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.

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The chordal metric on the Riemann sphere

Definition

Let Σ:C^→S2 be the stereographic homeomorphism of Stereographic projection identifies the Riemann sphere with the unit two-sphere. The chordal metric on C^ is χ(p,q):=∥Σ(p)−Σ(q)∥2(p,q∈C^), that is, the Euclidean chord length between the corresponding points of the unit sphere.

Because Σ is a bijection, χ(p,q)=0 exactly when p=q, and the metric properties are inherited from the Euclidean metric of R3. The explicit coordinate formula on the finite plane is computed on the companion examples page.

Depends on

Used by

Dependency tree · two levels

6 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