R0048-24756 · q-20261015-advance-20261113-r05-turing-machine-decision-model-0081
deterministic single-tape signature、exact configuration semantics與decider total-correctness boundary。操作=tm-recognizer-loop-boundary；資料={"states":["scan","accept","reject"],"input_alphabet":["a5","b5"],"tape_alphabet":["a5","b5","_"],"blank":"_","start_state":"scan","accept_state":"accept","reject_state":"reject","transitions":[["scan","a5","scan","a5","R"],["scan","b5","accept","b5","S"],["scan","_","scan","_","S"]],"target_symbol":"b5","input":["a5","a5"]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。
G001 — deterministic single-tape signature、exact configuration semantics與decider total-correctness boundary。操作=tm-recognizer-loop-boundary；資料={"states":["scan","accept","reject"],"input_alphabet":["a5","b5"],"tape_alphabet":["a5","b5","_"],"blank":"_","start_state":"scan","accept_state":"accept","reject_state":"reject","transitions":[["scan","a5","scan","a5","R"],["scan","b5","accept","b5","S"],["scan","_","scan","_","S"]],"target_symbol":"b5","input":["a5","a5"]}。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 = [tm-recognizer-loop-boundary]
操作後
derived = [[states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary]]
條件：無
直接列來源完整欄序，不需JavaScript；原題、布林旗標、數學物件與非聲稱保持分層。
規則：source_ordered_fields_without_JS · 依賴：G001
操作前
source roles = [[scan, accept, reject], [a5, b5], [a5, b5, _], _, scan, accept, reject, [[scan, a5, scan, a5, R], [scan, b5, accept, b5, S], [scan, _, scan, _, S]]]
操作後
derived = [[accept, reject, scan], [a5, b5], [_, a5, b5], [[scan, _, scan, _, S], [scan, a5, scan, a5, R], [scan, b5, accept, b5, S]], 是]
條件：無
三個清單皆非空且唯一；input是blank-free tape子集，但state與字母標籤不要求不相交。每個(from,read)的來源NUL-joined key唯一、halt無出邊。partial table合法，不補reject規則；canonical transition序與UTF16集合序分開。
規則：TM_complete_signature_partial_transition_table_allowed · 依賴：G001, S001
操作前
source roles = [b5, 是, [[accept, reject, scan], [a5, b5], [_, a5, b5], _, scan, accept, reject, [[scan, _, scan, _, S], [scan, a5, scan, a5, R], [scan, b5, accept, b5, S]]]]
操作後
derived = [[[accept, reject, scan], [a5, b5], [_, a5, b5], _, scan, accept, reject, [[scan, _, scan, _, S], [scan, a5, scan, a5, R], [scan, b5, accept, b5, S]]], 是]
條件：無
要整個signature與所有transition符合指定schema，不能由幾個成功trace給任意TM全域證書。
規則：TM_EXACT_canonical_scan_schema_not_sampled_machine · 依賴：G001, S002
操作前
source roles = [[a5, a5], b5, [[scan, _, scan, _, S], [scan, a5, scan, a5, R], [scan, b5, accept, b5, S]]]
操作後
derived = [[scan, 2, [[0, a5], [1, a5]]], [scan, 2, [[0, a5], [1, a5]]], 是, 否]
條件：無
逐input的非目標字元copy/R可達head=|w|的blank；scan/blank規則寫blank、S、仍scan，整個configuration精確重複。決定性使此input永遠loop，這才反證此recognizer是decider，不靠有限budget未停。
規則：TM_actual_target_free_input_reaches_EXACT_blank_SELFLOOP · 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。([accept, reject, scan], [a5, b5], [_, a5, b5], [[scan, _, scan, _, S], [scan, a5, scan, a5, R], [scan, b5, accept, b5, S]], b5, [a5, a5], [scan, 2, [[0, a5], [1, a5]]], [scan, 2, [[0, a5], [1, a5]]], 是, 否, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
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: 5ebb10a0492535951a4bd392d779e43b1a9c4e1a1a5f3f69c4baed493162b77ecandidate record SHA-256: 02b5b822d250e1371cb5011966d42a2632e708f95063d14561e1df1da0c131d5semantic review receipt SHA-256: 049a9e07e69fead88d93b34f0937b9470a06d71c1a8d097058fc83554529bdd0question-first witness SHA-256: 0c71ebb418f3de347d232d159fc25e93036f4ab9166bcfb5ee5b4be86d5c55b9Lean: NOT_RUN · human review: NOT_PERFORMED