Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-generatedPipeline-generatedprecheck passjudge 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.

FALSE: a Möbius transformation with three fixed points can be nonidentity

Statement

A Möbius transformation with three fixed points may be nonidentity.

Facts & Assumptions

Given: A Möbius transformation M with three distinct fixed points.

[L1]

A Möbius transformation with prescribed values on three distinct sphere points is unique (A unique Möbius transformation carries any ordered triple of distinct sphere points to any other).

Refutation

technique · direct
1.1

The identity map is Möbius and has the same values as M on those three fixed points.

given
2.1

Fact [L1] makes a Möbius transformation with those three prescribed values unique, so M must already be the identity. Hence the statement is false.

L1given∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

5 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