Corrigendum and update: 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 mass⁴, withS (r) = Ae/r (1 + αr) + (α + β) r². 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 predictsrₜ ≃ 0. 0034. For plateau/attractor potentials this corresponds to N ≈ 59. 4 and nₛ ≈ 0. 9663with running αₛ ≈ −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.