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R0009-05212 · q-20261008-advance-20261011-r07-tends-to-relation-0062
The complete total map f:Fin(6)→Fin(2) has images=[0, 1, 1, 0, 0, 1] indexed from 0; Fin(6)={0,…,5}. Every table entry must lie in the target type. S=[0, 1, 2]. principal(S) contains all source subsets containing S; the empty generator is allowed, and no NeBot premise is added. T=[0], ordered candidates=[100, 0, 0]. For each c, answer whether c∈S and f(c)∉T; do not evaluate f at a candidate outside its type.
G001 — The complete total map f:Fin(6)→Fin(2) has images=[0, 1, 1, 0, 0, 1] indexed from 0; Fin(6)={0,…,5}. Every table entry must lie in the target type. S=[0, 1, 2]. principal(S) contains all source subsets containing S; the empty generator is allowed, and no NeBot premise is added. T=[0], ordered candidates=[100, 0, 0]. For each c, answer whether c∈S and f(c)∉T; do not evaluate f at a candidate outside its type.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 index=0∈Fin(6)
After
image=0∈Fin(2)
Conditions: none
Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing.
Rule: complete_principal_map_row · Uses: G001
Before
source index=1∈Fin(6)
After
image=1∈Fin(2)
Conditions: none
Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing.
Rule: complete_principal_map_row · Uses: G001, S001
Before
source index=2∈Fin(6)
After
image=1∈Fin(2)
Conditions: none
Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing.
Rule: complete_principal_map_row · Uses: G001, S002
Before
source index=3∈Fin(6)
After
image=0∈Fin(2)
Conditions: none
Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing.
Rule: complete_principal_map_row · Uses: G001, S003
Before
source index=4∈Fin(6)
After
image=0∈Fin(2)
Conditions: none
Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing.
Rule: complete_principal_map_row · Uses: G001, S004
Before
source index=5∈Fin(6)
After
image=1∈Fin(2)
Conditions: none
Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing.
Rule: complete_principal_map_row · Uses: G001, S005
Before
Fin(6)→Fin(2);S=[0, 1, 2];full map=[0, 1, 1, 0, 0, 1]
After
principal(S)={A:S⊆A};empty generators allowed,no NeBotConditions: none
The declared convention allows empty S;its family of supersets then contains the empty set,and no proper-filter or NeBot condition is added.This is a finite principal-generator model,not a general sequence or point limit.
Rule: finite_principal_generator_convention · Uses: G001, S006
Before
candidate=100;inside Fin(n)=No;inside S=No
After
image if in S=null;obstruction=No
Conditions: none
Check type and S-membership before table access;outside S do not read the table,so negative or outside indices cannot masquerade as legal map evaluations.
Rule: typed_principal_candidate_obstruction · Uses: G001, S007
Before
candidate=0;inside Fin(n)=Yes;inside S=Yes
After
image if in S=0;obstruction=No
Conditions: none
Check type and S-membership before table access;outside S do not read the table,so negative or outside indices cannot masquerade as legal map evaluations.
Rule: typed_principal_candidate_obstruction · Uses: G001, S008
Before
candidate=0;inside Fin(n)=Yes;inside S=Yes
After
image if in S=0;obstruction=No
Conditions: none
Check type and S-membership before table access;outside S do not read the table,so negative or outside indices cannot masquerade as legal map evaluations.
Rule: typed_principal_candidate_obstruction · 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.[No, No, No]
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: df8feb5fba796fcf31747af0dfd00c34189517220f324371d7e7eb786cf5f9ddcandidate record SHA-256: cdea98aaf88562eef3e73aafa68f8d8cbdb990f60ab901ef220920241ec4ffe7semantic review receipt SHA-256: 71e7db519df31f3a164533e472e293cb64f001b475a8d002b4a5c2740a237b56question-first witness SHA-256: 5a43f4f81b6256281f8d139a4010bbde127be803c528e5878857269c8f854462Lean: NOT_RUN · human review: NOT_PERFORMED