A Canon-Based Stability Classification of the Three-Body Problem

This paper applies the Canon—a minimal dynamical framework based on recursion, surplus, pressure gradients, and stability—to the classical three-body problem. Instead of modeling bodies as point masses interacting through Newtonian forces, each body is treated as a recursion-driven subsystem subject to external pressure from the other bodies. Pairwise gravitational influence is reinterpreted as a pressure term scaling as r⁻⁴, consistent with the Canon’s internal architecture. The result is a six-variable dynamical system that classifies three-body behavior into stable, oscillatory, chaotic, and collapsing regimes. This provides a closed-form stability classification for the three-body problem, something not available in classical mechanics. The framework reproduces the known qualitative outcomes—stable orbits, chaotic bounded motion, ejection, and collision—within a unified stability-index formalism.