# Shared-response expert ranking

Run:

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

The fixed-seed synthetic experiment uses 9 candidate fields in dimension 160, a diagonal positive mass matrix, and an exactly rank-4 candidate-difference subspace.

## Mechanism checks

- Pairwise margin identity: maximum absolute numerical error `1.15e-14`.
- Quotient-space invariance: after adding an M-orthogonal perturbation with magnitudes 0, 1, 10, and 100, maximum change in pairwise score differences was `0`, `2.66e-15`, `5.77e-15`, and `5.06e-14`.
- Margin transition: the nearest competitor had margin `0.0397911`; the formula predicted a flip at corruption magnitude `alpha=0.0230828`. The sweep at alpha/threshold = 0, .25, .5, .75, 1, 1.25, 1.5 produced top-1 correctness 1, 1, 1, 1, 1, 0, 0, so the observed transition is bracketed by 1.0 and 1.25 times prediction.
- Exact shared correction selected the same best candidate as the unavailable truth: candidate 2.

The synthetic timing loop measured approximately `0.135 ms` for all 9 residual evaluations versus `0.052 ms` for shared-response scoring. The number of residual evaluations is reduced by exactly 9x, while total speedup in this tiny vectorized benchmark is only about 2.6x.

This is a math/toy verification, not evidence of a neural-operator performance win. It does not test learned experts, nonlinear PDE residuals, approximate Jacobian solves, GPU behavior, or noisy/biased response corrections.