A Cohesion UFT Stability Classification of the Three-Body Problem

This paper applies the Cohesion Unified Field Theory operator set to the classification of three-body orbital stability. Three test systems are classified: the stable
Chenciner-Montgomery figure-eight orbit, the same orbit with a 1% position perturbation (marginally unstable), and the Pythagorean problem (chaotic, ejection at step
∼ 9890). The Cohesion UFT operators — torsion asymmetry τasym, slip accumulation
S(t), recursion coherence κ(t), cascade depth D(t), and structural coherence Ψ(t) —
replace the previous Canon framework terminology throughout. The two-timescale
memory architecture is retained: long-term memory (S, D) persists across 2-cycle
resets and encodes accumulated angular momentum asymmetry; short-term memory
(the coherence history buffer) is cleared every two orbital cycles, forcing the system
to re-evaluate orbital periodicity from a clean state. All three systems are correctly
classified. The primary discrimination signal for marginal instability is the variability
of the mean pairwise separation E(t): the perturbed figure-eight shows 9.1× higher
E(t) variability than the stable orbit, reflecting the growing perturbation amplified by
the coherence-rebuild mechanism of the 2-cycle reset. The universal toggle threshold
Φtoggle = 32/(3π
2 − 4) = 1.2496 governs the gear-shift between stable (hexapolar) and
transitional (bipolar) orbital states