"$S^3$ Spatial Topology, Sol Geometry, and JWST Anomalies.'' Paper X in MEF Series

We derive cosmological predictions from the twelve-dimensional Riemannian framework $\mathcal{M}_{12} = (S^1_{\mathrm{Sol}} \times S^3) \times K_8$, which in Papers I–VIII obtained the complete CKM and PMNS mixing matrices, the cosmological constant ($\Lambda_{\mathrm{eff}} \approx 10^{-122} M_{\mathrm{Pl}}^4$), the Higgs boson mass, the Weinberg angle, and the dark matter abundance ratio—all from manifold geometry with zero continuous free parameters.

Three cosmological results emerge without observational input. First, the $K_8$ spectral bridge predicts the baryon acoustic oscillation scale $L_{\mathrm{BAO}} = e^{-3\pi/2} \sqrt{3/\Lambda} \approx 146$ Mpc, in agreement with the observed $147 \pm 0.3$ Mpc to better than 1%. Second, the internal orbifold aspect ratio $\tau_2 = 1.86$ matches the ratio of cosmological imprint scales $r_s/d_{\mathrm{eq}} \approx 1.86$ to 0.5%. Third, the Sol temporal geometry, through its Anosov flow coupling to protogalactic angular momentum, produces a parameter-free disk formation timescale $\tau_{\mathrm{align}} = 2 t_{\mathrm{dyn}}$ derived from the twelve-dimensional Einstein equations—enabling disk galaxy formation in protocluster environments by redshift $z \sim 8$.

The Sol mechanism provides a unified explanation for the excess massive galaxies (Labbé et al. 2023) and the unexpectedly early ordered rotating disks (Ferreira et al. 2023) observed by the James Webb Space Telescope: these are the same galaxies, formed through a single geometric mechanism. The $\mathrm{Spin}^c$ holonomy of $K_8$—independently responsible for the Weinberg angle at particle scales—produces CMB low-multipole power suppression of $\sim 8\%$ at $\ell = 2$ and $\sim 14\%$ at $\ell = 3$, consistent with the Planck observation of 10–15% deficit.

All geometric structures were established before any comparison with JWST data. Six falsifiable predictions are presented, testable by JWST, Euclid, DESI, and the Roman Space Telescope within the present decade.