Major Conjectures and Cosmological Tests M: The Cosmological Falsifiability of the Navier-Stokes Existence and Smoothness Problem

This paper proposes an innovative pathway for testing the smoothness problem of the Navier-Stokes (NS) equations via cosmological observations. The studytranslates the global regularity problem of the three-dimensional NS equations intothe context of turbulence dynamics in the baryon-photon plasma of the early universe. Under the two fundamental assumptions of information conservation andcomputability of physical processes, we derive that if the NS equations possessfinite-time singularities, the statistical suppression of the corresponding paths wouldinduce a characteristic cutoff in the turbulent energy spectrum, which in turn mapsonto a softening turn in the angular power spectrum of the cosmic microwave background (CMB) at a specific scale (ℓ∗ ∼ 2140). Based on Planck 2018 satellite data,we detect a characteristic signal with 3.6σ significance in the range 1500 ≤ ℓ ≤ 3000,whose position is consistent with the theoretical prediction. Should next-generationCMB-S4 experiments fail to detect this signal with higher confidence, it could constitute falsification of the physical scenario where ”NS singularities emerge in theearly universe.” This research provides, for the first time, an operational cosmological testing scheme for this Millennium Prize mathematical problem.