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R0010-05553 · q-20261008-advance-20261012-r07-function-mapping-0003
The complete total map f:Fin(3)→Fin(8) has images=[2, 0, 5] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.
G001 — The complete total map f:Fin(3)→Fin(8) has images=[2, 0, 5] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.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
f:Fin(3)→Fin(8);source indices start at0
After
complete total map,not a partial program function
Conditions: none
Every legal source element has one codomain value.Fin(0) is empty;an outside query is ill-typed,not a hole of a partial function at a legal input.
Rule: total_finite_mapping_scope · Uses: G001
Before
f input=0∈Fin(3)
After
f(0)=2∈Fin(8)
Conditions: none
Audit source and codomain eligibility for every entry;an unqueried entry may not be illegal.
Rule: complete_mapping_entry · Uses: G001, S001
Before
f input=1∈Fin(3)
After
f(1)=0∈Fin(8)
Conditions: none
Audit source and codomain eligibility for every entry;an unqueried entry may not be illegal.
Rule: complete_mapping_entry · Uses: G001, S002
Before
f input=2∈Fin(3)
After
f(2)=5∈Fin(8)
Conditions: none
Audit source and codomain eligibility for every entry;an unqueried entry may not be illegal.
Rule: complete_mapping_entry · Uses: G001, S003
Before
[2, 0, 5]
After
[[0, 2], [1, 0], [2, 5]]
Conditions: none
List[i,f(i)] for every source index;do not invent graph points for unused codomain elements.An empty source has an empty graph.
Rule: complete_finite_function_graph · Uses: G001, S004
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.[[0, 2], [1, 0], [2, 5]]
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: b31bd5a5ff750d242df6279049c2e815478bb35a4042eef9ee24861ae2cf6a69candidate record SHA-256: 8f2d8d4b62fd9fef4d2c294f7446f788460aa0580c810398a1169d1cc994f254semantic review receipt SHA-256: 0328166a2e335aac7a5fb34556e68c80ba7d16612e822b3999c8ac348a9ca06fquestion-first witness SHA-256: 0da18e4e6cf71ece5ec5f00dd0cd161217b6d251672bc0b46d79fe7e6253f5fcLean: NOT_RUN · human review: NOT_PERFORMED