Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-04
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 Riemann zeta function is entire

Statement

False claim: the Riemann zeta function is entire.

Facts & Assumptions

Given: The global continuation theorem for zeta.

[L1]

Zeta is meromorphic on C and has a simple pole at 1 (The Riemann zeta function extends meromorphically to the complex plane with its only pole at 1).

Refutation

technique · direct
1.1

By [L1], zeta has a pole at 1 and therefore is not holomorphic there.

L1given
2.1

An entire function is holomorphic on all of C, so step 1.1 rules that out. Hence zeta is not entire.

step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

7 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