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 a sector with an explicit branch choice

Example

On the sector

S:={ reiθ:r>0, ∣θ∣<π/4 },

the map

f(z):=z2−1z2+1

is a normalized Riemann map sending 1 to 0.

Facts & Assumptions

Given: The sector S and the map f above.

[L1]

The square map biholomorphically sends S onto the right half-plane (Power maps are biholomorphisms on sectors of width less than 2π/n).

Verification

technique · direct
1.1

By [L1], z↦z2 sends S biholomorphically onto the right half-plane. Composing with the Cayley map w↦(w−1)/(w+1) gives a biholomorphic map from S onto D, namely the displayed f.

L1givenalgebra
2.1

Direct substitution gives f(1)=0, and f′(z)=4z(z2+1)2,f′(1)=1>0. So the map is normalized at 1.

step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

22 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