# Gale-Nullspace Feature Mixer MVP

`gale_mixer_experiment.py` implements the core construction for `X in R^(a x b)`:
SVD of `X.T` is used to obtain `Y in R^((b-a) x b)` with rows in the left
nullspace of `X`; it also implements the normalized residual penalty
`||Y D X.T||_F^2/(||Y||_F^2 ||X||_F^2 + eps)`.

Run:

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

The script writes `results.json` and prints it. It runs three fixed-seed
mechanism checks:

1. Exact SVD nullspace: predicted `||Y X.T||` is floating-point roundoff.
2. Perturbation sweep `Y + gamma Z`: predicted residual norm scales as
   `gamma^1`, and the squared normalized penalty as `gamma^2`.
3. Diagonal gauge sweep: `D=cI` preserves annihilation, while a nonconstant
   diagonal generally breaks it; the measured residual is approximately linear
   in gauge spread near zero.

It also runs a small held-out linear-probe comparison. The probe target is
constructed to contain both primary and dual summaries, so this is only a
mechanism signal, not a language-model or equal-parameter attention result.