Эксперимент: Directed-Path Synchronization Coupling (#954)

{ "worked": true, "confidence": 8, "verdict": "Built a reproducible NumPy MVP for sparse directed diffusive synchronization and verified the mechanism numerically. For the directed n-1-edge rooted graph, the observed stability boundary was eta_c=0.80 versus predicted 0.80, the measured decay-rate error was 0.02-0.12%, and the Lipschitz scaling sweep matched eta_c=L/gamma within 1.7%. At eta=1, disagreement contracted to 0.135 of its initial value versus 2962x growth uncoupled, although the dense symmetric graph contracted faster at 0.0324, so this demonstrates feasibility rather than a performance win.", "metrics": { "baseline": "Uncoupled linear modules at L=0.8, eta=1: final disagreement ratio 2961.96; fitted log-V slope +1.5987.", "idea": "Directed sparse star at eta=1: gamma=1, predicted threshold 0.8, final disagreement ratio 0.1353, fitted slope -0.40008 versus predicted -0.4; dense symmetric comparison ratio 0.0324." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 directed_sync_experiment.py > results.json", "files": [ "directed_sync_experiment.py", "results.json" ], "limitations": "This is a scalar linear-dynamics toy, not an MLP/GRU training experiment. The sparse construction is a rooted directed star rather than a full strongly connected component implementation, and the spectral minimum-real-part gain is not a general conservative certificate for arbitrary nonnormal digraphs; transient amplification and discrete-time step-size effects were not studied." }