Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-08-30
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.

The residue of Gamma at z=-2

Example

Res⁡(Γ,−2)=12.

Facts & Assumptions

Given: The pole-residue formula for Gamma.

[L1]

Res⁡(Γ,−n)=(−1)n/n! for every integer n≥0 (Meromorphic continuation of Gamma).

Verification

technique · direct
1.1

Substitute n=2 into [L1]. Then Res⁡(Γ,−2)=(−1)2/2!.

L1given
2.1

Since (−1)2=1 and 2!=2, step 1.1 simplifies to Res⁡(Γ,−2)=1/2.

step 1.1algebra∎

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