Alphabeta Math
ExampleConstruction: 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.

The unit-disc extremal problem is solved by the identity

Example

For Ω=D and z0=0, the extremal map is the identity f(z)=z, and the extremal derivative is 1.

Facts & Assumptions

Given: The extremal family F(D,0).

[L1]

If h:D→D is holomorphic and h(0)=0, then ∣h′(0)∣≤1, with equality only for rotations (Schwarz lemma with the equality cases).

Verification

technique · direct
1.1

Every map h∈F(D,0) satisfies h(0)=0 and h′(0)>0, so [L1] gives 0<h′(0)≤1.

L1given
2.1

The identity map belongs to F(D,0) and has derivative 1 at 0, so the extremal derivative is exactly 1. Equality in [L1] forces any extremizer to be a rotation, and the positivity of the derivative leaves only the identity.

L1step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

10 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