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R0048-24760 · q-20261015-advance-20261113-r05-turing-machine-decision-model-0085
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a9, b9], tape_alphabet=[a9, b9, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a9, scan, a9, R], [scan, b9, accept, b9, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b9, legal target-free input=[a9, a9]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
G001 — Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a9, b9], tape_alphabet=[a9, b9, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a9, scan, a9, R], [scan, b9, accept, b9, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b9, legal target-free input=[a9, a9]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
source roles = [tm-recognizer-loop-boundary]
After
derived = [[states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary]]
Conditions: none
List the full source field order without JavaScript,keeping original data,Boolean flags,mathematical objects and nonclaims distinct.
Rule: source_ordered_fields_without_JS · Uses: G001
Before
source roles = [[scan, accept, reject], [a9, b9], [a9, b9, _], _, scan, accept, reject, [[scan, a9, scan, a9, R], [scan, b9, accept, b9, S], [scan, _, scan, _, S]]]
After
derived = [[accept, reject, scan], [a9, b9], [_, a9, b9], [[scan, _, scan, _, S], [scan, a9, scan, a9, R], [scan, b9, accept, b9, S]], Yes]
Conditions: none
All three lists are nonempty and unique;input is a blank-free tape subset,but state and alphabet labels may overlap.Source NUL-joined(from,read) keys are unique,and halting states have no outgoing rules.A partial table is legal,not filled with rejection;transition collation and UTF16 set order differ.
Rule: TM_complete_signature_partial_transition_table_allowed · Uses: G001, S001
Before
source roles = [b9, Yes, [[accept, reject, scan], [a9, b9], [_, a9, b9], _, scan, accept, reject, [[scan, _, scan, _, S], [scan, a9, scan, a9, R], [scan, b9, accept, b9, S]]]]
After
derived = [[[accept, reject, scan], [a9, b9], [_, a9, b9], _, scan, accept, reject, [[scan, _, scan, _, S], [scan, a9, scan, a9, R], [scan, b9, accept, b9, S]]], Yes]
Conditions: none
Require the exact full signature and all schema transitions;sample successful traces do not certify an arbitrary TM.
Rule: TM_EXACT_canonical_scan_schema_not_sampled_machine · Uses: G001, S002
Before
source roles = [[a9, a9], b9, [[scan, _, scan, _, S], [scan, a9, scan, a9, R], [scan, b9, accept, b9, S]]]
After
derived = [[scan, 2, [[0, a9], [1, a9]]], [scan, 2, [[0, a9], [1, a9]]], Yes, No]
Conditions: none
Copy/R across every target-free input symbol reaches blank at head|w|.The blank rule writes blank,stays S and remains scan,so the entire configuration repeats.Determinism proves this input loops forever,refuting this recognizer as a decider,not by budget exhaustion.
Rule: TM_actual_target_free_input_reaches_EXACT_blank_SELFLOOP · Uses: G001, S003
S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.([accept, reject, scan], [a9, b9], [_, a9, b9], [[scan, _, scan, _, S], [scan, a9, scan, a9, R], [scan, b9, accept, b9, S]], b9, [a9, a9], [scan, 2, [[0, a9], [1, a9]]], [scan, 2, [[0, a9], [1, a9]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 3355b499fd27f5d508576a29f39e841dd0850186c75717bdb1636009a4f96c27candidate record SHA-256: e0f809355af741c65faa9c7d2b4709815bf47aec3048c2273da3c2d0e33768e5semantic review receipt SHA-256: 049a9e07e69fead88d93b34f0937b9470a06d71c1a8d097058fc83554529bdd0question-first witness SHA-256: 0c71ebb418f3de347d232d159fc25e93036f4ab9166bcfb5ee5b4be86d5c55b9Lean: NOT_RUN · human review: NOT_PERFORMED