Alphabeta Math
DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-08-28
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.

Möbius transformations of the Riemann sphere

Definition

For complex numbers a,b,c,d with ad−bc≠0, the associated Möbius transformation is the map M:C^→C^ given on the finite plane by M(z)=az+bcz+d whenever cz+d≠0, and extended by M(−d/c)=∞(c≠0),M(∞)={a/c,c≠0,∞,c=0.

Two coefficient quadruples that differ by a common nonzero scalar define the same map. The next theorem packages this as the quotient by scalar matrices.

Depends on

Used by

Dependency tree · two levels

3 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