Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-adaptedPipeline-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-07
How 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 singular A2 dot orbit collapses

Example

In type A2, choose λ with ⟨λ+ρ,α1∨⟩=0 and ⟨λ+ρ,α2∨⟩>0. Then s1⋅λ=λ, so the dot orbit has ∣S3∣/2=3 distinct weights rather than six.

Facts & Assumptions

Given: The dot-action and linkage conventions The strong linkage order on weights.

Verification

technique · direct
1.1givenalgebra

The zero pairing means the shifted weight is fixed by s1, hence s1⋅λ=λ.

2.1step 1.1algebra∎

Its stabilizer contains {1,s1} and is exactly this subgroup for a generic point on that wall, so orbit-stabilizer gives three distinct translates. The regular six-vertex diagram therefore cannot be used unchanged.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

3 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