Alphabeta Math
False statementConstruction: 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.

FALSE: conformal equivalence preserves Euclidean area

Statement

If two plane domains are conformally equivalent, then they have the same Euclidean area.

Facts & Assumptions

Given: The domains D(0,1/2) and D.

[L1]

A conformal equivalence is a biholomorphism between complex domains (Conformal equivalence and the automorphism group of a domain).

Refutation

technique · direct
1.1

The map f(z)=2z is holomorphic and bijects D(0,1/2) onto D, with holomorphic inverse w↦w/2. Hence [L1] makes these two domains conformally equivalent.

L1givenalgebra
2.1

Their Euclidean areas are different: Area⁡(D(0,1/2))=π4,Area⁡(D)=π. So conformal equivalence does not preserve Euclidean area.

step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

2 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