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 horizontal strip

Example

On the strip

S:={ z∈C:∣Im⁡z∣<π/2 },

the map

f(z):=ez−1ez+1

is a normalized Riemann map sending 0 to 0.

Facts & Assumptions

Given: The strip S and the map f above.

[L1]

The exponential maps the principal strip biholomorphically onto the slit plane (The exponential is the inverse biholomorphism from the principal strip to the slit plane).

Verification

technique · direct
1.1

The strip S maps by z↦ez biholomorphically onto the right half-plane, and the Cayley map w↦(w−1)/(w+1) sends that half-plane biholomorphically onto D. Hence f is a biholomorphic map from S onto D.

L1givenalgebra
2.1

Direct computation gives f(0)=0 and f′(z)=2ez(ez+1)2,f′(0)=12>0. So f is normalized at the chosen basepoint.

step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

19 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