Roth Key Inequality

Abstract

The auxiliary-polynomial estimates imply Roth’s key local approximation inequality.

Theorem 1.1 (Roth Key Inequality).

Lean statement: D5/S3/Arith/DiophantineApproximation/RothKeyInequality.roth_key_inequality

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

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

Commentary.

The auxiliary-polynomial estimates imply Roth’s key local approximation inequality.

References

• Truth anchor: D5/S3/Arith/DiophantineApproximation/RothKeyInequality.roth_key_inequality
• Dependency: D5/S3/Arith/DiophantineApproximation/BoxMonomial
• Dependency: D5/S3/Arith/DiophantineApproximation/CountingVolume
• Dependency: D5/S3/Arith/DiophantineApproximation/MvPolynomialEvalBound
• Dependency: D5/S3/Arith/DiophantineApproximation/PolynomialIndex