Transactional Unimodular CSL theory: obtainin a CMB-consistent calibration of the TUCSL entropic curvature β

In TUCSL minisuperspace, the onset of inflation is weighted by a tunnelling densityP (r) ∝ exp[−S(r)] for the dimensionless vacuum-energy parameter r := V /Planck mass^4, withS(r) = Ae/[r(1 + αr)] + (α + β)r^2. This structure implies a unique, parametrically narrowpeak r⋆ > 0. In earlier TUCSL work (Paper XIII) we quoted a naıve order-of-magnitudeestimate β ∼ 1036 based on a maximal-independence microstate counting in the bandageregion. Here we correct the interpretation of that number: it should be regarded as anupper-bound-like estimate, because correlations among unimodular “cells” and transactionalselection reduce the effective entropic curvature entering Seff . Assuming the baseline single-field slow-roll mapping to CMB observables, the observed scalar amplitude fixes the slow-rollparameter at the peak and thereby calibrates the physically relevant β. We find thatβ ∼ 1032 yields a preferred scale quartic root of V⋆ ≃ 7.81e + 15 GeV , H⋆ ≃ 1.45e + 13 GeV , and predictsr_t ≃ 0.0034. For plateau/attractor potentials this corresponds to N ≈ 59.4 and n_s ≈ 0.9663with running α_s ≈ −5.67e − 04, consistent with current CMB constraints. The revised βshould be viewed as a data-calibrated effective parameter pending a first-principles derivationof correlation/selection corrections within TUCSL.