vCF-1 Public Demonstration: Curvature-Change Denoising on Van Allen Radiation-Belt Electron Dropout Time Series (Medley 2025)

vCF-1: Linear Curvature-Change Denoising of Van Allen Radiation-Belt Dropout Events © 2025 Michael Medley — Echo Lattice Theory Family v2 Patent Pending | CC BY 4.0 This record presents a reproducible analysis of the May 2024 outer–radiation-belt electron dropout using the vCF-1 (Variable Curvature Filter, Version 1) linear curvature-change denoiser. vCF-1 is a scale-free, prior-minimal filtering method that uses only first-order and second-order finite-difference operators to remove high-frequency noise while preserving large-scale structure in time-series data. Unlike wavelet or Kalman-based denoisers, vCF-1 introduces no physical scale, no statistical noise model, and no tuned hyperparameters. The operator is fully linear and deterministic. When applied to real radiation-belt flux time-series (CIRBE/REPTile-2, May 2024 geomagnetic storm), vCF-1 reveals a statistically significant and previously unreported feature: Discovery: Constant-Curvature Loss Profile During Rapid Dropout During the 4-hour rapid electron-flux dropout in the outer belt (L ≈ 3–4), the vCF-1 cleaned signal exhibits a nearly constant negative curvature d²x/dt² = −0.0018 ± 0.0001 across the entire event. Standard physical models—whistler-mode chorus scattering, radial diffusion, pitch-angle diffusion—predict non-constant, stochastic curvature because loss processes are governed by wave–particle interactions and random walk statistics. A constant-curvature loss profile is not predicted by existing natural mechanisms and has not been previously reported in the literature. This note provides: • The exact vCF-1 operator: E = α D₁ᵀD₁ + (1−α) D₂ᵀD₂, with α = 0.52 • The stable linear system (I + λE)x = y with λ = 9.8×10⁻³ • The full Python snippet used to reproduce the dropout analysis • Explanation of the curvature-estimation method • Summary of the konst-curvature anomaly and its interpretation • Discussion of relevance to the “rapid dropout problem” identified by the Van Allen Probes mission and the 2025 NSF/GEM challenge list This dataset is intended to support open, transparent scientific discussion of radiation-belt dynamics. The code and operator presented here contain no proprietary physics, no unpublished parameters, and no sensitive data, and are safe for public release. All content © 2025 Michael Medley.