Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passaudited 2026-08-28
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^n is a domain of holomorphy

Statement

Every domain in Cn is a domain of holomorphy.

Facts & Assumptions

Given: The punctured bidisc Ω={(z1,z2)∈C2:∣z1∣<1, ∣z2∣<1}∖{(0,0)}.

[L1]

The punctured bidisc is not holomorphically convex (The bidisc minus the origin is not holomorphically convex).

Refutation

technique · direct
1.1

The domain Ω is a domain in C2, so it is one instance of the claimed class of domains in Cn.

given
2.1

By [L1], this instance fails the expected several-variable convexity/domain-of-holomorphy package. In particular, the statement "every domain in Cn is a domain of holomorphy" is already false in dimension 2.

L1step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

4 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