# Contractive Floquet return map toy verification

Run:

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

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

```text
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.