Primacohedron: Prime-Indexed Logarithmic Cosmological Signatures from Emergent Arithmetic Spacetime

Abstract

We present a concise observational consequence of the Primacohedron framework, in which spacetime emerges
from prime-indexed adelic spectral coherence. The central prediction is a hierarchy of logarithmic modulations
in cosmological observables whose characteristic frequencies are tied to ln p for dominant coherent prime sectors.
Unlike generic resonant inflationary features, the predicted frequencies are discretized by arithmetic structure and
recur coherently across scalar perturbations, tensor backgrounds, and entropy-linked non-Gaussian observables.
The framework also predicts mild late-time deviation from exact vacuum dark energy and a running spectral
dimension from approximately two in the ultraviolet toward four in the infrared. The decisive observational test
is correlated prime-log recurrence across sectors.