Contractive Floquet return map toy verification

Run:

/home/maxwelhelp/main/bin/python3 floquet_toy.py

The experiment uses a two-coordinate stroboscopic map with phase theta and transverse deviation r:

r_next = q*r + delta
theta_next = theta + shear*r_next

It tests three quantitative predictions from the proposed mechanism:

1. With zero defect, transverse error is exactly |q|^n |r0|; the transition is at q=1, with exponential rate log(|q|).
2. For q<1 and constant defect, the asymptotic error is delta/(1-q) and therefore scales linearly with defect size.
3. Phase shear can make phase-sensitive/pointwise error large while transverse orbital error contracts as q^n.

results.json contains the full parameter sweeps and a secondary 1000-cycle comparison. In that comparison, the unconstrained map has q=1.02 and the contractive map has q=0.8, with Gaussian per-period defects (sigma=0.004). The observed median terminal orbital errors are approximately 4.02e7 and 0.00428, respectively; all contractive trials remain inside the radius-0.05 tube, while none of the unconstrained trials do. The empirical transverse contraction estimates are 1.02 and 0.8.

This is a mechanism verification, not a trained neural ODE benchmark. It does not establish that a neural architecture can learn the desired contraction from finite noisy oscillator data.