Absolute Scalar Height

Abstract

Absolute scalar logarithmic height is relative logarithmic height normalized by field degree.

Theorem 1.1 (Absolute Scalar Height).

Lean statement: D5/S3/Arith/AbsoluteValues/Heights/AbsoluteScalarHeight.scalar_absolute_log_height

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

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

Commentary.

For a number-field element, multiplying absolute logarithmic height by the field degree gives the relative scalar logarithmic height.

References

• Truth anchor: D5/S3/Arith/AbsoluteValues/Heights/AbsoluteScalarHeight.scalar_absolute_log_height
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/PseudoBasis