · 依賴：G001
操作前
source roles = [missing_factorial, 2, [15, 30, 45], 2, 3]
操作後
derived = [[0, 1, 2], 3, 否, coefficients_require_division_by_k_factorial]
條件：無
missing_derivative缺的是0至n各階資料（含f(a)），不是要求每個值都為0；wrong_center不能把同一jet直接換基底中心，即使常數特例可能相同。missing_factorial仍須除k!，即使低階或零值可能偶然不變。remainder_claim缺更高階控制／解析性，No不等於所有特例必不相等。
規則：Taylor_definition_boundary_keeps_actual_jet_and_center · 依賴：G001, S001
S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。(missing_factorial, 2, [15, 30, 45], 2, 3, 否, coefficients_require_division_by_k_factorial)
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。
覆核日期：2026-10-26
原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: f6512f1f9ba1c5c4cf60bc2abc4f0e97eed82df2c3508719efb3ddf0702eb148candidate record SHA-256: 7f669c36b218231c09e2663054ca0d81b483c4a2d04fc886a56146b98b877921semantic review receipt SHA-256: 9b43b9823e9bd2478d6caa5b57ffed161c2c8956af86974e901d5662ad994386question-first witness SHA-256: eb97596068e2d5648033bab2b8f6ca9b653bbe8cb77c0f8e1d16d0c40e46f50bLean: NOT_RUN · human review: NOT_PERFORMED