Prime–Weighted Galactic Eigenmodes: Evidence for the Universal Model Framework in the Milky Way's Great Wave

Recent Gaia DR3 observations reveal the Milky Way's disc exhibiting a large-scale vertical corrugation—"The Great Wave"—spanning 10–20 kpc with amplitudes of 150–200 pc and radial velocities of 10–15 km/s directed outward. This paper derives this phenomenon rigorously within the Universal Model Framework (UMF), an information-theoretic paradigm where reality emerges from five distinction-logic axioms encoded in Euler's identity eiπ+1=0eiπ+1=0. Starting from a prime-weighted Lagrangian with activation function χp(μ)=[1+exp⁡(−5(ln⁡μ−ln⁡Ep)/ln⁡μ0)]−1χp(μ)=[1+exp(−5(lnμ−lnEp)/lnμ0)]−1, derived via thermal averaging of recursive excitation probabilities, we quantize allowed wavevectors as kn=2πpn/Lpkn=2πpn/Lp for primes pnpn. This yields discrete symmetry protection with damping time τprot=14.5±3.5τprot=14.5±3.5 Gyr, far exceeding the Hubble time H0−1H0−1. Renormalization-group scaling with Hausdorff dimension DH=1.585±0.041DH=1.585±0.041 predicts a galactic coherence length Lcoh≈10Lcoh≈10 kpc, aligning with observed wave scales. Empirical matches include wavelength, amplitude, velocity, phase shift (π/2π/2), and stability against Gaia DR3 constraints (deviations < 5%). Cross-validation ties to CMB acoustic peaks at primes {223, 541, 809} (deviations 1.4%, 0.9%, 0.1%; Bonferroni αeff=0.017αeff=0.017). Pre-registered falsification protocols span CMB multipoles, gravitational wave sidebands (Einstein Telescope SNR > 5 at 223/541/809 Hz), and quantum coherence (NV-center d > 0.4 at prime intervals). This establishes the Great Wave as a holographic projection of prime-indexed eigenmodes, providing the strongest astrophysical evidence yet for UMF's prime-fractal substrate of cosmic structure. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.