# Observable-reduced neural world model MVP

`observable_reduced_experiment.py` implements the linear special case of the proposed observable reduction.

For the aggregate observation `y=a+q` and `g(a)=r*a`, the exact identity is

`y'' = (r-alpha-beta)y' + beta*r*y`.

The script:

1. Integrates the hidden two-compartment system exactly with matrix exponentials.
2. Fits the reduced second-order coefficients from finite-difference derivatives.
3. Sweeps `alpha,beta` to test `c_y=beta*r` and `c_v=r-alpha-beta`.
4. Sweeps sample interval relative to `tau=1/(alpha+beta)`.
5. Compares long-horizon RK4 rollout against a generic first-order model `y'=k*y`.

Run:

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

Outputs are written to `results.json` and the console. This MVP does not train a neural residual network or estimate all three rates from coefficients alone: two observable coefficients cannot identify three rates without additional information. It tests the exact structural reduction and its numerical forecasting consequence.