Abstract. This paper establishes a formal mathematical continuum bridgingclassical hydrostatic mass-proportional transformations with the global regularityand finite-time blow-up problems of the three-dimensional incompressible Navier–Stokes equations.We begin by constructing a Lebesgue-measure isomorphism from a static fluidanalogy, recovering geometric domain areas without appeal to transcendentalconstants (Theorem 2.2). Extending this to time-dependent kinematics via theReynolds Transport Theorem, we prove that the global Lebesgue measure μ(Ω(t))is an invariant of any incompressible flow (Theorem 4.1).We then carry out a careful micro-scale localisation around a suspected singularset S, applying a three-fold H¨older inequality to the local convective–dissipationinteraction (Proposition 5.2). A rigorous peer-review of the resulting estimatesreveals two explicit obstructions: (i) a circular-logic loop arising from the need tocontrol higher-order Sobolev norms, and (ii) a non-local pressure contribution thatcannot be dominated by purely local volume bounds due to infrared divergences inthe Riesz kernel.We then reformulate the entire problem as the Viscous Dominance Conjecture:the existence of a universal constant δ > 0 such that the vortex-stretching integralnever exceeds (1 − δ) times the viscous dissipation (Conjecture 7.1). If true, thisconjecture implies global enstrophy decay and, consequently, global regularity. Weidentify the geometric origin of δ in the trace-free structure of the strain-rate tensorand in the directional alignment constraints studied by Constantin and Fefferman(7).The paper includes a deterministic C++ Lagrangian simulation (RK4 integration,N = 1000 particles) that confirms mass-measure conservation at machine precisionunder chaotic non-linear advection (Section 11), together with visualisations ofthe three-dimensional velocity field, vorticity tubes, pressure map, and Littlewood–Paley Besov spectrum.Disclaimer. The present paper does not claim to resolve the Clay MillenniumProblem. Every unproved statement is explicitly labelled as a Conjecture or OpenProblem. The paper is presented as a structured research programme whoseobjective is to identify the precise remaining bottlenecks and to propose concretesub-problems whose resolution would advance the global theory.