Prime Number Wave Collapse

This paper introduces a novel framework in which prime numbers are modelednot as isolated arithmetic facts, but as destructive interference minima betweentwo analytic waves: a symmetry function Ψ(n) and a structure function Φ(n).The resulting collapse residual, ∆(n) = |Ψ(n) − Φ(n)|2, reaches deep minima atprime positions and rises for composites.Spanning 19 orders of magnitude, the model achieves RMSLE < 0.08 andAUC = 1.000, suggesting primes are governed by a geometric interferenceprinciple rather than pure randomness or combinatorial structure. The collapsefield provides a continuous, real-valued primality signal—revealing that primesare not merely distributed with probabilistic density, but are the analytic groundstates of number theory.