Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-generatedPipeline-generatedprecheck passjudge pass (gpt-5.6-terra)audited 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.

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FALSE: conformal maps preserve Euclidean lengths

Statement

Conformal maps preserve Euclidean lengths.

Facts & Assumptions

Given: The affine map f:C→C, f(z)=2z.

[F1]

A biholomorphism is conformal in this page's orientation-preserving sense (Biholomorphisms are conformal and have holomorphic inverse).

[F2]

A map is biholomorphic when it is bijective, holomorphic, and has holomorphic inverse (Biholomorphic maps between complex domains).

Refutation

1.1

The map f(z)=2z is holomorphic on C, bijective, and has holomorphic inverse f−1(w)=w/2, so [F2] and [F1] make it conformal.

F1F2given
2.1

But the unit tangent vector 1 at 0 is sent to f′(0)⋅1=2, whose Euclidean length is 2≠1. Therefore a conformal map need not preserve Euclidean lengths.

step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

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