Roth Base Case

Abstract

A one-variable index estimate supplies the base case of the Roth argument.

Theorem 1.1 (Roth Base Case).

Lean statement: D5/S3/Arith/DiophantineApproximation/RothBaseCase.index_le_base

Proof. Machine-checked in Lean as D5/S3/Arith/DiophantineApproximation/RothBaseCase.index_le_base (✓ std3). ∎

Citation. Ralf Stephan (2026). Subspace-Theorems. URL: https://github.com/rwst/Subspace-Theorems/tree/bfd830f481b296989fa5f0c1e48d9316f72270d8.

Commentary.

A one-variable index estimate supplies the base case of the Roth argument.

References

• Truth anchor: D5/S3/Arith/DiophantineApproximation/RothBaseCase.index_le_base
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/Gelfond
• Dependency: D5/S3/Arith/DiophantineApproximation/IndexRename