Roth Auxiliary

Abstract

An auxiliary polynomial realizes prescribed derivative vanishing with degree and height bounds.

Theorem 1.1 (Roth Auxiliary).

Lean statement: D5/S3/Arith/DiophantineApproximation/RothAuxiliary.exists_auxiliary_deriv

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

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

Commentary.

An auxiliary polynomial realizes prescribed derivative vanishing with degree and height bounds.

References

• Truth anchor: D5/S3/Arith/DiophantineApproximation/RothAuxiliary.exists_auxiliary_deriv
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/GaussLemma
• Dependency: D5/S3/Arith/DiophantineApproximation/AuxiliaryPolynomial
• Dependency: D5/S3/Arith/DiophantineApproximation/MvPolynomialEvalBound
• Dependency: D5/S3/Arith/DiophantineApproximation/RothLemma