Alphabeta Math
False statementConstruction: 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.

FALSE: the Gamma function is entire

Statement

False claim: The Gamma function is entire.

Facts & Assumptions

Given: The meromorphic continuation theorem for Gamma.

[L1]

Gamma extends meromorphically to C with simple poles at 0,−1,−2,… (Meromorphic continuation of Gamma).

Refutation

technique · direct
1.1

By [L1], Gamma has a pole at 0 and therefore is not holomorphic there.

L1given
2.1

An entire function is holomorphic on all of C, so step 1.1 contradicts the claim. Hence Gamma is not entire.

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