R0048-24711 · q-20261015-advance-20261113-r05-turing-machine-decision-model-0036
deterministic single-tape signature、exact configuration semantics與decider total-correctness boundary。操作=tm-exact-step-trace；資料={"states":["q010","q110","qa10","qr10"],"input_alphabet":["010"],"tape_alphabet":["010","X10","_10"],"blank":"_10","start_state":"q010","accept_state":"qa10","reject_state":"qr10","transitions":[["q010","010","q110","X10","R"],["q010","_10","qr10","_10","S"],["q110","_10","qa10","_10","L"]],"input":["010"],"steps":2}。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-exact-step-trace；資料={"states":["q010","q110","qa10","qr10"],"input_alphabet":["010"],"tape_alphabet":["010","X10","_10"],"blank":"_10","start_state":"q010","accept_state":"qa10","reject_state":"qr10","transitions":[["q010","010","q110","X10","R"],["q010","_10","qr10","_10","S"],["q110","_10","qa10","_10","L"]],"input":["010"],"steps":2}。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-exact-step-trace]
操作後
derived = [[input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, 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 = [[q010, q110, qa10, qr10], [010], [010, X10, _10], _10, q010, qa10, qr10, [[q010, 010, q110, X10, R], [q010, _10, qr10, _10, S], [q110, _10, qa10, _10, L]]]
操作後
derived = [[q010, q110, qa10, qr10], [010], [010, X10, _10], [[q010, _10, qr10, _10, S], [q010, 010, q110, X10, R], [q110, _10, qa10, _10, L]], 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 = [[010], q010, _10]
操作後
derived = [[q010, 0, [[0, 010]]]]
條件：無
初始head0、input放0起的整數格，其餘全blank；稀疏記錄僅保非blank。tape可往負index伸展。
規則：TM_exact_initial_configuration_blank_elsewhere · 依賴：G001, S002
操作前
TM exact integer head move0 := sum(0, 1)
操作後
TM exact integer head move0 = 1
條件：無
依原始角色與已證中間量精確代值，分母先核非零，不用浮點近似。
規則：exact_rational_arithmetic · 依賴：G001, S003
操作前
source roles = [0, [q010, 0, [[0, 010]]], 010, [q010, 010, q110, X10, R]]
操作後
derived = [step, [q110, 1, [[0, X10]]]]
條件：無
先在舊head寫字（blank刪格），再換state及移head；全部L/R/S按原rule，不混成停機語意。
規則：TM_source_rule_exact_read_write_state_move · 依賴：G001, S004
操作前
TM exact integer head move1 := sum(1, -1)
操作後
TM exact integer head move1 = 0
條件：無
依原始角色與已證中間量精確代值，分母先核非零，不用浮點近似。
規則：exact_rational_arithmetic · 依賴：G001, S005
操作前
source roles = [1, [q110, 1, [[0, X10]]], _10, [q110, _10, qa10, _10, L]]
操作後
derived = [step, [qa10, 0, [[0, X10]]]]
條件：無
先在舊head寫字（blank刪格），再換state及移head；全部L/R/S按原rule，不混成停機語意。
規則：TM_source_rule_exact_read_write_state_move · 依賴：G001, S006
操作前
source roles = [[010], 2, [[q010, 0, [[0, 010]]], [q110, 1, [[0, X10]]], [qa10, 0, [[0, X10]]]], [step, step]]
操作後
derived = [qa10, accept, 否]
條件：無
已halt才接受／拒絕；budget用盡或stuck不是普通reject，也不證永久不停止。一個input的有限trace不提供all-input decider證書。
規則：TM_finite_trace_input_budget_scope_NOT_global_decider · 依賴：G001, S007
S008 · 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。S007 · 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。S006 · premise_and_result_audit — 以精確有理數重算 TM exact integer head move1，不以小數近似替代。S005 · 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。S004 · premise_and_result_audit — 以精確有理數重算 TM exact integer head move0，不以小數近似替代。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。([010], 2, [[q010, 0, [[0, 010]]], [q110, 1, [[0, X10]]], [qa10, 0, [[0, X10]]]], [step, step], qa10, accept, 否, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
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: 2eba6523e33ebb818dd936b49f5767a474d71abab6b7d588d8dfc70c36dafd1fcandidate record SHA-256: 7bbc3c04366b98e56adc4e7122c00f183b8d1cfa1eca55400cd49e748fd7f364semantic review receipt SHA-256: 049a9e07e69fead88d93b34f0937b9470a06d71c1a8d097058fc83554529bdd0question-first witness SHA-256: 0c71ebb418f3de347d232d159fc25e93036f4ab9166bcfb5ee5b4be86d5c55b9Lean: NOT_RUN · human review: NOT_PERFORMED