Does Coherence Nest? CMB Anomalies, the Oort Cloud, and Domain Boundaries
Four large-angle CMB anomalies have persisted across COBE, WMAP, and Planck: a low-ℓ power deficit below ℓ ≲ 30, an anomalously suppressed quadrupole, odd-ℓ power systematically exceeding even-ℓ power, and alignment of the quadrupole and octupole axes to within ~10°. Each is individually modest. Together they suggest correlated large-angle structure that statistical isotropy does not anticipate.
All four follow from a single topological identification: the Poincaré homology sphere S³/2I with a non-orientable Möbius surface on a totally geodesic S² ⊂ S³. The Molien series for the binary icosahedral group empties five harmonic shells, producing the deficit. The observer's radial position suppresses the quadrupole through Gegenbauer projection. The non-orientable identification breaks even-odd parity. The twist axis aligns the low multipoles by construction, with the observed ~10° misalignment arising as parallax from the observer's displacement. Two geometric inputs (a curvature radius R ≈ 5.3 Gpc and an observer distance d = 2.1 Gpc) control all four features. The CMB-constrained R then independently recovers the cosmological constant Λ = 3/R² to 2%, a fifth observable with no additional freedom. Full CMB paper here: https://ssrn.com/abstract=6614358
The question I've been chasing is whether this structure stops at cosmic scale or keeps going. At galactic scale, there's an empirically persistent acceleration scale a₀ that defines a coherence length L_f = v_c²/a₀ of roughly 13 kpc. Inside that radius, the gravitational potential is uniform enough for observers to share the same local physics. Outside it, the dominant mode changes. At solar system scale, the Oort Cloud sits at roughly the same kind of boundary: inside, the Sun's gravity dominates and the ecliptic defines the symmetry plane. Outside, galactic tides take over.
If the topology that explains the CMB anomalies projects into every gravitationally coherent scale, these aren't separate phenomena. They're the same structure nesting downward, with each boundary marking where one coherent domain gives way to the next. Same wave, different witness stand.
The connection to coherence physics as discussed here: every persistent structure has a domain within which it maintains its identity. What sets the size of that domain, and what happens at the boundary when one domain gives way to the next, is the question regardless of whether you approach it through field theory or through spectral geometry.
The gaps are real and public. The galactic derivation of L_f uses flat rotation curves, which don't exist at stellar scale. Whether the nesting can be derived from first principles at every level is genuinely open.