R0051-26129 · q-20261015-advance-20261115-r07-many-one-reduction-0079
明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"one_way_yes_only","source_carrier":[0,1,2,3,4,5],"target_carrier":[0,1],"source_yes":[0],"target_yes":[0],"mapping":[0,0,0,0,0,0],"target_decider":[true,false]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。
G001 — 明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={"mode":"one_way_yes_only","source_carrier":[0,1,2,3,4,5],"target_carrier":[0,1],"source_yes":[0],"target_yes":[0],"mapping":[0,0,0,0,0,0],"target_decider":[true,false]}。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 = [mreduction-decider-transfer-boundary]
操作後
derived = [[mode, membership_rows, total, reduction, target_decider, target_decider_correct, constructed_source_decider_or_null, constructed_source_decider_correct, requested_forward_transfer_certificate, reverse_or_infinite_computability_claim, boundary]]
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 = [Reduction ORIGINAL map, [0, 1, 2, 3, 4, 5], [0, 1], [0, 0, 0, 0, 0, 0]]
操作後
derived = [[0, 1, 2, 3, 4, 5], [0, 1], [0, 0, 0, 0, 0, 0], [[0, 0, 是], [1, 0, 是], [2, 0, 是], [3, 0, 是], [4, 0, 是], [5, 0, 是]], 是, null]
條件：無
source數值排序要連image一起移動；target也數值排序。null／outside／Boolean不是合法integer target值，False不能當0；qualification保實際rawimage與首invalid row，不先捏造total map。
規則：Reduction_original_domain_IMAGE_pairs_sorted_together_STRICT_types · 依賴：G001, S001
操作前
source roles = [Reduction ORIGINAL map, [0], [0], [0, 1, 2, 3, 4, 5], [0, 1], [0, 0, 0, 0, 0, 0]]
操作後
derived = [[[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否]], 是, 否]
條件：無
每個x都驗x∈A iff f(x)∈B，包含yes與no兩方向；invalid image的target predicate是null而非False。totality與membership責任合取才是此有限reduction。
規則：Reduction_EVERY_yes_AND_no_membership_IFF_not_yes_only · 依賴：G001, S002
操作前
source roles = [one_way_yes_only, [0, 1], [是, 否], [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否]]]
操作後
derived = [[0, 1], [是, 否], 是, [是, 是, 是, 是, 是, 是], 否, 否, 否]
條件：無
decider先連原始target carrier再重排，必為真正Boolean表。只有total map才構造A表，partial給null。reverse_misuse的A表可正確但仍拒反向用途；yes-only可含partial/vacuous yes，不能私加total前提。有限表只證這些finite domains，不證無限computability。
規則：Reduction_original_TARGET_decider_alignment_FORWARD_transfer_mode_boundary · 依賴：G001, S003
S004 · 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。S003 · 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。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。(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)
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: c917e42f90f5a45e1a3438c6f66e282be656f80f5cdb2be1cc83f200accb2f22candidate record SHA-256: 704bdaf4ea7444cbbaae571acd9bb6daace78795c5ca5b5362f80f0d720dc447semantic review receipt SHA-256: 90df1e889242e9afdf01e068788ee8500ef366ffcfc0496e30a6800de32631c3question-first witness SHA-256: ae1e849608590ca856c9f3b6911ba58e3bf53c608eb7369606192a770f48bd5cLean: NOT_RUN · human review: NOT_PERFORMED