Solution to Neutrino and Dark Matter Interactions and S₈ Tension

The persistent S₈ tension between early- and late-universe probes signals a potential departure from the standard ΛCDM paradigm. In a recent Nature Astronomy article, neutrino–dark matter (ν–DM) interactions were shown to alleviate this tension, with a ~ 3σ preference for a non-zero interaction strength u_ ≈ 10⁻⁴. Here, we reinterpret this signal through the lens of Entanglement-Weighted Operational Geometry (EWOG), a framework in which effective dissipative couplings emerge from the entanglement-weighted coarse-graining of quantum-gravitational degrees of freedom. We then perform a rigorous, multi-theory model comparison—pitting EWOG against ν–DM, ΛCDM, and five other beyond-ΛCDM templates (string theory, loop quantum gravity, conformal cyclic cosmology, celestial holography, noncommutative geometry, and twistor theory)—using a suite of statistical measures: AIC, BIC, Bayes factors, profile likelihoods, and a joint S₈–coupling figure of merit. Using the exact same dataset (Planck+BAO+ACT+DES Y3 cosmic shear), we find that both EWOG and ν–DM are strongly favored over ΛCDM (≈ -7.2, ≈ -3.1), while other one-parameter extensions are statistically indistinguishable from ΛCDM or disfavored. This work establishes EWOG as a viable, physically motivated alternative to particle-based ν–DM interactions and provides a template for high-stakes cosmological model selection.