Эксперимент: Analytic Markov-Routing Lyapunov Controller (#620)

{ "worked": false, "confidence": 9, "verdict": "Built a two-mode Markov-switching linear cocycle with normalized tangent propagation, empirical stationary-measure checks, finite-difference Lyapunov sensitivity tests, a persistence sweep, and a target-exponent controller. Stationary masses matched the theoretical distribution in the primitive interior, but finite-difference derivatives were too noisy for quadratic scaling, boundary variance did not increase as predicted, and the controller failed to move from p=0.2 toward its target. The promised effect was therefore not demonstrated.", "metrics": { "baseline": "No meaningful baseline win established; fixed/uncontrolled routing was used as the reference and the controller remained near p=0.2 with exponent about 0.018 versus target 0.0341.", "idea": "Stationary residual max 0.0069 at p=0.5 and 0.0105 at p=0.95; finite-difference derivatives at p=0.35 ranged 0.0575 to -0.0408 as h decreased; seed standard deviation was 0.00023 at p=0.05 versus 0.00112 at p=0.5; controller final p=0.2004." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "README.md" ], "limitations": "This was a small linear 2D toy rather than a trained nonlinear RNN or mixture-of-experts model. Runs were shortened for runtime, no full autodifferentiated router training or FLOP/speed comparison was performed, and exponent-collision/resonant-translation boundaries were not separately constructed." }