CounterexampleConstruction: Literature-sourcedVerification: 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.

Finite dimensional does not imply finite or locally finite

Statement refuted

Every finite-dimensional simplicial complex is finite and locally finite.

Let the vertex set be ${v} \cup {w_{n} : n \geq 1}$ and let the simplices be the empty face, all singletons, and all edges ${v, w_{n}}$ . Every simplex has dimension at most $1$ , so the complex is finite dimensional. But it has infinitely many edges, so it is not finite, and the vertex $v$ lies in infinitely many simplices, so it is not locally finite.

Depends on

Local finiteness, finiteness, and finite dimensionality of a simplicial complex

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

2 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)