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 acoustic reparametrisation of CMB peak positions (ℓ₁√2 ≈ l_A), confirmed across three telescopes (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 = 5.7 × 10⁻⁴ (3.3σ MC), with the hemispherical asymmetry amplitude predicted as A = p/ℓ₁ = 0.073 (Planck PR4: 0.073 ± 0.010, <1% match); (2) Evolution rate — the dark energy EOS w₀ = −1 + 2/(p+1) = −0.875 is derived geometrically, falling in the thawing quintessence class preferred by DESI DR2; (3) Thermodynamics — μ = 0 exactly (Kirchhoff's law); (4) Topology — r = 0, Ω_k = 0 exactly (SEC uniqueness theorem). The single parameter w₀ = −0.875 simultaneously reduces every major ΛCDM tension: H₀ (5→1.9σ), S₈ (2.6→1.8σ), A_L (3.6→1.4σ), w₀ (4.4→2.2σ), hemispherical asymmetry (3→0.2σ). The growth rate fσ₈ is fitted with Δχ² = −10 relative to ΛCDM across five DESI redshifts. Nucleosynthesis is resolved via conformal flatness (Weyl = 0, V ∝ A³, η invariant). The model requires only three free parameters (p, H₀, D₀) versus ΛCDM's six.