A TUCSL-Motivated Mechanism for Page-like Curves from Transactional Noise Kernels

We develop and analyze a TUCSL-motivated mechanism that can generate a Page-like turnover for a fine-grained entropy proxy of Hawking radiation. The mechanism isformulated in terms of a colored transactional noise ξ(v) along horizon generators, whosetwo-point function is controlled by a positive kernel C_f (v, v′) obtained by smearing projectedstress–energy correlators. We (i) derive exact analytic expressions for windowed early–latecorrelations for exponential kernels, with particular emphasis on the regime in which thetemporal gap is comparable to the coarse-graining scale; (ii) propose a positive-definitetwo-channel kernel with a controlled “post-Page” activation of a long-memory component;(iii) show that the resulting Gaussian mutual information between successive emission binsand the past can exceed the local thermality increment, producing a Page-like turnover in atransparent entropy-balance recursion; and (iv) confront the parameter space with laboratorybounds on CSL-like rates and correlation lengths, emphasizing the extreme hierarchy betweenstellar-mass Page times and experimentally constrained collapse timescales. We discusstwo consistent interpretations: (a) the transactional noise as an effective unraveling of anunderlying unitary completion, or (b) a strong scale/curvature suppression of the effectivecollapse rate for macroscopic black holes.