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.摘要 本研究揭示了有限时间纳维-斯托克斯（Navier–Stokes）爆破所需的对齐结构与MROS框架的时间相干律之间存在几何不相容性。若发生有限时间奇点，世界B对齐条件要求涡量-应变对齐场κ（kappa）在高涡量区域趋近于1。而MROS框架的欧米茄锁定（Omega-lock）与时间相干公理表明，κ趋近于1会迫使有效时间流τ坍缩至0，但任何有限时间爆破均要求τ保持为正。这一矛盾排除了该公理框架下有限时间爆破的可能性。随后通过紧性论证可推导出一致对齐间隙κ ≤ 1 − ε*。本结果对该框架内的坍塌兼容构型完成了完整的几何分类。