Cosmological Imprints of K₈ Compactification: The Orbifold Aspect-Ratio Identity rₛ/deq = τ₂ and CMB Low-Multipole Suppression from Spinᶜ Holonomy : MNRAS Preprint

We present two cosmological predictions of the twelve-dimensional Riemannian framework M₁₂ = (S¹Sol × S³) × K₈, which obtains the cosmological constant (Λeff ≈ 10⁻¹²² MPl⁴), the Weinberg angle, and the dark matter abundance ratio from compactification geometry with zero continuous free parameters. First, the internal orbifold aspect ratio τ₂ = 1.86—dynamically locked by Spinᶜ flux stabilisation through a closed-form polynomial Qw² = 12τ₂⁴ + 2τ₂²—identifies the observed ratio of cosmological imprint scales rₛ/deq ≈ 147/79 ≈ 1.86 as a single internal geometric datum rather than a coincidence of six independent parameters. Second, the Spinᶜ holonomy on K₈ assigns successive quarter-period phases \1, i, -1, -i\ to the four fixed points of the T²/Z₂ orbifold; the corresponding Z₄ 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 Δ C₂/C₂ ≈ -8% and Δ C₃/C₃ ≈ -14%, with negligible suppression at ≥ 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, S³ 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.