R0051-26203 · q-20261015-advance-20261116-r01-contraction-mapping-theorem-0078
完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"noncomplete_space","scale":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。
G001 — 完整metric、total self-map與forall-pairs q<1 contraction責任。操作=contract-boundary；資料={"mode":"noncomplete_space","scale":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 = [contract-boundary]
操作後
derived = [[mode, space_description, mapping_description, outside_fixed_point, q_as_fraction, theorem_application_claim]]
條件：無
本頁直接列完整來源欄序，不需JavaScript；contract的6/4/6/6與IVT的8/7/8由原mode選，不補欄也不由答案形狀猜。
規則：source_ordered_fields_without_JS · 依賴：G001
操作前
source roles = [noncomplete_space, 3]
操作後
derived = [noncomplete_space, X=(0,3), T(x)=(x+3)/2, fixed_point=3_outside_X, [1, 2], 否]
條件：無
q1的two-point identity有兩fixed points；非self-map不能迭代於同空間；(0,s)上(x+s)/2的fixed point s在外；sampled_pairs只保來源範圍敘述，沒提供可重算的完整metric/map，不冒稱已驗numeric反例。
規則：Contraction_original_boundary_mode_actual_scope_not_invented_witness · 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。(noncomplete_space, X=(0,3), T(x)=(x+3)/2, fixed_point=3_outside_X, [1, 2], 否)
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: 01b64360e4018cb2760319d667239761a49e46b5a7c80b1aa8bcfd44731610adcandidate record SHA-256: be51d21bb6f3ec9daf04d40d3471fb644a4836e89a9fe9688feddb24f336d4aesemantic review receipt SHA-256: 90df1e889242e9afdf01e068788ee8500ef366ffcfc0496e30a6800de32631c3question-first witness SHA-256: ae1e849608590ca856c9f3b6911ba58e3bf53c608eb7369606192a770f48bd5cLean: NOT_RUN · human review: NOT_PERFORMED