Do short-time chaos indicators predict long-term orbit stability?
In plain words
Quick tests of chaotic behavior over a few thousand turns could replace expensive long simulations if they reliably flag the orbits that eventually escape.
Precise statement
For realistic hadron collider maps, determine whether indicators computed over $10^{3}$ to $10^{4}$ turns (frequency-map diffusion, finite-time Lyapunov exponents, reversibility error, or machine-learned combinations) classify initial conditions stable for $10^{6}$ to $10^{8}$ turns with misclassification below 1 percent, and identify where in amplitude space they fail.
What would settle it
A benchmark on several lattices comparing indicator classifications with long-term tracking outcomes.
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