# Lyapunov Fading-Memory Optimizer MVP

`run_experiment.py` implements the exponential-memory update for a diagonal quadratic:

- `theta <- theta - eta * gradient + eta * kappa * (memory - theta)`
- `memory <- rho * memory + (1-rho) * theta`, with `rho=exp(-beta*eta)`

It checks the continuous characteristic polynomial, scans the exact discrete update matrix for its spectral-radius stability boundary, and compares SGD, classical momentum, and fading memory at equal steps on a two-mode ill-conditioned quadratic.

Run:

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

The generated `results.json` records the fixed-seed numerical results. In the tested configuration, the characteristic polynomial residuals are at floating-point precision and predicted/empirical stability limits agree on the scan grid. The method eliminates stiff-mode sign changes in the selected stable run, but has substantially higher loss at equal steps than SGD and momentum; this is evidence for oscillation suppression/stability, not a speedup.