Bombieri Vaaler Relative

Abstract

From numbers at least one, select a smaller subfamily with bounded geometric mean.

Theorem 1.1 (Bombieri Vaaler Relative).

Lean statement: D5/S3/Arith/AbsoluteValues/Heights/BombieriVaalerRelative.exists_injective_prod_pow_le

Proof. Machine-checked in Lean as D5/S3/Arith/AbsoluteValues/Heights/BombieriVaalerRelative.exists_injective_prod_pow_le (✓ std3). ∎

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

Commentary.

From numbers at least one, select a smaller subfamily with bounded geometric mean.

References

• Truth anchor: D5/S3/Arith/AbsoluteValues/Heights/BombieriVaalerRelative.exists_injective_prod_pow_le
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/BombieriVaalerMaxNorm
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/RestrictScalars
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/RowEntryHeight