# Conley-Certified Latent World Model MVP

Run with:

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

`experiment.py` trains a small 20D-observation autoencoder world model on a bistable scalar map, computes held-out latent residuals, constructs a padded latent-cell transition graph, and reports terminal SCC counts and a residual-versus-cell-width certificate proxy. It also performs the cheap interval-padding sanity check.

The sanity check numerically confirms the basic inclusion statement: padding by the maximum residual contains every observed true encoded image, while padding by half the maximum residual does not.

Important implementation finding: in this MVP the baseline already minimizes the one-step latent prediction residual `(g(E(x))-E(f(x)))^2`. The proposed semiconjugacy penalty is mathematically the same residual added a second time, rather than a distinct constraint. Therefore the idea changes optimization weighting but does not introduce a new identifiable learning signal. The reported run showed baseline max residual 0.04042 and semiconjugacy max residual 0.02604, but reconstruction worsened from 0.02426 to 0.15046 and terminal SCC count increased from 3 to 10; both passed the loose `epsilon < cell_width` proxy. This is not evidence of a reliable certification win.

Results are saved to `results.json`.