Finite-Time Strong Concentration Candidate Initial Data for the Incompressible Navier–Stokes Equations: An Operator Pre-Screening Framework and Dynamical Diagnosis Paradigm

This paper addresses the open problem of finite-time singularity formation for the three-dimensional incompressible Navier–Stokes (N–S) equations. A two-stage constructive paradigm is established: (1) the SV7 operator dynamical rapid pre-screening, which performs semi-quantitative graded screening of initial data based on the decomposition of the strain-rate operator S and the spin operator A, substantially reducing the cost of analytical derivation; (2) five synergistic dynamical criteria for conservative infinite-dimensional systems, serving as a posteriori diagnostic tool on time-series data to identify precursors of finite-time strong concentration. Ten sets of explicit initial data satisfying the Helmholtz solenoidal projection are provided, including a family of nested vortex clusters together with three heterogeneous configurations governed by physically independent mechanisms: localized Beltrami ABC vortices, black-hole accretion-disk sink-source vortex filaments, and three-arch coupled vortex arches for solar coronal structures. All ten high-score candidates are subjected to SV7 scoring and reductio analysis of dynamical escape channels, supplemented by one negative control configuration. This framework does not constitute a rigorous mathematical proof of finite-time blowup for the N–S system. All empirical thresholds are calibrated empirically within the endogenous vortex-cluster sample family. The complete workflow is falsifiable and supplies standardized initial data, parameters and judgment protocols for high-resolution numerical verification.