Эксперимент: Defect-and-Jacobian Residual Dynamics (#360)

{ "worked": true, "confidence": 8, "verdict": "Built and ran a gated defect/Jacobian residual dynamics module for a reduced Klein–Gordon oscillator. The residual identity error was 0, the Taylor remainder log-log slope was 2.003 versus the predicted 2, its quadratic coefficient was 0.33345 versus 0.33343, and the gate midpoint/slope were 0.08035/3.000 versus predicted 0.08000/3. The residual model also improved one-step RMSE from 0.02396 to 0.01416 and 60-step rollout RMSE from 0.37699 to 0.24086, so the mechanism manifested in this toy test.", "metrics": { "baseline": "Full-state MLP: one-step RMSE 0.0239556; 60-step rollout RMSE 0.376986", "idea": "Defect/Jacobian residual MLP with sigmoid defect gate: one-step RMSE 0.0141616; 60-step rollout RMSE 0.240856; Taylor slope 2.0027 vs 2 predicted; gate midpoint 0.08035 vs 0.080 predicted; gate logit slope 3.000 vs 3 predicted" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "This is a single Fourier-mode/reduced Klein–Gordon toy rather than a spatial PDE with FFT derivatives or a resolution sweep. It uses one fixed random seed, a small MLP, short training, and does not establish scaling, FLOP parity, or gains on a neural operator or high-dimensional simulator." }