The Causal Discretisation of Stochastic State Transitions: Resolving the Navier-Stokes Singularity via the Brownian Observer Paradox

Time behaves similarly to light; this discretisation under observation of time enables a solution to the Navier-Stokes equations. The Navier-Stokes Existence and Smoothness problem stalls fundamentally upon the assumption of a continuous spacetime continuum, permitting kinetic energy to concentrate infinitely into uncomputable singularities. This paper establishes a definitive bridge between pure continuous theory and discrete physical reality. By demonstrating that time under observation must inherently discretise to avoid the Brownian boundary paradox, we replace continuous limits with a strictly causal O(N) concurrent discrete-path summation. This proves that 3D fluid turbulence cannot collapse into a continuous mathematical singularity; it must strictly resolve into finite, quantifiable physical states.