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R0054-27576 · q-20261015-advance-20261118-r06-regular-expression-0051
Use alphabet=[a, b, c] and typed regular-expression AST={"type":"symbol","value":"a"}. Words are arrays of alphabet symbols; distinguish empty language from the language containing the empty word. Decide word=[]. Give (alphabet, canonical_typed_AST, word, member, accepted_words_at_same_length, membership_scope).
G001 — Use alphabet=[a, b, c] and typed regular-expression AST={"type":"symbol","value":"a"}. Words are arrays of alphabet symbols; distinguish empty language from the language containing the empty word. Decide word=[]. Give (alphabet, canonical_typed_AST, word, member, accepted_words_at_same_length, membership_scope).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 = [regex-word-membership]
After
derived = [[alphabet, canonical_typed_AST, word, member, accepted_words_at_same_length, membership_scope]]
Conditions: none
List the complete operation/mode field order without JavaScript or answer-shape inference;Boolean,string,null and an unclaimed result remain distinct.
Rule: source_ordered_fields_without_JS · Uses: G001
Before
source roles = [Regex ORIGINAL membership.ast, [a, b, c], {'type': 'symbol', 'value': 'a'}]After
derived = [{'type': 'symbol', 'value': 'a'}, {type:"symbol",value:"a"}]Conditions: none
For EACH node qualify type,exact keys and symbol membership.A union checks raw arity>=2 BEFORE extensional deduplication,so its canonical form may have one child.Concatenation retains order and star retains its child.Do not revalidate canonical output as raw input with a new arity gate.
Rule: Regex_EACH_typed_node_exact_keys_symbol_scope_union_set_concat_order · Uses: G001, S001
Before
source roles = [[a, b, c], 0]
After
derived = [1]
Conditions: none
The bounded universe has sum |alphabet|^k words,including epsilon,and source budget<=4096.This defines complete bounded enumeration,not unbounded equivalence.
Rule: Regex_COMPLETE_bounded_word_universe_not_unbounded_equivalence · Uses: G001, S002
Before
source roles = [Regex ORIGINAL membership.language, symbol, {'type': 'symbol', 'value': 'a'}, 0]After
derived = [[]]
Conditions: none
The empty language has no words;epsilon has the single empty word;a symbol has its one token within the queried length bound.Words are token arrays,not reinterpreted character splits.
Rule: Regex_atomic_language_EMPTY_versus_EPS_versus_literal_symbol · Uses: G001, S003
Before
source roles = [[a, b, c], {'type': 'symbol', 'value': 'a'}, [], 0]After
derived = [No, []]
Conditions: none
Recompute through the FULL queried length and retain every accepted word at that length.The empty word differs from a symbol;absence from an insufficient shorter bound is not nonmembership.
Rule: Regex_WHOLE_queried_word_exact_membership_complete_same_length_slice · Uses: G001, S004
S005 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.S004 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.S003 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.S002 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.S001 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.([a, b, c], {type:"symbol",value:"a"}, [], No, [], complete_membership_not_absence_from_an_insufficient_bound)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: d54396237bd857fc711d960e5b5278aac5160852e2fd7090b8667604edf53df6candidate record SHA-256: 7be124f8def788ac00d56f04171b40f2aa5d75989b2049e96518a08df88d079asemantic review receipt SHA-256: 0a76d8e93c08bb16998a0483f3dfc0504f269fc3e1982e6cd868cab0a2856d54question-first witness SHA-256: 09127b736c225714dfa0b7ceb0e6a6e66df27438b480cad8217d3c2f99ce9437Lean: NOT_RUN · human review: NOT_PERFORMED