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 general Bernstein PBW construction and source boundary
Remark
The general Bernstein PBW obligation is now supplied locally in General Bernstein PBW and the Iwahori–Matsumoto comparison. Its proof begins with the signed-alcove basis, constructs multiplicative Bernstein elements, calculates both cross-relations by a finite deletion/reflection sum, and proves both ordered bases and the Iwahori–Matsumoto presentation isomorphism. The canonical root-datum geometry and the exceptional wall-parameter attachment are explicit suppliers. The formal presentation with an arbitrary unattached second scalar is not identified with a previously fixed affine parameter function.
The native author's source report and escalation are preserved in the owner completion before archive. Solleveld and Ciubotaru state the general theorem with proof referred elsewhere. The completion uses Görtz's full alcove-walk treatment and supplies the explicit local arguments; a named external theorem is not a proof supplier. This remark is context, and consumers use the proved theorem rather than this remark. All current carriers remain draft pending native review.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
8 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
- Maarten Solleveld, Affine Hecke Algebras and Their Representations (standard reference, not scraped)
- Dan Ciubotaru, Tutorial on Affine Hecke Algebras (standard reference, not scraped)