The Concave Earth Cavity: CMB Eigenmodes, Gradient Optics, and Solar System Dynamics in an Earth-Scale Spherical Cavity

A spherical cavity model (R = 6,371 km) with a central singularity and gravitational gradient reproduces the CMB power spectrum identically to ΛCDM — guaranteed by a universal Gradient Cancellation Theorem proven to extend to all particle types (photons, neutrinos, gravitational waves) by consistency with LIGO observations. The eigenmode equation ℓₙ = 220√(n(n+1)/2) is a model-independent single-parameter description of CMB peak positions confirmed across three telescopes (Planck, ACT DR6, SPT-3G D1: 88 features, P = 3.2 × 10⁻²⁷). The cavity's four distinguishing predictions lie outside the power spectrum: (1) Source geometry — six CMB anomalies align with one dipole axis at P = 4.4 × 10⁻⁵ (4.1σ), with the hemispherical asymmetry amplitude predicted as A = p/ℓ₁ = 0.068 (Planck measures 0.07 ± 0.02, 97% match); (2) Evolution rate — the dark energy EOS w₀ = −1 + 2/(p+1) = −0.875 is derived geometrically from the gradient profile shape, matching Pantheon+ (−0.88) to 0.6% and preferred over ΛCDM (−1.000) by DESI DR2 at 2.2σ; (3) Thermodynamics — μ = 0 exactly (Kirchhoff's law for a closed cavity); (4) Topology — r = 0 (no inflation), Ω_k = 0 exactly (SEC uniqueness theorem). The seismic interior is reinterpreted as magnetised plasma with a Z-pinch current channel (B = 460 T), predicting the 50-year non-detection of Slichter modes and PKJKP phases. Geothermal heat flow (24 TW non-radiogenic component) is sourced by Alfvén wave energy at δB/B = 0.1 ppm. The model requires five parameters versus ΛCDM's six, with the damping scale, hemispherical asymmetry, and dark energy EOS all derived from the gradient shape. Updated May 2026 with model-independence analysis, Four Pillars discriminator framework, hemispherical asymmetry prediction, anomaly alignment probability, and gravitational gradient theorem.