Roth Theorem

Abstract

Selected-place approximants beyond exponent two form a finite set.

Theorem 1.1 (Roth Theorem).

Lean statement: D5/S3/Arith/DiophantineApproximation/RothTheorem.finite_setOf_prod_min_one_le

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

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

Commentary.

Selected-place approximants beyond exponent two form a finite set.

References

• Truth anchor: D5/S3/Arith/DiophantineApproximation/RothTheorem.finite_setOf_prod_min_one_le
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/AbsoluteScalarHeight
• Dependency: D5/S3/Arith/DiophantineApproximation/RothAuxiliary
• Dependency: D5/S3/Arith/DiophantineApproximation/RothKeyInequality
• Dependency: D5/S3/Arith/DiophantineApproximation/RothMovingChain