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.
The empty affine algebraic set corresponds to the unit ideal and the zero coordinate ring
Example
By definition, Conversely, every polynomial vanishes on the empty set, so Therefore the coordinate ring of the empty affine algebraic set is
This is the exact boundary case promised by the affine-set convention: the empty algebraic set matches the unit ideal and the zero ring.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
4 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
- J. S. Milne, Algebraic Geometry, Chapter 2a and 2i (standard reference, not scraped)
- Donu Arapura, Notes on Basic Algebraic Geometry, algebraic-set conventions in Chapter 1 (standard reference, not scraped)