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.

Schottky's theorem applied to a disc map with center value 1/2

Example

For each 0<r<1 there is a constant Cr>0 such that every holomorphic f:D→C∖{0,1} with f(0)=1/2 satisfies

∣f(z)∣≤Cr(∣z∣≤r).

Facts & Assumptions

Given: A radius 0<r<1 and a holomorphic map f:D→C∖{0,1} with f(0)=1/2.

[L1]

Schottky's theorem supplies a bound depending only on the center modulus and the target radius (Schottky's theorem).

Verification

technique · direct
1.1

Apply [L1] with R=1/2. This gives a constant C(1/2,r) depending only on r.

L1given
2.1

The constant from step 1.1 works for the present function, so one may take Cr:=C(1/2,r).

step 1.1∎

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