Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-generatedprecheck passaudited 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 normalized Riemann map from the upper half-plane sending i to 0

Example

The map

f(z):=i z−iz+i

is the normalized Riemann map from H to D sending i to 0.

Facts & Assumptions

Given: The upper half-plane H and the map f above.

[L1]

Automorphisms of the upper half-plane are real Möbius maps (Automorphisms of the upper half-plane are real Mobius maps).

[L2]

Blaschke factors are disc automorphisms (Blaschke factors are automorphisms of the disc).

Verification

technique · direct
1.1

The Cayley transform C(z)=(z−i)/(z+i) maps H biholomorphically onto D, and multiplication by i is a disc automorphism. Thus [L1] and [L2] make f a biholomorphic map H→D.

L1L2given
2.1

Direct substitution gives f(i)=0. Differentiating yields f′(z)=i2i(z+i)2,f′(i)=12>0. So f has the required normalization at i.

step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

16 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