Fractal Geometry, Recursive Dynamics, and Observational Cosmology
Creators: name: Del Bel, Julian
Publisher: name: Zenodo
Year: 2025

description: 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.
description: This thesis introduces a framework for understanding the propagation of gravitational waves and the geometry of spacetime, grounded in the scaling behavior of spatiotemporal  influences  governed  by  the  golden  ratio  ϕ  and  π. By  integrating  these fundamental  constants  into  the  fabric  of  gravitational  and  quantum  fields,  we  propose a unified theory that links General Relativity, Quantum Mechanics, and causal feedback through a new interpretation of spatiotemporal influence zones, gravitational holographs, and nonlinear wave propagation.  Specifically, we investigate the role of ϕ in nonlinear causality and retrocausal feedback loops,  and the function of π  in harmonic oscillations and the scaling of spacetime curvature.  The theoretical framework is supported by empirical data from gravitational wave observatories (e.g., GWOSC), where waveforms are analyzed for consistency with predicted scaling behaviors. We used GWOSC data to analyze gravitational waveforms, comparing observed signals with predicted pattern scaling framework.  The consistency of observed waveforms with the expected nonlinear propagation and non-local feedback behaviors pointed as strong  empirical  evidence  for  the  theory.   Virgo’s  data  was  used  to  further  test  the theoretical framework’s predictions on gravitational waves,  by cross-referencing data from multiple observatories.  Supplying a robust test of non-locality and retrocausality in the context of spacetime curvature and wave propagation.  LIGO data allows us to check if the nonlinear oscillations predicted by the framework, as well as causal feedback loops, are consistent with real-world observations.  The waveform fitting performed on LIGO data can be compared with the predictions from scaling to validate the thesis. We also explore novel experimental approaches that could further test and validate this theory, particularly in the context of non-local quantum gravitational signatures and holographic baryon asymmetry. Through this work, we aim to not only deepen our understanding of gravitational and quantum interactions but also provide a new paradigm for exploring the unification of these fields in the context of spatiotemporal dynamics.