Blowup above the exponent one third in viscous Katz-Pavlović dyadic models with small shell ratios

For the viscous Katz–Pavlović dyadic model with shell ratio Λ > 23/2, global regularity holds exactly for dissipation exponents α ≥ 1/3. We prove that this threshold is not universal: for Λ = 6/5, 13/10, 3/2, 17/10 and 9/5, suitable nonnegative finitely supported data lose regularity in finite time for every α ≤ αΛ, where αΛ > 1/3; for example α13/10 = 0.378. The blowup is carried by a self-similar energy front whose amplitude grows by a fixed factor κ > 1 per shell. The proof reduces the dynamics to one renormalized step of the front and verifies that step in interval arithmetic with the CAPD library; it is rigorous provided CAPD and the verifier are correct. The result concerns the dyadic model, not the Navier–Stokes equations. The conjectured threshold for every shell ratio is supported by computation only. The archive contains the paper (PDF, LaTeX source with the figures as PNG, LaTeX source with the figures as PDF), the interval verifier and its output for the five cases, an independent 60-digit re-check of the scalar inequalities, independent C and Julia computations, and a Lean 4 formalisation with Mathlib of eight elementary lemmas (the interval computation is not formalised). Version 1.1.0 adds the DOI of this archive (concept DOI 10.5281/zenodo.23247974) to the paper, the README and the citation file. The mathematics is unchanged from version 1.0.0 (doi:10.5281/zenodo.23247975).