Эксперимент: Exact Neural de Rham Backbone (#512)

{ "worked": true, "confidence": 9, "verdict": "Built an explicit ReLU-power exact de Rham backbone with exterior-wedge maps and autodiff verification. The mechanism manifested: Koszul compositions were exactly zero, the derivative identity had max error 0, and the operator norm scaled linearly with neuron scale (observed log-log exponent 1.0 versus predicted 1.0). The curl-free constraint was exact (4.5e-16 RMS), but the constrained model had much worse vector-fitting MSE than the larger unconstrained MLP, so this is a structural win rather than an accuracy win in this toy comparison.", "metrics": { "baseline": "Unconstrained 722-parameter MLP: MSE 0.001458, curl RMS 0.71645", "idea": "28-coefficient exact backbone: MSE 0.259014, curl RMS 4.54e-16; nilpotence max error 0, derivative identity max error 0, Koszul scaling exponent 1.0" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 exact_derham_experiment.py", "files": [ "exact_derham_experiment.py", "results.json" ], "limitations": "The PDE comparison was a small supervised vector-field surrogate rather than a full Poisson or incompressible-flow solve. Parameter counts were not matched (28 versus 722), no conditioning/eigenmode study or feature resampling was performed, and only the 0-form to 1-form exact-gradient case was trained." }