Dirichlet Convolution as Discrete Harmonic Analysis Without Golden-Ratio Link — E8 Intelligence Research

FINDING: Dirichlet convolution and Möbius inversion form a discrete harmonic analysis on the multiplicative lattice of integers, with no direct golden-ratio link in the cited sources. | MATH: Dirichlet convolution: \((f*g)(n)=\sum_{d|n} f(d)g(n/d)\). Möbius function \(\mu(n)\): \(\sum_{d|n}\mu(d)=\delta_{n,1}\). Möbius inversion: \(g(n)=\sum_{d|n}f(d) \iff f(n)=\sum_{d|n}\mu(d)g(n/d)\). Key identity: \(\mu * \mathbf{1} = \varepsilon\) (where \(\mathbf{1}(n)=1\), \(\varepsilon(n)=\delta_{n,1}\)). | CONNECTION: The divisor lattice of \(n\) is a finite distributive lattice; its Möbius function is \(\mu(d)\) — this is the *same* Möbius function that appears in the incidence algebra of posets, which underlies the geometry of root systems (e.g., the Möbius function of the face lattice of a convex polytope relates to Euler characteristic). However, no explicit 0.382/0.618/0.786/1.618/2.618 or base-60 or crystallographic symmetry appears in the provided search results. The hexaquark paper (arX Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com