Alphabeta Math
ExampleConstruction: AI-generatedVerification: AI-generatedPipeline-generatedprecheck passaudited 2026-08-29
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 disc automorphism carrying one prescribed point to another

Example

For a,b∈D, the map

fa,b(z):=φb(φa(z))

is an automorphism of D with fa,b(a)=b.

Facts & Assumptions

Given: Points a,b∈D.

[F1]

Every disc automorphism is a rotated Blaschke factor, and each Blaschke factor φc is itself a disc automorphism (Every automorphism of the disc is a rotated Blaschke factor).

Verification

1.1

By [F1], both φa and φb are automorphisms of D, so their composition fa,b=φb∘φa is again an automorphism of D.

F1given
2.1

Since φa(a)=0 and φb(0)=b, one has fa,b(a)=φb(φa(a))=φb(0)=b.

F1step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

4 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