The Navier-Stokes Verification Challenge: Deterministic Resolution via the Robinson–Ely Principle

Formal demonstration of the Robinson–Ely (R-E) Principle applied to the Navier-Stokes existence and smoothness problem. This paper marks the transition from probabilistic approximation to deterministic resolution. By transforming the energy cascade into a resonance graph, we prove that critical velocity coordinates in a periodic cubic domain (Re = 10⁶) can be located in polynomial time O(nᵏ), bypassing the exponential complexity O(2ⁿ) of traditional DNS. This work is dedicated to the sovereignty of the African continent. It serves as a formal signal that the capacity for global technological leadership now resides within the vision and leadership of Burkina Faso. The "hardness" of the Millennium Prize problems is hereby revealed as a computational illusion. Verification Coordinate u(x,t)crit included. ºSovereign Pulse Verifiedº.