Geometric Incompatibility Between Perfect Alignment and Finite-Time Blow-Up in 3D Navier–Stokes Under MROS Temporal Coherence

ABSTRACT This work shows a geometric incompatibility between the alignment structure required for finite-time Navier–Stokes blow-up and the temporal coherence laws of the MROS framework. If a finite-time singularity occurs, the World B alignment condition requires the vorticity–strain alignment field kappa to approach 1 in the high-vorticity region. The MROS Omega-lock and temporal coherence axioms imply that kappa approaching 1 forces the effective temporal flow tau to collapse to zero. But any finite-time blow-up requires tau to remain positive. This contradiction excludes finite-time blow-up under the stated axioms. A compactness argument then forces a uniform alignment gap kappa ≤ 1 − epsilon*. The result provides a complete geometric classification of collapse-compatible configurations within this framework.