Cyclic Orbits, Boolean Reachability and Difference Structure in Finite Boolean Spaces
Jyri Lisjutin · Zenodo (CERN European Organization for Nuclear Research) · 2026
We consolidate cyclic rotations of finite binary words, complementary weight layers, Boolean operations, and cyclic correlation in a common framework. A two-transition lemma classifies universally reaching central orbits and leads to the identity (g−2a)ℓ=2b+r in noncentral layers. A self-contained coset-correlation counting lemma yields (g−1)(ℓ−1)≤r+1 for every noninvertible distinguished shift. This inequality gives a short, unified proof of the main rigidity ranges for all five defects r=1,...,5; analytic classifications identify eleven additional low-dimensional cyclic classes, with finite computation as a check. The B⁶ profile classes and extended-signature counts have been independently recalculated. The weight-two exceptional counts are now established analytically for arbitrary n≥4.