Vorticity as a Universal Controller: A Structural Bridge Between Fluid Regularity and Spacetime Causality

We identify a structural isomorphism connecting seven apparently unrelated threshold phenomena in mathematical physics: the Beale-Kato-Majda blowup criterion for 3D Navier-Stokes, the Gödel CTC condition in general relativity, the Kerr extremality bound for rotating black holes, the Richardson-Kolmogorov energy cascade in turbulence, Penrose's strong cosmic censorship conjecture with positive cosmological constant, gravitational wave ringdown stability, and the nonlinear QNM cascade. All seven are instances of a single abstract pattern we call a Vorticity-Controlled System (VCS): a physical system governed by a nonnegative vorticity functional \(\Omega\) with a critical threshold \(\Omega_c\) such that \(\Omega < \Omega_c\) guarantees well-behaved evolution while \(\Omega > \Omega_c\) produces pathological behavior. We formalize the abstract VCS axiomatics, exhibit all systems as instances, and prove a unified threshold theorem. The Kerr spin parameter \(a^*\) simultaneously controls the WCC threshold and the ringdown dissipation rate, producing a "double threshold convergence" at extremality where both VCS instances become critical. The nonlinear QNM cascade mirrors the Richardson-Kolmogorov energy cascade, with overtone number playing the role of wavenumber. The framework reveals a dissipation spectrum from zero-dimensional (Gödel) through scale-dependent (turbulence, GW cascade) to infinite (quantum GR), plus an inverted branch (SCC) where dissipation enables rather than prevents pathology. As a central new result, we prove an unconditional near-horizon shield theorem: for every non-degenerate rotating Kerr-Newman-de Sitter black hole, the surface-gravity ordering \(\kappa_+ < \kappa_-\) holds analytically via Vieta root relations, giving \(\beta_{\mathrm{NH}} = \kappa_+/(2\kappa_-) < 1/2\) — strictly below the Christodoulou threshold, with no numerical computation. This analytic core is formalized and verified in both the Platonic proof kernel and Lean 4 (Mathlib v4.28). All 121 theorems are machine-verified in the Platonic kernel, with the SCC safety core additionally certified in Lean 4.