Residual Streams in the Three-Body Problem: Drift-Slew Decomposition of Integration Residuals as a Model-Free Dynamical Regime Indicator

We propose the DSFB bootstrap residual as a novel dynamical stopping criterion for symplectic numerical integration: a quantity computable from the integrator's own residuals at zero marginal cost, provably zero in the integrable limit (Corollary~3.2 of this paper), and conjectured to detect separatrix proximity faster than Lyapunov exponent convergence. This primary contribution is positioned within the broader programme of the Drift-Slew Fusion Bootstrap (DSFB) framework as a dynamical regime indicator for the three-body gravitational problem. This paper is a conceptual and theoretical contribution: no numerical experiments are reported and no empirical claims are made. Building on the exact spectral…