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 single stalk does not determine a global section
If two sections have the same germ at one point, they only agree on some possibly tiny neighbourhood of that point. Nothing in The stalk of a presheaf at a point or Germs of sections lets one recover the values of either section away from that neighbourhood.
For example, on the sheaf of continuous real-valued functions on , a function supported near and the zero function have the same germ at but are different global sections. Stalkwise arguments therefore need either all points at once or a neighbourhoodwise statement that can be glued.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
6 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
- Ravi Vakil, Foundations of Algebraic Geometry, Class 4 (standard reference, not scraped)