Conditional Finite-Time Singularity in the 3D Navier-Stokes Equations via Boundary-Induced Eigenframe Alignment

The Millennium Prize problem concerns the global regularity of solutions to the 3D Navier-Stokes equations. Standard analytical approaches typically focus on proving that the enstrophy remains bounded globally. In this paper, we investigate a structural "Dissipation Deficit" mechanism at a no-slip boundary. We derive a Riccati-type differential inequality describing the vorticity evolution at a stagnation point. Crucially, we demonstrate that the breakdown of regularity depends on the geometric persistence of the vortex stretching term. While generic turbulence exhibits a depletion of nonlinearity due to eigenframe misalignment, we identify a specific boundary topology where this depletion is suppressed. We prove that conditional on the geometric alignment of the vorticity vector with the stretching eigenvector of the rate-of-strain tensor, initial data exceeding a critical threshold leads to infinite vorticity in finite time T* < infinity. This result demonstrates that the classical system admits singularities if the boundary geometry prevents the rotation of principal axes.