Induction Through Cyclotomic Zero Intervals

Abstract

Theorem 1.1 (Zero direction).

Lean statement: D5/S3/Combinatorics/DigitHankel/CyclotomicDigitHankelVanishingInduction.zero_direction

Proof. Machine-checked in Lean as D5/S3/Combinatorics/DigitHankel/CyclotomicDigitHankelVanishingInduction.zero_direction (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Bartosz Sobolewski, Maciej Ulas (2026). Hankel determinants of weighted binary sums of digits. DOI: 10.48550/arXiv.2607.09376. URL: https://arxiv.org/abs/2607.09376v1.

Commentary.

For d at least two and any d-th root of unity zeta, every n in the cyclotomic zero set has vanishing binary digit Hankel determinant at 2 times zeta.

Truth anchor: D5/S3/Combinatorics/DigitHankel/CyclotomicDigitHankelVanishingInduction.zero_direction
Dependency: D5/S3/Combinatorics/DigitHankel/CyclotomicDigitHankelVanishing