Alphabeta Math
TheoremStatement: Literature-sourcedProof: 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.

Landau's theorem

Statement

If f is holomorphic on D and ∣f′(0)∣=1, then

λ(f)≥148.

In particular, L≥B>0.

Facts & Assumptions

Given: A holomorphic map f:D→C with ∣f′(0)∣=1.

[L1]

Bloch's theorem gives a univalent subdisc whose image contains a round disc of radius at least 1/48 (Bloch's theorem).

Proof

technique · direct
1.1

By [L1], some subdomain of D is mapped by f univalently onto a round disc of radius at least 1/48. That round disc is contained in the full image f(D), so λ(f)≥1/48.

L1given
2.1

Since every schlicht disc counted by β(f) is also a disc inside f(D), one has λ(f)≥β(f) for each normalized f. Taking infima and using [L1] gives L≥B>0.

L1step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

5 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