The classifiers already compute banana-tip footprints (Poincare cut v_par = 0, minus to plus). Expose them and add per-orbit rotation numbers, as the data backend for resonance analysis and barrier diagnostics from short traces.
Scope:
- Output the per-orbit tip series (s_k, theta_k or field-line label alpha_k) for the classification window (order 1e2 bounces), behind an output flag.
- Per-orbit rotation number of the tip angle via the weighted Birkhoff average (exponential bump window, Das-Yorke) with the RRE refinement (Ruth, Bindel, arXiv:2403.19003) as an option; plain-mean fallback for comparison.
- Stability target: rotation number reproducible to 1e-4 at 200 bounces on a regular orbit (acceptance test on an integrable case).
- Downstream (separate work): rotation-number profiles nu(s) per pitch class, resonance positions and island widths, overlap profiles.
This is read-side only relative to the pushers; no changes to integrators.
The classifiers already compute banana-tip footprints (Poincare cut v_par = 0, minus to plus). Expose them and add per-orbit rotation numbers, as the data backend for resonance analysis and barrier diagnostics from short traces.
Scope:
This is read-side only relative to the pushers; no changes to integrators.