Alphabeta MathHow 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 delta-complex structure on the torus
Example
Start with a square whose opposite sides are identified to form a torus. Cut the square along one diagonal. The result is a delta-complex with two 2-simplices, three 1-simplices, and one 0-simplex after the side identifications are imposed.
This example is kept on the B page precisely because it is not an abstract simplicial complex: the same edge and vertex occur several times in the face maps of the two triangles. It is useful as a compact model of the torus, but it does not replace the A-page convention that simplices are determined by their vertex sets.
Used by
Nothing in the library uses this result yet.
Dependency tree · 0 levels
Nothing. This result depends on no other item in the library.
Sources
- Allen Hatcher, Algebraic Topology (standard reference, not scraped)