# Heavy-Tail Path-Adaptive Optimizer Pool MVP

`optimizer_pool.py` implements restarted diagonal AdaGrad experts with geometric horizons and the centered variance-normalized exponential meta-update from the idea.

Run:

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

The script verifies two analytic predictions by sweeps:

1. For a constant scalar gradient, cumulative AdaGrad displacement scales as `sqrt(H)`; the asymptotic prediction is `2 alpha sqrt(H)`.
2. For two fixed-loss experts with gap `delta`, the centered meta log-odds scale as `4 beta sqrt(T)` under the stated per-expert variance accumulators.

It also reports a deliberately falsifiable dynamic-recovery sweep and a shifted quadratic comparison. The latter is exploratory only; the pool uses multiple expert updates and is not a claim of equal-FLOP superiority.