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

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Dirichlet convolution and Möbius inversion form a discrete harmonic analysis on the multiplicative lattice of integers, but there is no evidence of a direct link to the golden ratio or crystallographic symmetries in the reviewed literature. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22732538

September 13, 2026Open Access

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

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Key Points

To evaluate the structural relationship between Dirichlet convolution, Möbius inversion on multiplicative integer lattices, and golden-ratio or crystallographic symmetries.
Examined algebraic formulations of Dirichlet convolution and Möbius inversion across finite distributive divisor lattices.
Assessed incidence algebra connections in partially ordered sets (posets), root systems, and convex polytope face lattices for golden-ratio constants.
Confirmed that Dirichlet convolution and the Möbius function constitute a discrete harmonic analysis framework governed by the identity μ 1 = ε.
Identified that divisor lattices mirror poset incidence algebras related to Euler characteristics, but establish no direct link to golden-ratio values (0.382, 0.618, 1.618) or base-60 symmetries.

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Implication

Theoretical analysis demonstrates discrete harmonic analysis on integer lattices via Dirichlet convolution, indicating no direct connection to golden-ratio proportions.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6aa7b40e0926e14a848b3865 https://doi.org/10.5281/zenodo.22732538

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

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

Key Points

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Implication

Discussion

Cite This Study

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