R0048-24721 · q-20261015-advance-20261113-r05-turing-machine-decision-model-0046
deterministic single-tape signature、exact configuration semantics與decider total-correctness boundary。操作=tm-exact-step-trace；資料={"states":["q020","q120","qa20","qr20"],"input_alphabet":["020"],"tape_alphabet":["020","X20","_20"],"blank":"_20","start_state":"q020","accept_state":"qa20","reject_state":"qr20","transitions":[["q020","020","q120","X20","R"],["q020","_20","qr20","_20","S"],["q120","_20","qa20","_20","L"]],"input":["020"],"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":["q020","q120","qa20","qr20"],"input_alphabet":["020"],"tape_alphabet":["020","X20","_20"],"blank":"_20","start_state":"q020","accept_state":"qa20","reject_state":"qr20","transitions":[["q020","020","q120","X20","R"],["q020","_20","qr20","_20","S"],["q120","_20","qa20","_20","L"]],"input":["020"],"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 = [[q020, q120, qa20, qr20], [020], [020, X20, _20], _20, q020, qa20, qr20, [[q020, 020, q120, X20, R], [q020, _20, qr20, _20, S], [q120, _20, qa20, _20, L]]]
操作後
derived = [[q020, q120, qa20, qr20], [020], [020, X20, _20], [[q020, _20, qr20, _20, S], [q020, 020, q120, X20, R], [q120, _20, qa20, _20, 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 = [[020], q020, _20]
操作後
derived = [[q020, 0, [[0, 020]]]]
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, [q020, 0, [[0, 020]]], 020, [q020, 020, q120, X20, R]]
操作後
derived = [step, [q120, 1, [[0, X20]]]]
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, [q120, 1, [[0, X20]]], _20, [q120, _20, qa20, _20, L]]
操作後
derived = [step, [qa20, 0, [[0, X20]]]]
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 = [[020], 2, [[q020, 0, [[0, 020]]], [q120, 1, [[0, X20]]], [qa20, 0, [[0, X20]]]], [step, step]]
操作後
derived = [qa20, 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。([020], 2, [[q020, 0, [[0, 020]]], [q120, 1, [[0, X20]]], [qa20, 0, [[0, X20]]]], [step, step], qa20, 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: e584ba8ef5fa90ade0e329ef4716175720373c39eca34e862bdadcb8fe6e7ea0candidate record SHA-256: 29a15363e7fd4609870e44e5e70fade68c686ed47fb5852c46312cea46565b49semantic review receipt SHA-256: 049a9e07e69fead88d93b34f0937b9470a06d71c1a8d097058fc83554529bdd0question-first witness SHA-256: 0c71ebb418f3de347d232d159fc25e93036f4ab9166bcfb5ee5b4be86d5c55b9Lean: NOT_RUN · human review: NOT_PERFORMED