Question 12435: Check the Whole Finite Vertex Map for Bijectivity

Original question and givens

The complete map on Fin(6)={0,…,5} has images=[0, 1, 3, 4, 5, 2] in source-label order, all in the target carrier of the same size. Give (n,mapping,bijective?). This family allows the unique empty map when n=0.

• G001 — The complete map on Fin(6)={0,…,5} has images=[0, 1, 3, 4, 5, 2] in source-label order, all in the target carrier of the same size. Give (n,mapping,bijective?). This family allows the unique empty map when n=0.

Definition and 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.

• mko-graph-isomorphism

Step-by-step derivation

complete mapping=[0, 1, 3, 4, 5, 2];target label=0

source fiber=[0];exactly one=Yes

complete mapping=[0, 1, 3, 4, 5, 2];target label=1

source fiber=[1];exactly one=Yes

complete mapping=[0, 1, 3, 4, 5, 2];target label=2

source fiber=[5];exactly one=Yes

complete mapping=[0, 1, 3, 4, 5, 2];target label=3

source fiber=[2];exactly one=Yes

complete mapping=[0, 1, 3, 4, 5, 2];target label=4

source fiber=[3];exactly one=Yes

complete mapping=[0, 1, 3, 4, 5, 2];target label=5

source fiber=[4];exactly one=Yes

n=6;all target fibers=[[0], [1], [5], [2], [3], [4]]

bijective=Yes;empty carrier uses unique empty map

Reverse checks

• 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.

Result

(6, [0, 1, 3, 4, 5, 2], Yes)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

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.