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R0010-05637 · q-20261008-advance-20261012-r04-set-membership-0012
The finite type is Fin(6)={0,…,5}. Complete characteristic table bits=[0, 0, 0, 1, 1, 1] uses 0/1 membership from index 0; ordered queries=[0, 1, 2]. Give (type-eligibility mask, membership truth values or ill-typed).
G001 — The finite type is Fin(6)={0,…,5}. Complete characteristic table bits=[0, 0, 0, 1, 1, 1] uses 0/1 membership from index 0; ordered queries=[0, 1, 2]. Give (type-eligibility mask, membership truth values or ill-typed).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
declared finite type or bounded integer universe
After
membership truth is distinct from eligibility to ask the question
Conditions: none
Being outside the type is not the same as false membership.Check only the declared finite type or integer set,not all set theory or unrestricted comprehension.
Rule: finite_membership_scope · Uses: G001
Before
legal index=0∈Fin(6);bit=0
After
membership=False
Conditions: none
In the complete characteristic table,1 means true membership and0 false;both are valid typed judgments.
Rule: complete_characteristic_bit · Uses: G001, S001
Before
legal index=1∈Fin(6);bit=0
After
membership=False
Conditions: none
In the complete characteristic table,1 means true membership and0 false;both are valid typed judgments.
Rule: complete_characteristic_bit · Uses: G001, S002
Before
legal index=2∈Fin(6);bit=0
After
membership=False
Conditions: none
In the complete characteristic table,1 means true membership and0 false;both are valid typed judgments.
Rule: complete_characteristic_bit · Uses: G001, S003
Before
legal index=3∈Fin(6);bit=1
After
membership=True
Conditions: none
In the complete characteristic table,1 means true membership and0 false;both are valid typed judgments.
Rule: complete_characteristic_bit · Uses: G001, S004
Before
legal index=4∈Fin(6);bit=1
After
membership=True
Conditions: none
In the complete characteristic table,1 means true membership and0 false;both are valid typed judgments.
Rule: complete_characteristic_bit · Uses: G001, S005
Before
legal index=5∈Fin(6);bit=1
After
membership=True
Conditions: none
In the complete characteristic table,1 means true membership and0 false;both are valid typed judgments.
Rule: complete_characteristic_bit · Uses: G001, S006
Before
query=0;legal in Fin(6)=Yes
After
False
Conditions: none
Check typing before reading a bit;do not replace ill-typed with False.For Fin(0),every integer query is outside the type.
Rule: typed_membership_query_guard · Uses: G001, S007
Before
query=1;legal in Fin(6)=Yes
After
False
Conditions: none
Check typing before reading a bit;do not replace ill-typed with False.For Fin(0),every integer query is outside the type.
Rule: typed_membership_query_guard · Uses: G001, S008
Before
query=2;legal in Fin(6)=Yes
After
False
Conditions: none
Check typing before reading a bit;do not replace ill-typed with False.For Fin(0),every integer query is outside the type.
Rule: typed_membership_query_guard · Uses: G001, S009
S010 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S009 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.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.([Yes, Yes, Yes], [False, False, False])
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: 3dfbd5a715cae57adf1f11860a8201178b3ef70684292dee961dd926cf9eb51fcandidate record SHA-256: 46e5cdbff89b9098b8de5b5114e1ffa6bef029976052ced112ac87d1ecf15fc4semantic review receipt SHA-256: 0328166a2e335aac7a5fb34556e68c80ba7d16612e822b3999c8ac348a9ca06fquestion-first witness SHA-256: 0da18e4e6cf71ece5ec5f00dd0cd161217b6d251672bc0b46d79fe7e6253f5fcLean: NOT_RUN · human review: NOT_PERFORMED