Prime Harmonics in Symbolic Geometry: A Frequency-Space Model for Prime Number Emergence

This working paper presents a novel symbolic geometry framework for understanding prime number distribution. By modeling prime emergence as a function of coherence and harmonic interference on a discretized symbolic sphere, we identify persistent frequency bands (≈0.17–0.19, 0.42–0.48) that correlate strongly with primes. The model demonstrates optimal performance at fine angular resolutions (1° facet granularity), suggesting that prime numbers arise as resonance artifacts of symbolic standing waves. Spectral and wavelet analyses confirm the stability and non-randomness of these prime-associated harmonics across ranges. This interdisciplinary approach bridges wave-based systems and discrete number theory through symbolic rendering.