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.

A normalized Riemann map for the slit plane

Example

Let S:=C∖(−∞,0], and let z denote the principal root branch on S. Then

f(z):=z−1z+1

is a normalized Riemann map sending 1 to 0.

Facts & Assumptions

Given: The slit plane S and the principal square-root branch on it.

[L1]

The principal root branch biholomorphically maps the slit plane onto a sector, in particular onto the right half-plane when n=2 (A slit-plane root branch biholomorphically parametrizes a sector).

Verification

technique · direct
1.1

By [L1], z maps S biholomorphically onto the right half-plane. Composing with the Cayley map w↦(w−1)/(w+1) gives the displayed biholomorphic map f:S→D.

L1givenalgebra
2.1

One has f(1)=0, and f′(z)=1z (z+1)2,f′(1)=14>0. So f is normalized at 1.

step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

21 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