Alphabeta Math
ExampleConstruction: AI-generatedVerification: 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.

A holomorphic function on the punctured bidisc extends across the origin

Example

On the punctured bidisc {(z1,z2):∣z1∣<1, ∣z2∣<1}∖{(0,0)}, the function

f(z1,z2)=z11−z1z2

is holomorphic and extends holomorphically across the origin as the same formula.

Facts & Assumptions

Given: The punctured bidisc and the function f(z1,z2)=z1/(1−z1z2).

[L1]

In complex dimension at least two, a holomorphic function on a punctured domain extends uniquely across the puncture (An isolated puncture is removable in complex dimension at least two).

Verification

technique · direct
1.1

On the full bidisc one has ∣z1z2∣<1, so 1−z1z2≠0. Therefore the same formula defines a holomorphic function on the whole bidisc, and its restriction to the punctured bidisc is the displayed f.

givenalgebra
2.1

This explicit extension agrees with the abstract existence statement of [L1] for the missing point (0,0).

step 1.1L1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

6 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