A closed quantum universe with a massless scalar in unimodular time: a truncated Efimov tower for negative Lambda, and an exploratory Gamow-law check for small positive Lambda

For a closed Friedmann universe with a massless scalar field and a unimodular (dynamical) cosmological constant, we compare with the known flat-space results in unimodular time. (i) At Lambda = 0 the Wheeler-DeWitt equation is a Bessel equation, giving the threshold phase delta0(k) = nu ln(3/2) - arg Gamma(i nu), nu = sqrt(3/2) k, in closed form; this phase was obtained earlier for the same model, in a scalar-clock setting, by Berkimbayev (arXiv:2608.19261). Used as the boundary phase of the unimodular-time Hamiltonian, it shows that curvature removes the accumulation of negative-Lambda levels at Lambda -> 0-, while the log-periodic (Efimov) tail at large |Lambda| survives. (ii) For small positive Lambda the classically recollapsing universe, reflected at the singularity, is a resonance of the unimodular-time Hamiltonian (as trapped closed universes are quasistationary states with decay widths in fluid-clock models); an exploratory, post hoc analysis finds its width matches the Gamow law T/(2|delta'|), i.e. about 1/T cycles before escape to de Sitter expansion. Two tests written into a protocol before they were run failed and are reported; the protocol's timestamps are self-recorded (local commit log), with no hashes and no external registration. The protocol, amendments, review summaries (all reviews by independent AI instances) and all scripts are in the source archive. A modest extension of known results. Note on versions. Version 2 supersedes version 1, which stays available. It follows an independent post-publication review. Withdrawn: the claim that the closed-form threshold phase is new (it is Eq. 15 of Berkimbayev 2026), version 1's statement that the registered convention was displaced by O(sqrt T) (it decays more slowly, roughly as T^0.3), the O(sqrt T) ambiguity stated for the estimator conventions, and "pre-registered ... with hashes" and "blind review log". Corrected: the description of Maydanyuk (2011), the attribution to Gielen and Menéndez-Pidal (the single run for Lambda < 0 is classical there), the "classical period" wording, and the evaluation point of the Kemble transmission (which changes the Kemble-T ranges). Rerun: the resonance window ends are now root-found, which adds two resonances at k = 8 and one at k = 13 (21, 32, 46 resonances); no conclusion changed. Added: credit to Berkimbayev, Kuzmichev, Unruh, Daughton-Louko-Sorkin and Gryb-Thébault, and the deviations from the protocol. Full list in REVIEW_POSTPUB.md in the deposit.