Λ Constant, Axis Aligned: CMB Anomalies from Topology

Three features of the cosmic microwave background (low-ℓ power suppression, parity asymmetry, and quadrupole-octupole alignment) have persisted across COBE, WMAP, and Planck. Often characterized as anomalies or statistical flukes, these features are not anticipated by statistical isotropy. We show that a nested, non-orientable topology (S¹ = ∂Möbius ↪ S³) predicts all three from geometry alone. Suppression is a global eigenmode constraint; parity and alignment are local statistics shifted by a phase field representing the cost of observing from somewhere specific. The same locality cost (~6.5% in phase position) that explains the parity gap also predicts the alignment departure via Möbius frame rotation, and connects to the Hubble tension through geometric coupling. What has been called the "axis of evil" may be the universe revealing the geometry of its beginning.

v5 erratum: the parity statistic P(30) ≈ 0.85 used in §III.B does not correspond to the Planck estimator. The Planck TT parity ratio is R_TT(30) ≈ 0.81 (A&A 641, A7, Fig. 25), which maps to P ≈ 0.55 under the paper's convention — not 0.85. The parity inversion, the derived locality shift Δf∥ = 0.065, and the "3% agreement" cross-check are retracted. The suppression prediction (ℓ_cut ≈ 31), the parity sign (odd preference from non-orientable topology), and the alignment mechanism (twist axis) are unaffected. See the attached erratum for full details. A revised treatment is in preparation.

v5 update: topology updated to (S¹ = ∂Möbius ↪ S³). Parity formula corrected (sin² → cos²), shifting intrinsic prediction from 0.79 to 0.75. Isotropic baseline corrected from 1.0 to 0.5. New concept: the parity gap (0.75 → 0.85) is inverted to derive a locality field Δf_∥ ≈ 0.065 (~6.5%), which then predicts the alignment departure Δθ ≈ 12° via frame rotation. One parameter explains both gaps - connection to Hubble tension noted. Core derivations and predictions refined. v4 scrapped due to error in figures during upload.