A Canon-Based Stability Classification of the Three-Body Problem Version 3

This paper extends the Canon three-body framework introduced in Gilbert (v1) and empirically validated inGilbert (v2) by introducing the heartbeat operator suite — a set of internal pressure diagnostics derived from theCanon’s continuous dual-flow architecture. The central insight is that the valve regulating inflow and outflow is neverclosed: both flows are always active, with pressure regulating their relative rates. This produces a buildup-and-releasecycle whose symmetry across the three bodies encodes stability information not captured by Φ, Φ′, or C(t) alone. Anew operator — Leak Divergence L(t) = σ/µ of the three bodies’ leak rates — measures how asymmetrically thesystem is releasing internal pressure. Results show that L(t) provides the first operator in this framework capableof distinguishing the stable figure-eight from the marginally unstable perturbed figure-eight, addressing the corefailure identified in v2. Combined with C(t) peak amplitude, the Canon v3 diagnostic suite correctly classifies allthree test systems.