Эксперимент: Delay-Shape Master-Stability Coupling (#833)

{ "worked": true, "confidence": 8, "verdict": "Built a reproducible delayed master-stability MVP in verify_delay_shape.py, including companion-matrix spectral analysis, finite-rollout Lyapunov estimation, and a symmetric-versus-directed heterogeneous network comparison. The boundary prediction rho(C)=1 was confirmed to machine precision, and measured exponents matched log rho with maximum error 1.65e-15. At delay 2, the directed heterogeneous network changed the predicted transverse exponent from +0.01066 for the symmetric ring to -0.27413, while measured disagreement slope changed from +0.02132 to -0.27505, demonstrating the proposed stability mechanism. The generic claim that increasing delay always progressively shrinks the stable region was not observed in this scalar recurrence: the boundary plateaued at alpha=0.28 for delays 1-8.", "metrics": { "baseline": "8-node symmetric ring: max transverse eigenvalue magnitude=1.00000; predicted worst log spectral radius=+0.01066; measured disagreement log slope=+0.02132; final disagreement=0.00478", "idea": "8-node directed heterogeneous row-stochastic matrix: max transverse eigenvalue magnitude=0.26414; predicted worst log spectral radius=-0.27413; measured disagreement log slope=-0.27505; final disagreement=1.65e-24; maximum exponent-fit absolute error=1.65e-15" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 verify_delay_shape.py", "files": [ "verify_delay_shape.py", "results.json" ], "limitations": "This is a scalar constant-Jacobian toy, not a trained GRU or sequence-prediction task. The directed matrix was selected by random search rather than optimized through a differentiable master-stability loss. No GPU benchmark, FLOP-matched accuracy test, time-varying Jacobian, complex nonlinear modules, or broad delay/coupling network sweep was performed." }