# Adaptive Barrier-Margin Regularization MVP

## Implementation
`experiment.py` implements the proposed residual
`r = kappa * epsilon - psi`, a squared softplus penalty, detached disturbance/uncertainty estimates, the clipped adaptive update, and an inference-time projection filter. The toy plant is a scalar bounded point-mass-like control task with Gaussian unmodeled force. Ordinary supervised policy learning, a fixed robust margin, and the adaptive margin use the same policy, data, optimizer, and 700 updates.

## Quantitative mechanism checks
Results are in `results.json`.

1. **Adaptive fixed point:** for disturbance absolute-error mean `e=0.32`, delta=`0.1`, the update predicts `epsilon*=e/(1-delta)=0.355556`; observed after 100 updates: `0.355556`.
2. **Convergence factor:** with rho=`0.25`, the linear error factor predicts `1-rho*(1-delta)=0.775`; observed: `0.775000`.
3. **Scaling and coverage:** for Gaussian error standard deviation sigma, the update predicts `epsilon*=sigma*sqrt(2/pi)/(1-delta)`, hence epsilon scales linearly with sigma. This is observed (0.04468, 0.08937, 0.17873, 0.35747 for sigma 0.05, 0.1, 0.2, 0.4). However, this mean-error fixed point gives only about 0.624 coverage for a two-sided absolute Gaussian error, not the claimed 0.9 coverage; the empirical coverage sweep in `results.json` confirms approximately 0.624 at every sigma. The 0.9 quantile itself gives 0.9 coverage, demonstrating the calibration mismatch.

## Mini-experiment
Adaptive margins increase with disturbance amplitude and substantially reduce policy/filter intervention compared with baseline (zero intervention in this toy run because the policy learns inside the reconstructed margin). But post-filter violation rises from `0.0003` at sigma 0.05 to `0.1223` at sigma 0.4; adaptive epsilon is below the 90th-percentile error and therefore does not provide the stated 1-delta coverage. The fixed margin has higher tracking MSE (1.077) and becomes less safe at high disturbance (0.204 violation at sigma 0.4), while baseline has about 0.497 violation throughout.

## Decision
The adaptive barrier mechanism and its parameter dynamics manifest, but the proposed uncertainty update does not establish the stated coverage guarantee. Therefore this MVP is marked **worked=false** for the full idea: it is a useful adaptive regularizer signal, not a validated coverage-preserving safety method. A quantile/conformal calibration update would be needed before claiming the safety effect.