Patch Fluctuations, Latency Noise, and Decoherence-like Effects Stochastic Latency Fields, Phase Noise, and Effective Decoherence in a Finite-Capacity Physical Theory

We develop the stochastic fluctuation branch of the finite-capacity latency–erasure program by introducing a noise sector for the latency field . Rather than treating latency as a purely smooth background quantity, we allow for local patch-to-patch fluctuations generated by finite-capacity update irregularities. The field is decomposed into a mean component and a stochastic component, , and the fluctuation sector is modeled by a linear relaxational stochastic equation with diffusion and noise. We derive the resulting two-point correlation structure, show how latency fluctuations induce phase noise in clocks and oscillatory systems, and obtain an effective decoherence-like damping factor for coherent phase evolution. In the Gaussian regime, the coherence envelope is controlled by the variance of the integrated stochastic latency process. The theory therefore predicts a direct connection between finite-capacity patch fluctuations, fractional frequency noise, and exponential or near-exponential coherence loss depending on the underlying noise spectrum. We further formulate explicit coherence-envelope and residual-noise test strategies, derive illustrative exclusion logic in the plane, and introduce a first-pass order-of-magnitude comparison framework for experimentally accessible stochastic-latency scales. This establishes the fourth major phenomenological branch of the finite-capacity program, extending it from deterministic weak-field, cosmological, and hysteretic sectors to stochastic laboratory signatures.