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.
Semilocally simply connected spaces with explicit basepoint convention
Definition
A space is semilocally simply connected at when there is a neighbourhood of and a basepoint-preserving inclusion whose induced map on fundamental groups is trivial (Neighbourhood of a point and neighbourhood base, with this library's convention that a neighbourhood need not be open, The homomorphism on fundamental groups induced by a pointed continuous map, Based loops and the fundamental group). It is semilocally simply connected when this holds at every point. The neighbourhood need not itself be simply connected.