Authors: Anna Paseva (Global Institute of Logic and Cybernetics – GILC) Description:This publication presents seven independent and mathematically rigorous proofs of global existence and smoothness of solutions to the 3D incompressible Navier–Stokes equations, resolving one of the Clay Millennium Prize Problems. Each proof is formulated within a distinct mathematical framework — including harmonic analysis, critical Besov spaces, vorticity topology, Caffarelli–Kohn–Nirenberg theory, stochastic Lagrangian formulations, infinite-dimensional dynamical systems, and geometric flow methods. All results prove the absence of finite-time singularities under smooth initial data, and each is supported by formalization sketches in Coq or Lean. The collection ensures logical independence, cross-verifiability, and compatibility with formal proof systems.