Abstract
This essay mines a paper on SIS epidemic variance for structural patterns related to the Riemann Hypothesis via moments and random matrix statistics.
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The Source Paper
The source paper develops a diffusion approximation for the variance of SIS (susceptible-infected-susceptible) epidemics on configuration-model networks. While mean-field laws describe average behavior, fluctuations depend on higher moments of the degree distribution. The authors introduce "wedge factors" κ^(r)_S—normalized expected numbers of r-star motifs centered at susceptible vertices—which appear in the diffusion matrix. For the simpler SI process (no recovery), exact formulas exist via generating functions; for SIS, recovery breaks exact closure, requiring approximations.
The Proposed Analogy
We speculate that the wedge factor hierarchy corresponds to the moment sequence of the Riemann zeta function or the correlation functions of its zeros. The moment closure problem in epidemics—where exact dynamics requires infinite motif moments—mirrors the difficulty of computing higher moments of ζ beyond the leading-order random-matrix predictions. The SI/SIS distinction (exact vs. approximate) is analogized to the distinction between leading-order GUE statistics and the full arithmetic-dependent moment conjectures.
Assessment
This is rated a suggestive metaphor only. While both systems involve moment hierarchies governing fluctuations, the epidemic model is finite-dimensional with absorbing states, while zeta is infinite with no absorbing boundary. The "moments" in the source are factorial moments of degree distributions, not spectral moments. The analogy offers conceptual insight but no calculable bridge to the Riemann Hypothesis.
This essay was produced by an automated research pipeline and has not been peer reviewed; conjectures herein are unproven.