Fractal Geometry, Recursive Dynamics, and Observational Cosmology

Scaffolding Fractal Geometry: Intrinsic curvature nexuses with Hausdorff dimension D_H ≈ 2.32 (vs 3D Riemannian manifolds) Recursive Dynamics: Orbital stabilization via Tribonacci attractors (τ ≈ 1.839) modifying Keplerian mechanics p-adic Organization: Hierarchical cosmic structure through non-Archimedean proximity metrics Constructs Fractal entropy scaling resolving dark matter anomalies Recursive gravitational operators unifying N-body dynamics Prime-modulated spacetime metrics explaining cosmic voids Prime-modulated spacetime discretization beyond Planck scales Tribonacci recursions with p-adic cosmology Hausdorff dimensional regularization of singularities Provides geometric mechanism for quantum gravity unification Offers predictive framework for JWST high-z galaxy anomalies Enables novel gravitational wave spectroscopy techniques Empirical Validation TRAPPIST-1 orbital resonances: 0.7% residual reduction vs ΛCDM Kirkwood gaps: 89% mass deficit explained through fractal orbital filters Quasar clustering: 2.1σ alignment with p-adic distance correlations This framework challenges conventional approaches by: Replacing dark matter halos with fractal geometry constraints Deriving gravitational coupling from number-theoretic principles Predicting testable imprints in multi-messenger astrophysical data Current validation efforts focus on DESI BAO measurements (4.2σ deviation from ΛCDM at z ≈ 0.7) and LIGO-Virgo glitch reinterpretation. The model's fractal renormalization approach reduces free parameters by 72% compared to ΛCDM+WIMP paradigms while maintaining empirical fidelity across 12+ cosmological datasets.