Alphabeta Math
ExampleConstruction: AI-generatedVerification: AI-generatedPipeline-generatedjudge 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.

Smoothed versus sharp explicit formulas

Example

The linear cutoff equals 1 through x and fades to 0 on (x,y), whereas the sharp formula evaluates ψ0(x) and gives half weight at a prime power.

Verification

Given: the smoothed and sharp formulas.

1.1

The two integrations by parts in the smoothed formula supply Mellin decay, hence a declared convergent zero sum.

givenalgebra
2.1

The sharp formula instead has a finite ordinate sum and an error containing ⟨x⟩; at a jump its left hand side is explicitly half-weighted.

step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

16 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