Integrable Misalignment Forbids Blowup: A New Scale-Invariant Geometric Continuation Theorem for Three-Dimensional Navier-Stokes, Proved from the Classical Base

We introduce a family of scalar functionals of the three-dimensional incompressible Navier-Stokes flow, the alignment defects, measuring the failure of the vorticity direction to be coherent, weighted by vorticity magnitude against a kernel more singular than the Biot-Savart kernel by twice the defect order, so that each dominates the vortex-stretching term after one Cauchy-Schwarz split with an integrable partner. We prove a two-parameter continuation theorem: for a partner exponent between two and six and a defect order above the threshold it sets, if a fixed time power of the alignment defect stays integrable on the maximal interval of a strong solution, the solution does not break down; and we prove the theorem at the endpoint the threshold names, where the partner estimate runs in Lorentz spaces and the hypothesis is invariant under the natural scaling. The proofs are complete from five classical inputs, the Constantin-Fefferman geometric depletion bound, Sobolev and Lorentz interpolation, the energy identity, and the enstrophy breakdown alternative, and close by a Gronwall argument whose coefficient is integrable in time, the enstrophy power cancelling to exactly two for every member of the family. Interior members are subcritical with the exponent printed; the endpoint members are critical, and at partner exponent three the endpoint gives a scale-invariant criterion on the time integral of the defect of order one half. The criteria are distinct from the peak-vorticity, critical-norm, and qualitative-coherence criteria by separating examples, and the conditioned form of the hypothesis is provably equivalent to global regularity while the data-uniform form posited here is not. We then take exactly one statement on supply, the effective alignment-defect axiom, a data-uniform locally bounded modulus for the defect, and deduce global existence, uniqueness, and smoothness, so the standard existence-and-smoothness statement holds conditionally on it. The axiom is typed premise grade; its truth is the effectivity gap. The primary falsifiable criterion is parameter-free at fixed exponents: one smooth-data solution with finite maximal time and finite integrated defect power refutes the continuation theorem.