# Green-Margin Residual Dynamics MVP

`run_experiment.py` implements a finite-horizon Green-kernel calculation for a diagonal contracting/expanding backbone, scalar fixed-point verification, and a small matched 20-layer residual linear-regression comparison. `results.json` contains the raw output.

## Toy mechanism verification

Backbone: scalar stable multiplier `a=0.7`, so the infinite-horizon Green norm is `Gamma=1/(1-a)=3.3333`, and perturbation gain is `Lambda=eta`.

| Prediction | Predicted | Observed | Result |
|---|---:|---:|---|
| q slope versus eta = Lambda*Gamma | 3.3333 | 3.3333 | exact |
| contraction boundary eta_c=1/(Lambda*Gamma) | 0.3000 | 0.3159 | 5.3% error |
| response gain = 1/(1-q) | 1.2, 1.5, 2, 3, 5, 10, 30 | same values; max relative error 1.8e-15 | exact |

The boundary uses a finite 300-step convergence/divergence test, so its observed threshold is slightly above the asymptotic value. A mixed diagonal backbone also produced finite Green norms for both stable (`a=.7`) and unstable (`a=1.15`, backward Green branch) channels: 3.333 and 6.399.

## Mini experiment

CUDA was used. Both models have the same depth, width, and parameterization. The margin model rescales residual maps whenever its estimated Green margin exceeds target `q0=.8`.

| Metric | Baseline | Green-margin |
|---|---:|---:|
| final MSE | 0.17585 | 0.26123 |
| max parameter gradient | 8.0576 | 0.3305 |
| final raw q estimate | 5.1004 | 76.8434 |
| final effective q after scale | 5.1004 | 0.8000 |
| final residual scale | 1.0 | 0.01041 |

Thus the certificate mechanism manifested strongly: the controller maintained effective q at 0.8 and reduced peak gradients by about 24x. It did not improve this tiny regression's loss; the aggressive global rescaling also caused underfitting.

## Reproduction

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