Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-generatedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-27
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: every domain in C^2 is a domain of holomorphy

Statement

False claim: every domain in C2 is a domain of holomorphy.

Facts & Assumptions

Given: Real numbers 0<r,s<1 and the Hartogs figure domain Ω:=H(r,s).

[L1]

A domain that contains a Hartogs figure but not its hull is not a domain of holomorphy (A domain containing a Hartogs figure but not its hull is not a domain of holomorphy).

Refutation

technique · direct
1.1

The domain Ω=H(r,s) contains the Hartogs figure H(r,s) itself, while its hull is the full bidisc H^(r,s), which strictly contains Ω.

givenalgebra
2.1

Therefore [L1] applies directly and shows that Ω is not a domain of holomorphy, refuting the claim.

step 1.1L1∎

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