A ceiling for the smooth-forcing blowup mechanism under fractional dissipation
Result. The smooth-forcing layer mechanism of the September 2026 Boussinesq blowup result cannot be pushed into the hypodissipative regime that a rough-forcing construction already reaches. Its own correction hierarchy (J = 2k + 8 levels, each gaining Pi^5 lambda^-(1-delta)), its seed rule (force below lambda^-6 after k derivatives) and its ratio rule (120 k <= Q), combined with the dissipative growth condition for its own amplitude system, cap the dissipation exponent it can carry at alpha <= 5.38e-04 in the (-Laplacian)^alpha convention, that is 1.08e-03 in the |grad|^alpha convention, attained at exactly one controlled derivative of the force (k = 1, Q = 120, margin delta <= 0.2583). That is 86 times below the exponent (22 - 8 sqrt 7)/9 already proved with a C^(1,eps) force by Cordoba, Martinez-Zoroa and Zheng. The gap is structural: the amplitude margin saturates at 1/2 however many derivatives are demanded, while the frequency ratio those derivatives cost grows at least linearly, and the exponent is the margin divided by four times the ratio. Evidence. The one ingredient of the bound that is not transcribed from the published design is the dissipative extension of the amplitude system, so the paper reports the audit that makes it credible: the OpenAI Lean certificate rebuilt (11,424 jobs, zero sorryAx, three standard axioms) and replayed through the Lean kernel from an empty environment, both halves (2,972 s and 1,588 s, exit 0); the amplitude system validated against direct pseudospectral simulation of the nonlinear equations, including the growth, steering and holding cycle, matching to 3.06e-06 in the steering gain on a background flattened to fourth order; the cost of localization to the damping law measured as 3.6 alpha/(ell lambda) and negligible at the separations in use; and the published hypodissipative threshold recovered exactly from its own exponent budget, with the binding constraint identified and the admissible frequency ratios shown to close at that threshold, excluding geometric cascades. Statements are labelled machine-verified, derived or conjectural. Two claims from an earlier round are retracted in the text, and this version supersedes v0.01, which reported the same audit without stating the bound it implies. The paper does not prove blowup for any equation, does not verify the mathematics of either announced proof beyond what a kernel replay establishes, and does not claim the layer mechanism, which belongs to Cordoba and Martinez-Zoroa. Self-published preprint, not peer reviewed.
Authors
- Felipe Santibañez-Leal (ORCID: https://orcid.org/0000-0002-0150-3246)
Institutions
- Eos Neuroscience (United States) (US)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-09-17
- DOI
- https://doi.org/10.5281/zenodo.22821237
- Primary Topic
- Fractional Differential Equations Solutions
- Type
- preprint