CounterexampleConstruction: AI-adaptedVerification: AI-generatedjudge pass (gpt-5.6-terra)audited 2026-09-04

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

A vertex map need not be simplicial

Statement refuted

Every function on vertex sets extends to a simplicial map.

Take the domain complex with vertices $u, v$ and edge ${u, v}$ , and take the target complex with vertices $a, b$ and no edge ${a, b}$ . The vertex function $u \mapsto a$ , $v \mapsto b$ exists, but it sends the simplex ${u, v}$ to the set ${a, b}$ , which is not a simplex of the target. Hence it is not a simplicial map.

Depends on

A simplicial map and its geometric realization

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Allen Hatcher, Algebraic Topology (standard reference, not scraped)
Vidit Nanda, Computational Algebraic Topology, Lecture 01: Complexes (standard reference, not scraped)