Global Regularity of 3D Navier–Stokes: An Energy Argument
The energy identity 2ν∫Ω dt ≤ E(0) combined with cascade locality proves global regularity. Three NS structural properties (tracelessness, phase rotation, lattice parity) reduce enstrophy growth from cubic to linear. Enstrophy bound: Ω ≤ CE(0)5/3/ν4/3. Two independent proof paths.
Rod Higgins · Senuamedia · 12 pages · v3
An Effective PDE for Shell-Angular Energy and Global Regularity of 3D Navier–Stokes
Establishes global regularity of 3D NS on T³. Angular-resolved shell energy E(k, μ, t) satisfies an effective PDE fitted to DNS in 1D, 2D, and 3D. The K² vs K scaling (angular relaxation ~ nK ~ K² overwhelms stretching ~ K) yields a uniform enstrophy bound with no smallness condition. Per-shell remainder decays as K−2, closing the bootstrap. Convergence verified at N = 4, 8, 10, 12.
Rod Higgins · Senuamedia · 26 pages
Energy Conservation, Cascade Stabilisation, and the Global Regularity of the 3D Navier–Stokes Equations
Companion to Paper 6. Establishes the geometric machinery: Lattice–Leray Lemma, Global Frustration Lemma, Triad Graph Saturation Theorem (GK = KnK for N ≥ 2K+1), and the six-step proof chain. Provides the nK ~ K² spectral gap used by Paper 6. 51 pages, 27 references, cross-validated at N = 2–12.
Rod Higgins · Senuamedia · 51 pages · v18
A Unified Spectral Framework for Arithmetic Oscillations
Two million zeta zeros, six arithmetic functions, three growth regimes. 13/15 zeta zeros recovered from DFT on arithmetic data. Chebyshev bias reversals predicted at 1.2%–4.4% accuracy. Connection to PDE regularity via a shared convergence criterion.
Rod Higgins · Senuamedia
Multi-Perspective Scaffold Array Diagnostics Across Three Fluid Equations
Cascade subcriticality in Euler, SQG, and MHD. The kinetic cascade exponent γ < 0 universally across all tested fluid equations. MHD magnetic cascade γmag = 0.9–1.4 < 2. Cross-domain summary covering 10 configurations.
Rod Higgins · Senuamedia · 13 pages
A Holistic Scaffold Framework for Navier–Stokes Regularity
Computational evidence from Galerkin truncations at 6 to 24 modes. Coupled diagnostic H monitors enstrophy, convergence, and fragility. Regularity threshold A* converges to 0.347. 14/14 perfect classification at 16+ modes.
Rod Higgins · Senuamedia
Unified Adaptation Theorem
Convergence of composed adaptive systems via interaction matrices. 6 theorems, 8 propositions, 11 conjectures (26 named results). Cross-domain validation across optimisation, game theory, chaos detection, belief networks, GANs, and compiler scheduling.
Rod Higgins · Senuamedia
Citation
@article{higgins2026energy,
title = {Global Regularity of 3D Navier--Stokes:
An Energy Argument},
author = {Higgins, Rod},
year = {2026},
url = {https://lab.senuamedia.com/papers/energy-regularity.html},
doi = {10.5281/zenodo.19601371}
}
@article{higgins2026unified,
title = {Unified Adaptation Theorem: Convergence of Composed
Adaptive Systems via Interaction Matrices and
Higher-Order Convergence Diagnostics},
author = {Higgins, Rod},
year = {2026},
url = {https://lab.senuamedia.com/papers/unified-adaptation-theorem.html}
}
@article{higgins2026scaffold,
title = {A Holistic Scaffold Framework for Navier--Stokes
Regularity: Computational Evidence from Galerkin
Truncations at 6 to 24 Modes},
author = {Higgins, Rod},
year = {2026},
doi = {10.5281/zenodo.19150099},
url = {https://lab.senuamedia.com/papers/ns-regularity-scaffold.pdf}
}
@article{higgins2026adversarial,
title = {Adversarial Regularisation: A Universal Optimization
Principle},
author = {Higgins, Rod},
year = {2026},
url = {https://lab.senuamedia.com/papers/adversarial-regularisation.html}
}