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 identity established for linear Laplacian relaxation in dsfb-tutte, we extend the residual primacy framework to the nonlinear Hamiltonian setting, where the identity becomes approximate and the central results become precisely-stated conjectures.The core argument proceeds from an approximate spectral decomposition of the integration residual in the linearized variational equations, grounded in the shadowing lemma interpretation that the bootstrap residual measures the rate at which the numerical trajectory loses its true-orbit shadow.We argue that the DSFB drift channel accumulates the slow, globally-organized frequency content of the trajectory---corresponding to surviving KAM tori, near-integrable motion, and long-period orbital structure---while the slew channel captures the fast content associated with resonant coupling, close approaches, and incipient chaos. We identify the Nekhoroshev stability time as a natural physical basis for the DSFB drift channel parameter, providing the first principled parameter selection rule for the framework in the Hamiltonian setting. All downstream claims about chaos detection, KAM breakdown identification, and safety-critical applicability are presented as conjectures or directions for future experimental investigation, not as established results. We further develop the epistemological argument that the three-body problem, lacking fixed external boundary conditions, is the natural domain of Endoduction - inference from internal residual organization - and that this stance is structurally superior to the model-dependent abductive approaches that dominate classical and modern perturbation theory.Keywords: three-body problem; Hamiltonian dynamics; DSFB; dynamical stopping criterion; drift-slew decomposition; symplectic integration; KAM theory; chaos detection; residual stream; endoduction; dynamical regime; separatrix; shadowing lemma; Nekhoroshev stability