Box Monomial

Abstract

A multivariate polynomial’s coefficient box controls its absolute multiplicative height.

Theorem 1.1 (Box Monomial).

Lean statement: D5/S3/Arith/DiophantineApproximation/BoxMonomial.absMulHeight_coeff_box

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

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

Commentary.

A multivariate polynomial’s coefficient box controls its absolute multiplicative height.

References

• Truth anchor: D5/S3/Arith/DiophantineApproximation/BoxMonomial.absMulHeight_coeff_box
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/GaussLemma
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/PseudoBasis
• Dependency: D5/S3/Arith/DiophantineApproximation/MvHasseDeriv