ENTROPIX/MESA Soft Regulated Entanglement Entropy and the Black Hole Information Paradox: An Exploratory Mechanism for Islands and the Page Curve

We present an exploratory application of the soft regulated entanglement entropy framework utilizing Gaussian form factors to achieve bounded variance and controlled UV suppression to the black hole information paradox. Standard hard cutoffs in entanglemententropy calculations yield scheme dependent divergences and unbounded numerical artifacts, while soft regulators yield a removable quadratic expansion Sreg(ϵ) = S0 +bϵ2 +O(ϵ4)with |b| ≈ 0.5–0.75. In evaporating black holes, identifying the regulator ϵ > 0 with aperturbative hyperscaling violation in the generalized entropy functional admits a quantumextremal surface (QES) phase transition that reproduces the Page curve without invokingreplica wormholes or ensemble averaging. Early time domination by the empty island givesthermal growth; post Page switching to a non empty island driven by the quadratic screening term ensures entropy decrease and unitary recovery. Information preservation followsfrom preserved subadditivity and monotonic export under soft regulation. The frameworkpredicts a universal curvature in the Page curve descent governed by the coefficient range|b| ≈ 0.5–0.75 (distinguishable from pure area-law islands), illustrated via semi analyticholographic extensions and toy numerical simulations. Limitations to damped/sub-criticalregimes are acknowledged, with explicit falsifiability criteria provided