The Prime Scalar Field: The Prime Pattern Solved. A

The Prime Scalar Field The Pattern of Prime Numbers: Fractals of a Quantized Harmonic Resonant Scalar Field Author: Damon Michael Dorsey - 4.21.2025 Abstract (A preliminary paper) Prime numbers are fundamental to mathematics and theoretical physics, yet their apparent randomness has long obscured their underlying structure. This paper introduces the Prime Scalar Field (PSF): a mathematical framework revealing that primes, when grouped as 3D coordinate triplets (PtN), form quantized, self-repeating harmonic waveforms that exhibit properties akin to scalar fields in quantum theory. Through polynomial analysis, wavefunction decomposition, frequency spectrum testing, and spatial visualization, we show that prime sequences form standing wave interference patterns, fractal self-similarity, and stable attractor modes across all scales. This theory provides undeniable data that the primes are far from random, but instead constitute the basic resonant informational substrate of physical reality.