The Invariant Measure Framework: Z = Ω/d as a Zero-Parameter Unification of Cosmological and Particle Physics Observables

A geometric framework deriving 35 testable physical observables from a single identification: the partition function Z = Ω(S²)/d = 4π/4 = π, with zero free parameters. The framework decomposes the gravitational coupling 8πG = 2dZG (d = 4 spacetime dimensions, Z = π) and constructs all predictions from the noncommutative fuzzy sphere S²_{N=3} (N = 3 fermion generations). Predictions span nine domains: cosmological parameters (Ωm = 1/π, Ωk = 1/32π³), dark energy dynamics (w(z) = −1 + (1/π)cos(πz), predicting phantom crossing at z ≈ 0.5 consistent with DESI DR2), CMB observables (ns, As, τ), particle physics (Higgs mass to 0.12σ from geometry via λ_phys = (π/24)(1 − 1/(Nπ)²), giving mH = v√(2λ_phys) = 125.27 GeV), gauge coupling corrections, and the CKM matrix. A fuzzy sphere distance correction δ²/d = 1/324, derived from the same noncommutative structure used in the Higgs mass prediction, resolves the sound horizon tension from 1.74σ to 0.01σ. Combined fit across all 35 predictions: χ²/dof = 0.55, p = 0.986. The identification Z = Ω(S²)/d = π is motivated by the thermodynamic interpretation of the Einstein field equations (Jacobson 1995) and independently confirmed via Hawking temperature, Bekenstein-Hawking entropy, and the Chamseddine-Connes spectral action. All input parameters are geometric (d, Z, N, β = 1/π, δ = 1/N²). No fitting. CAMB-validated. Preprint. Peer review invited.