False statementConstruction: AI-adaptedVerification: AI-generatedPipeline-generatedprecheck passjudge pass (gpt-5.6-terra)audited 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: a chordally locally uniform limit of holomorphic functions can never be identically infinity

Statement

A chordally locally uniform limit of holomorphic functions can never be identically $\infty$ .

Facts & Assumptions

Given: The sequence $f_{n} (z) = e^{n z}$ on the right half-plane.

[L1]

The family $e^{n z}$ converges chordally locally uniformly to $\infty$ on the right half-plane (The family e^(nz) converges chordally to infinity on the right half-plane without being holomorphically normal there).

Refutation

technique · direct

1.1

Fact [L1] provides an explicit holomorphic sequence whose chordal local uniform limit is the constant map $\infty$ .

L1given

2.1

That witness is exactly contrary to the statement, so the statement is false.

given∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

8 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

Matthias Weber, Complex Analysis, Ch. 5 §§5.1-5.2 (standard reference, not scraped)
Elias M. Stein and Rami Shakarchi, Complex Analysis, Ch. 2 §5.2 and Ch. 8 §3.2 (standard reference, not scraped)
Sheldon Axler, Paul Bourdon, and Wade Ramey, Harmonic Function Theory, Ch. 2 (standard reference, not scraped)