A Canon-Based Stability Classification of the Three-Body Problem Version 2: Empirical Validation and Extended Operators

This paper extends the Canon-based three-body stability framework introduced in Gilbert (v1) by adding empiricalvalidation against three known trajectory classes: the Chenciner-Montgomery figure-eight orbit (stable), a positionperturbed figure-eight (marginally unstable), and the Pythagorean three-body problem (chaotic/ejection). Two newoperators are introduced: the trend detector Φ′(t) and the symmetry-breaking index C(t). Results show that theCanon correctly discriminates strongly unstable configurations from stable ones using the combination of Φ, Φ′,and C, but cannot detect marginal instability from a short observation window. The boundary of the framework’sdiscriminative power is characterised precisely. The original claim of a “closed-form stability classification” isrefined: the Canon provides a pressure-based regime classifier that reliably identifies ejection dynamics but requiresa trend window to detect marginal instability.