"Harmonic Geometry" - A Multidimensional Fractal Approach

This report presents a unified fractal framework combining number theory, fractal geometry, and cosmology. It embeds Fibonacci and Lucas sequences, prime-based sets (semiprimes), and non-trivial zeros of the Riemann zeta function into 5D/6D manifolds, revealing deep harmonic structures across numerical and cosmic scales. By examining how minor deviations of zeta zeros from the critical line disrupt fractal coherence, the study provides a geometry-based argument supporting a conditional Riemann Hypothesis. It further draws parallels with cosmic phenomena—such as entropy-driven cycles and galactic fractality—suggesting that universal harmonics underlie both discrete mathematics and large-scale cosmology.  
The document includes:  
A theoretical overview linking prime distributions and zeta zeros with fractal geometries.  
Methodological details for generating, normalizing, and clustering integer-based sequences.  
Evidence and results demonstrating fractal alignment and the high sensitivity to zeta-zero placement.  
A concluding discussion on broader impacts—philosophical, ethical, and scientific—alongside future directions and applications. 
A Python script, with a 5D version of the model, where you can explore the clusters in a simplistic way.  
This comprehensive report aims to stimulate interdisciplinary dialogue and to challenge conventional knowledge, proposing that harmonic fractal principles may connect micro-level prime expansions to macro-level cosmic evolutions. 

https://orcid.org/0009-0008-6051-4114