Эксперимент: Adaptive SOS Lyapunov Certificate Ladder (#1061)

{ "worked": false, "confidence": 9, "verdict": "Built a small Parrilo-style SOS Lyapunov certificate ladder with coefficient-matching Gram matrices, PSD projection, shift-threshold sweeps, and a scalar rollout boundary check. The exact dynamics prediction gamma|a|=1 was recovered within 0.44% relative error, and the coarse threshold ordering was nonincreasing, but the approximate Gram solver produced large coefficient residuals and level 1 did not improve the certificate margin (-9.624 versus -6.531 at level 0). Therefore the central adaptive SOS mechanism was not numerically demonstrated and should not be considered a win.", "metrics": { "baseline": "Exact scalar rollout boundary: predicted gamma=1/|a|; maximum observed relative error 0.4375%. SOS level-0 Motzkin margin -6.531, residual 6.883; shift threshold coarse estimate epsilon=1.0.", "idea": "SOS level-1 Motzkin margin -9.624, residual 9.642; coarse threshold epsilon=1.0. threshold_monotone=true in the coarse scan, but level_improves=false and certificates were infeasible or unreliable." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 sos_ladder.py", "files": [ "sos_ladder.py", "results.json" ], "limitations": "No production SDP solver was available, so the Gram feasibility step used an approximate alternating-projection method with poor residuals. The neural/RNN experiment, constrained nonnegative-region multipliers, robust perturbation tests, training comparison, and geometric Lyapunov-decay evaluation were not tested." }