Alphabeta Math
ExampleConstruction: AI-adaptedVerification: 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.

The elementary Bloch proof on this page yields the explicit lower bound 1/48

Example

The proof of Bloch's theorem gives the concrete universal estimate

β(f)≥148(∣f′(0)∣=1).

Facts & Assumptions

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

[L1]

Bloch's theorem on this page proves β(f)≥1/48 (Bloch's theorem).

Verification

technique · direct
1.1

Fact [L1] gives the lower bound β(f)≥1/48 for every normalized holomorphic disc map.

L1given
2.1

Applying step 1.1 to the present function is exactly the stated example.

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

4 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