Abstract

Standard cosmology explains most large-scale observations through the LCDM framework supplemented by an inflationary primordial sector. Yet the microphysical origin of inflation, the smallness and nature of dark energy, and the ultraviolet structure of spacetime remain open. This paper isolates a compact and falsifiable cosmological consequence of the Primacohedron framework: if macroscopic spacetime emerges from prime-indexed adelic spectral coherence, cosmological observables should carry logarithmic residues tied to prime frequencies. The strongest prediction is not merely an oscillatory feature, but a correlated hierarchy of log-periodic modulation across scalar perturbations, tensor backgrounds, and entropy-curvature non-Gaussianity. The same framework also predicts a running spectral dimension from approximately two in the ultraviolet to four in the infrared, and a small late-time deviation of the dark-energy equation of state from exact vacuum behaviour. The decisive test is cross-sector recurrence: the scalar and tensor sectors should exhibit compatible logarithmic spacings governed by ln p for dominant coherent prime sectors. Failure to find such correlated spacing in future high-precision cosmological data would strongly constrain this cosmological realization of the Primacohedron.

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