Persistence of invariant graphs for twist maps under analytic perturbations

What the math gives to ML

The paper gives a constructive persistence mechanism for analytic invariant graphs carrying rigid irrational rotations under Gevrey perturbations of twist maps. Its transferable asset is a parameterized direct KAM correction scheme that controls graph defects through frequency arithmetic and small-divisor estimates rather than ordinary contraction alone. This can become a recurrent or state-space neural module with a quasi-periodic phase memory and a learned transverse invariant graph. The key falsifiable prediction is an arithmetic stability boundary: frequencies with smaller small-divisor amplification should preserve bounded long-horizon trajectories at larger perturbation amplitudes.