Grade-2 Universality in Planetary Defense: Cross-Domain Bridges for NEO Deflection and Debris Cascade

We establish cross-domain mathematical bridges connecting near-Earth object (NEO) deflection, orbital debris dynamics, and fluid mechanics through a formally verified framework. The central insight is Grade-2 universality: the differential equation dx/dt = βx² − αx, with threshold x_c = α/β, governs both Kessler debris cascades (x = ρ = debris density, α = drag removal, β = collision fragmentation) and Navier-Stokes energy balance (x = √G = Gevrey norm, α = ν = viscosity, β = C₃ = trilinear bound). We prove: (1) threshold existence and bifurcation structure—subcritical states decay (x < x_c → dx/dt < 0), supercritical states grow unboundedly (x > x_c → dx/dt > 0); (2) NS viscosity bounds Kessler drag coefficient—atmospheric regularity ensures debris removal; (3) defense completeness—the detect-deflect-clean chain forms a closed system where adequate debris removal restores subcriticality. All 10 bridge theorems are verified in the Platonic proof kernel with 0 novel axioms (all 32 declarations are type definitions). As a byproduct, we derive the early detection dominance principle: investment in detection yields the highest risk reduction per unit cost across the defense chain.

Keywords: planetary defense, Grade-2 dynamics, Kessler syndrome, orbital debris, Navier-Stokes, bifurcation, formal verification

MSC 2020: 70F15 (celestial mechanics), 37N05 (dynamical systems), 76D05 (Navier-Stokes), 68V15 (theorem proving)