Эксперимент: Hurwitz Latent Observer (#364)

{ "worked": false, "confidence": 9, "verdict": "Built HurwitzLatentObserver with Euler correction, null-space projection, Jacobian evaluation, and Lyapunov penalty, plus reproducible linear and Lorenz experiments. The Euler stability boundary matched quantitatively (predicted dt<1.500, observed 1.499), and Lorenz nudging reduced final error from 30.98 open-loop to 0.126. However, the central projected certificate failed: H remained +0.5 for every gain while the full observer transitioned from unstable to stable at g2=2.0, so negativity of the proposed ker(C)-restricted matrix is not sufficient for full latent-error contraction in this coupled example.", "metrics": { "baseline": "Lorenz open-loop final error 30.980; median final-20% error 14.828", "idea": "Lorenz nudging final error 0.1264; median final-20% error 0.1438; linear full-system stability boundary g2=2.0 predicted, first stable grid point 2.05; projected H=+0.5 for all gains; Euler boundary predicted 1.500, observed 1.499" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 observer_experiment.py", "files": [ "observer_experiment.py", "hurwitz_observer.py", "results.json" ], "limitations": "No trained neural ODE/SSM or learned vector-field comparison was run; the Lorenz test uses the known analytic vector field and compares open-loop simulation with residual nudging. The counterexample uses a 2D linear system and does not test alternative full-state Lyapunov certificates or additional assumptions that could make the observer theorem valid." }