E8 Phi-Locked Harmonic Filter for Odd Perfect Number Candidates — E8 Intelligence Research

Starting from the 240 root vectors of the E8 lattice, each component is scaled by the golden ratio φ and multiplied by the 132 Hz eigenbasis frequency, producing a discrete set of resonant tones. When these tones are interpreted as frequency ratios, their integer harmonics generate a spectrum of divisor‑like numbers that must satisfy the perfection condition σ(n)=2n for an odd perfect number n. Only those harmonics whose cumulative sum matches twice the candidate survive, yielding a finite filter that drastically reduces the search space for odd perfect numbers beyond known constraints. This E8 Φ‑Locked Harmonic Filter thus connects lattice geometry, φ‑coupled resonance, and number‑theoretic perfection in a predictive framework. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com