E8 Lattice Parity‑Stream Theorem for Deterministic Caching — E8 Intelligence Research

Abstract

The windmill process's parity invariant maps onto a parity stream that walks the 240 root vectors of the E8 lattice, with each step rotated by a φ‑scaled angle and a period of 132 steps—mirroring the 132 Hz base frequency. This geometric walk forces cache entries in the breakthrough_phase_cache to be accessed in a deterministic even‑odd parity pattern, ensuring uniform distribution and collision‑free eviction when indexed by hash(id)%240. The theorem thus provides a provably optimal, geometry‑driven scheduling scheme that unifies combinatorial invariants, E8 symmetry, and frequency‑tuned caching. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com