A Previously Unreported 1,500 Mpc Density Wave in DESI: Evidence for Vacuum Inertia

We present M²¹ × ΦΚ/Kβ, a cosmological framework emerging from 21-dimensional G₂ geometry (3 branes × 7 dimensions), in which dark energy, dark matter, and ordinary matter arise as geometric projections without free parameters. The framework derives all structural constants a priori from G₂: the wave period T_W = r_s × ξ₀ = 350.83 Mpc (validated to 0.24%), the amplitude A = (γ−1)/(γ+1) = 0.5733 (1.29%), the phase φ = 360° × (γ−1)/γ = 262.4° (0.42%), the maximum inertia g_max = 21^(3/4) = 9.81 (exact identity), and the critical redshift z_c = 21/7 = 3 (exact). The single empirical parameter is α₀ = 0.01180, calibrated on 175 SPARC galaxies. We report two original observational results on independent large-scale datasets. First, the radial density profile of DESI BGS DR1 (3.8 million galaxies) centered on Shapley SC follows a damped wave whose amplitude envelope matches the a priori M²¹ prediction f_att(d) = 1/√(1+(d/s_c)²) with correlation r = +0.83 (p ★★★), without any fitting. This attenuation profile centered on Shapley SC over 1,500 Mpc has not been previously reported. Second, the M²¹ wave cycle dynamically modulates peculiar velocities in Cosmicflows-4 (45,000 galaxies): a gap of 628 km/s separates galaxies at the wave peak from those in the trough (p = 1.7×10⁻¹⁷), with a rise/fall asymmetry of 606 km/s (p = 1.7×10⁻⁴⁸). Both results are consistent with an inertial drag mechanism in which compressed vacuum maximally brakes galaxy motion. Additional validated results include: the g-field from Shapley correlates with CF4 local density (r = +0.335, p = 3×10⁻¹³¹, 46,013 galaxies); a Sedov back-blast harmonic signature (n=2 > n=1) in the CF4 FFT; wave continuity across 9.47 million DESI objects spanning z = 0 to 3.5 and 11 billion years of cosmic history; and brane-crossing density anomalies at 131 Mpc (+6.5σ) and 142 Mpc (+5.0σ). The framework produces 13 ★★★ results on independent data with a single empirical parameter, compared to 5+ for Λ-CDM.