Cosmological Imprints of $K_8$ Compactification: The Orbifold Aspect-Ratio Identity $r_s/d_{\mathrm{eq}} = \tau_2$ and CMB Low-Multipole Suppression from $\mathrm{Spin}^c$ Holonomy : MNRAS Preprint

We present two cosmological predictions of the twelve-dimensional Riemannian framework $M_{12} = (S^1_{\text{Sol}} \times S^3) \times K_8$, which obtains the cosmological constant ($\Lambda_{\text{eff}} \approx 10^{-122} M_{\text{Pl}}^4$), the Weinberg angle, and the dark matter abundance ratio from compactification geometry with zero continuous free parameters. First, the internal orbifold aspect ratio $\tau_2 = 1.86$—dynamically locked by $\text{Spin}^c$ flux stabilisation through a closed-form polynomial $Q_w^2 = 12\tau_2^4 + 2\tau_2^2$—identifies the observed ratio of cosmological imprint scales $r_s/d_{\text{eq}} \approx 147/79 \approx 1.86$ as a single internal geometric datum rather than a coincidence of six independent $\Lambda\text{CDM}$ parameters. Second, the $\text{Spin}^c$ holonomy on $K_8$ assigns successive quarter-period phases $\{1, i, -1, -i\}$ to the four fixed points of the $T^2/\mathbb{Z}_2$ orbifold; the corresponding $\mathbb{Z}_4$ sum vanishes identically, and the same holonomy that produces the Weinberg angle at particle scales cancels the coherent neutrino-ISW contribution to the CMB at the lowest multipoles, yielding $\Delta C_2/C_2 \approx -8\%$ and $\Delta C_3/C_3 \approx -14\%$, with negligible suppression at $\ell \geq 5$. Both predictions agree with current data—the aspect-ratio identity to 0.5%, the CMB low-multipole suppression to within statistical uncertainty of the ~ 10% and ~ 15% Planck deficits. The BAO sound horizon, $S^3$ halo suppression, and Sol-induced disk-formation results of the same framework are reported separately in the companion preprints. Three falsifiable predictions for Planck legacy reanalysis, Simons Observatory, and Euclid are stated.