Prime Generation by Harmonic Collapse

We define a constructive mechanism for generating primes using the harmonic collapse formula Ck(n) = nk - 2, where n is an odd integer and k is an odd harmonic multiplier. For every odd n ≤ 500,000, empirical testing confirms that at least one such k produces a prime. The ratio n/prime aligns with the harmonic fraction 1/k, with strongest fidelity for low k. We analyze the collapse frequency, decay patterns, and recursive trace structure, and identify saturation thresholds corresponding to simplex closure. These results support the hypothesis that prime distribution is governed by harmonic collapse, not randomness. This work provides a reversible, residue-aligned model of prime generation with both structural and computational integrity.