We present a detailed TUCSL-motivated mechanism capable of producing a Page-liketurnover in a fine-grained entropy proxy for Hawking radiation. The mechanism is formu-lated as a stochastic effective description on null horizon generators: a colored transactionalnoise field with a positive-definite two-point kernel that is constrained by smearing of pro-jected stress-energy correlators and by unimodular closure conditions. We provide: (i) exactanalytic early–late window correlation formulas for exponential kernels, including a controlledanalysis of the regime in which the temporal gap is comparable to the coarse-graining scale;(ii) a positive-definite two-channel kernel ansatz with a post-Page activation of long mem-ory and a proof of positivity by construction; (iii) a rigorous Gaussian diagnostic based onincremental mutual information and conditional covariance, yielding a transparent entropy-balance recursion that exhibits a Page-like turnover without inserting the turnover by hand;and (iv) a careful discussion of parameter consistency in the presence of laboratory boundson CSL-like rates and correlation lengths, emphasizing the severe hierarchy between stellar-mass Page times and any unsuppressed effective nonunitarity. We clarify the logical status ofthe results and delineate what is demonstrated (correlation structure sufficient for purifica-tion in the proxy diagnostic) versus what remains to be derived (a full quantum-gravitationalcomputation of radiation von Neumann entropy)
Thomas Emilio Villa Villa (Mon,) studied this question.