Alphabeta Math
CounterexampleConstruction: AI-generatedVerification: AI-generatedPipeline-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-07
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.

Harmonic on a punctured domain need not extend

Statement refuted

A function harmonic on a punctured domain need not extend harmonically across the puncture.

Counterexample

Given: n≥2.

1.1

On R2∖{0} take log⁡∣x∣; for n≥3 take ∣x∣2−n, both harmonic by Radial harmonic functions away from the origin [given].

2.1

Each is unbounded as x→0, so it has no continuous, hence no harmonic, extension [given]. ∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

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Sources