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:

/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.