Alphabeta Math
ExampleConstruction: AI-adaptedVerification: AI-adaptedPipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-14
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.

Fourier transform of dirac and one

Example

Assume Countable Choice. On Rn with the 2π normalization,

Fδ0=1,F1=δ0.

Facts & Assumptions

Given: Countable Choice and the fixed bilinear Fourier convention.

[F1]

The elementary-transform theorem gives the formulas for delta and the constant distribution (Fourier transform of delta constants plane waves and polynomials).

Verification

technique · direct test calculation and the supplied transform table
1.1

For φ∈S, ⟨Fδ0,φ⟩=φ^(0)=∫φ=⟨1,φ⟩. Thus Fδ0=1.

F1
2.1

The constant-distribution formula in [F1] gives F1=δ0 directly. Together with step 1.1, this checks that the reciprocal pair carries no factor of (2π)n in the repository normalization. Countable Choice is used only through [F1].

F1step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

13 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