ENTROPIX- MESA Rigorous UV Completion and Stability of Soft Regulated Entanglement Entropy in Non Markovian Flows

Weprovide a rigorous UV completion for entanglement entropy in open quantum systemsusing Gaussian soft regulators. We resolve the previous conflation between the quadraticcoefficient b and the stability coefficient γ, proving that γ2 ≈ 2|b|. By employing a formal renormalization subtraction scheme, we eliminate UV divergences in the entanglementintegral, yielding a finite correction ∆S ∝ ϵ2. We extend this to non Markovian regimes(Redfield and Hu-Paz-Zhang), demonstrating that regulation bounds anomalous diffusionand suppresses transient negativity in entropy production rates. Numerical verification in1D harmonic chains confirms a variance reduction of 81.4%