This submission contains four documents relating to the impossibility of finite-time blow-up in the three-dimensional incompressible Navier-Stokes equations. Paper 1 presents the mathematical argument: a general dissipation bound derived from the NS energy equality establishing D ≥ K·||ω||∞ for all smooth solutions; an exact calculation for the Burgers vortex showing the scaling exponent is α = 2; a scaling analysis proving the bound is subcritical under NS rescaling; a five-step time-integrated BKM proof showing ∫₀ᵀ||ω||∞ dt ≤ E₀/K < ∞; and a seven-step contradiction proof combining Kelvin's circulation theorem with geometric confinement. No symmetry assumptions, no special initial data, no numerical evidence required. Paper 2 is companion commentary documenting the physical intuition, investigative methodology, and conceptual framework behind the mathematical work. Covers the forensic approach, the parabolic geometry argument, the Planck-scale continuous approach argument, and reflections on independent discovery from outside the mathematical establishment. Not a formal proof. The Millennium Prize Checklist cross-references all results against the Clay Institute formal requirements and the obstacles identified by Tao (2007), documenting how each is addressed. All open questions resolved. The Proof of Work is a chronological record of the intellectual process behind the mathematical results, reconstructed from contemporaneous working notes. Documents the sequence of questions, intuitions, and breakthroughs in the order they occurred, from the initial forensic methodology through each conceptual development to publication. Includes direct quotes from the working record at each stage.
Damian Donahue (Fri,) studied this question.