Seven Zenodo records, each linked at its current version. The summaries state what each record establishes.
Global Regularity of 3D Navier–Stokes: An Energy Argument
Under three cascade hypotheses (uniform intra-shell dispersion, a pointwise Kolmogorov flux closure, cascade contiguity) the enstrophy carried by the active shells satisfies ΩA ≤ C E(0)5/3/ν4/3, and any uniform-in-time enstrophy bound gives regularity by Prodi–Serrin. No bound on the total enstrophy is obtained; the hypotheses fail for explicit smooth data (a spectral-gap datum, localised vortices, the dissipation range, the exact shear flow), so the result is a conditional statement and no claim of global regularity is made.
Rod Higgins · Senuamedia · DOI 10.5281/zenodo.22710241
Angular Relaxation on the Integer Lattice and Global Regularity of 3D Navier–Stokes
An effective PDE for the angular-resolved shell energy E(K, μ, t), fitted to DNS in 1D (Burgers), 2D and 3D. Two lattice facts: the shell mixing graph is complete for N ≥ 2K+1, and the per-shell stretching can be written in terms of a shell anisotropy and the shell energy. The 2D data are reproduced within 2% with a vanishing stretching coefficient. The 3D closure is a fitted nine-coefficient description of the data, not a derived equation; no claim of global regularity is made.
Rod Higgins · Senuamedia · DOI 10.5281/zenodo.22710240
Energy Conservation, Cascade Stabilisation, and the Global Regularity of the 3D Navier–Stokes Equations
The 3D Galerkin solver with exact Fourier trilinear coupling, the discovery and correction of an energy-conservation defect in its first implementation (a missing −i factor), the scaffold-array and weighted-enstrophy diagnostics, and two lattice facts: the Leray projection forces a non-vanishing angular variance of the triad geometry through K = 55, and modes shared by several triads cannot maximise the stretching of all of them at once. The rigorous content is the conditional statement that a uniform-in-N enstrophy bound implies smoothness, the energy identities of the corrected system, and the two lattice lemmas.
Rod Higgins · Senuamedia · DOI 10.5281/zenodo.22710239
A Unified Spectral Framework for Arithmetic Oscillations
Truncated spectral amplitude sums over the non-trivial zeros of ζ, using 2,001,052 zeros from Odlyzko's tables with computed ζ′(ρn). The Mertens (Odlyzko–te Riele) sum crosses 1 at K = 58 and 2 near K = 1,040, with growth consistent with the conjectural (log T)5/4 law; the first zeros are recovered by Fourier analysis of M(x)/√x. The valid bound is Ingham's theorem with a Fejér kernel.
Rod Higgins · Senuamedia · DOI 10.5281/zenodo.22714412
Multi-Perspective Scaffold Array Diagnostics Across Three Fluid Equations
Fourier–Galerkin truncations of 3D Euler (N ≤ 8), 3D MHD (N ≤ 6) and 2D SQG (N ≤ 15) with a first-order splitting scheme. At ν = 0 the truncated systems relax to the Lee–Kraichnan absolute equilibrium: Ω/E reaches the lattice mean ⟨k2⟩ within 1% at every N, which accounts for the observed enstrophy growth. A finite Galerkin system cannot blow up, so these runs are not evidence about the three PDEs; critical SQG is regular by theorem, and inviscid SQG and 3D Euler blow-up remain open.
Rod Higgins · Senuamedia · DOI 10.5281/zenodo.22714408
A Holistic Scaffold Framework for Navier–Stokes Regularity
A hand-constructed cubic shell model on 3 to 12 scalar wavenumbers, a multi-level diagnostic H built from its trajectories, and a first real-coefficient 3D Fourier–Galerkin kernel. The shell model is not a Galerkin truncation of Navier–Stokes; H is an in-sample classifier; the first kernel omits the −i factor and injects energy. What stands: the doubling-time lemma, the mode-enumeration, triad-precomputation and Leray-projection structure that became the corrected solver, and the tables as a record of what the systems did under the stated protocol.
Rod Higgins · Senuamedia · DOI 10.5281/zenodo.22714407
Unified Adaptation Theorem
Sufficient conditions for convergence of sequentially composed contractive updates on a shared parameter: each update is a contraction and the matrix of block Lipschitz constants has spectral radius below one, giving a unique fixed point by the block-contraction theorem (Bertsekas–Tsitsiklis), with LaSalle describing the invariant set. PCGrad-type projection preserves first-order descent but admits non-unique limit points, one-dimensional stalls and period-two orbits. Diagnostics: the identity B = 1 + 2I, the convergence-score lemma, the balanced-matrix eigenvalues, and the local Hessian of B.
Rod Higgins · Senuamedia · DOI 10.5281/zenodo.22714409
Citation
@misc{higgins2026energy,
title = {Global Regularity of 3D Navier--Stokes:
An Energy Argument (v5)},
author = {Higgins, Rod},
year = {2026},
doi = {10.5281/zenodo.22710241},
url = {https://lab.senuamedia.com/papers/energy-regularity.html}
}
@misc{higgins2026unified,
title = {Unified Adaptation Theorem: Convergence of Composed
Adaptive Systems via Interaction Matrices and
Higher-Order Convergence Diagnostics (v3)},
author = {Higgins, Rod},
year = {2026},
doi = {10.5281/zenodo.22714409},
url = {https://lab.senuamedia.com/papers/unified-adaptation-theorem.html}
}
@misc{higgins2026scaffold,
title = {A Holistic Scaffold Framework for Navier--Stokes
Regularity (v3)},
author = {Higgins, Rod},
year = {2026},
doi = {10.5281/zenodo.22714407},
url = {https://lab.senuamedia.com/papers/ns-regularity-scaffold.html}
}
@article{higgins2026adversarial,
title = {Adversarial Regularisation: A Universal Optimization
Principle},
author = {Higgins, Rod},
year = {2026},
url = {https://lab.senuamedia.com/papers/adversarial-regularisation.html}
}