Preserved Curl, Scale Separation, & Topological Leakage

Magnetic helicity — the integral measuring linkage and twist of divergence-free field lines — serves as a physical curl inventory whose decay timescale exceeds the energy decay timescale by a factor controlled entirely by scale separation. A Monte Carlo sweep across carrier and dissipative scales produces a universal stiffness collapse onto the linear law τ_H/τ_U ≈ 0.97X + 0.03, where X = (k_rms/k_c)². Stochastic topology-change events with hazard rate proportional to a k^{2p}-weighted energy functional produce a phase boundary whose exponent is operator-specific. At p = 1 — the current-squared model J² ∝ k²|B|², which is the resistive dissipation rate divided by η — the integrated hazard is exactly X-independent, an analytical identity arising because the k² stress amplification cancels the k² diffusive decay in the time integral. The physical event rate at the phase boundary varies by less than 0.01% across a decade in scale separation. Monte Carlo validation across five hazard models (p ∈ {0, 0.5, 1, 1.5, 2}) confirms that the Poisson approximation captures all X-scaling, with residual clustering corrections |Δα| < 0.03. The repair ceiling — the product of the phase boundary and the stiffness-derived repair cost g(X) ~ 1/X — falls as X^{−1} at p = 1, entirely from the stiffness law. The operator resonance principle generalizes: in a system with decay operator k^{2q} and hazard functional weighted by k^{2p}, the integrated hazard scales as X^{p−q} and the phase boundary exponent is α = q − p. These results provide a concrete field-theoretic model for the curl-maintenance functional established in the geometry of self-correction framework.