Cube Slicing

Abstract

A Gaussian slice bound gives central sections of a convex symmetric set volume at least one.

Theorem 1.1 (Cube Slicing).

Lean statement: D5/S3/Arith/AbsoluteValues/Heights/CubeSlicing.one_le_volume_subtype_mem

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

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

Commentary.

A Gaussian slice bound gives central sections of a convex symmetric set volume at least one.

References

• Truth anchor: D5/S3/Arith/AbsoluteValues/Heights/CubeSlicing.one_le_volume_subtype_mem
• Dependency: D5/S3/Arith/AbsoluteValues/Heights/ProductOfBalls