Principia Fractalis

ttps://github.com/FractalDevTeam/Principia-Fractalis

Principia Fractalis: A Unified Framework for Mathematics, Physics, and Computation This comprehensive treatise presents a novel mathematical framework connecting fractal geometry to fundamental problems across mathematics, physics, and theoretical computer science. The work establishes rigorous connections between self-similar structures and major open problems, including formal approaches to the Riemann Hypothesis, P vs NP, the Hodge Conjecture, and Yang-Mills mass gap. Key Contributions: - Formal mathematical framework linking fractal resonance to zeta function zeros and prime distribution - Constructive proofs with computational verification (150+ digit precision) - Complete Lean 4 formalization of core theorems with 33 formally verified proofs - Applications to quantum field theory, cosmology, and consciousness quantification - Novel computational methods including O(log n) primality testing algorithms Scope: The text spans 1,086 pages across 35 chapters and 17 appendices, providing rigorous treatment of fractal analysis, spectral theory, computational complexity, and applications to physics. All theoretical results are supported by numerical verification, reproducible code, and formal proofs in Lean 4.