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 direct link to the golden ratio or crystallographic symmetries in the cited sources. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22732537

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 whether Dirichlet convolution and Möbius inversion link to golden-ratio constants or specific crystallographic symmetries within discrete harmonic analysis.
Analyzed algebraic properties of Dirichlet convolution and Möbius inversion on integer multiplicative lattices.
Evaluated incidence algebras of finite distributive lattices against geometric root systems and polytope face lattices.
Dirichlet convolution and Möbius inversion act as a discrete harmonic analysis system linked via the identity of the Möbius function and the constant function.
Integer divisor lattices share formal Möbius properties with the incidence algebras of partially ordered sets and root systems.
No direct mathematical link appears between these lattice operations and golden-ratio ratios, base-60 systems, or crystallographic symmetries in the examined sources.

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Implication

Theoretical analysis reveals discrete harmonic analysis in integer divisor lattices, indicating an absence of direct golden-ratio relationships.

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Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6aa7dfc60926e14a848b3d78 https://doi.org/10.5281/zenodo.22732537

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

Key Points

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Cite This Study

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

Key Points

No abstract yet

Implication

Discussion

Cite This Study

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