False statementConstruction: Literature-sourcedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-08-30

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 nonconstant meromorphic function on the plane omits at most one sphere value

Statement

A nonconstant meromorphic function on $C$ omits at most one value of $\hat{C}$ .

Facts & Assumptions

Given: The meromorphic exponential counterexample.

[L1]

The exponential meromorphic map on $C$ omits $0$ and $\infty$ (The exponential function omits 0 and infinity as a meromorphic map on the plane).

Refutation

technique · direct

1.1L1given

Fact [L1] is already a nonconstant meromorphic function on $C$ omitting two sphere values.

2.1step 1.1∎

Therefore the claim "at most one sphere value" is false.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

7 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

Aleksander Simonic, The Ahlfors lemma and Picard's theorems (standard reference, not scraped)