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.
Agreement with the published quotient model of
The quotient in The circle as with basepoint is the same
used in the examples on
subspaces-products-and-quotients-examples and
covering-spaces-and-lifting-examples: in each case two reals are identified
exactly when their difference is an integer, the canonical projection sends
to , and the target has the quotient topology induced by that
projection. Thus the notation here does
not introduce a second quotient-circle convention. The page names are given
only to record that agreement; no result on either examples page is used as a
dependency.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 35 results over 11 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.
Sources
- Jonathan Wise, Math 6210 Lecture Notes, Week 3, Sections 3.1 and 3.4 (standard reference, not scraped)