Эксперимент: Fourier-Mode Stability Shaping (#1114)

{ "worked": true, "confidence": 9, "verdict": "Built an exact Fourier-mode stability module for cyclic phase dynamics with analytic factors, complex Jacobian eigenvalues, perturbation simulation, and bounded weight shaping. Measured growth rates matched -kappa*mu within 0.31%, coupling scaling was linear, the explicit-Euler stability boundary matched within 1.25%, and a negative factor produced the predicted exponential growth within 0.014%. Fourier shaping changed an unstable mode from mu=-0.194879 and growth slope +0.194905 to mu=+0.113278 and slope -0.113170, reducing the 1000-step amplitude ratio from 1.2152 to 0.8930.", "metrics": { "baseline": "q=3, mode=1, uniform weights: mu=-0.194879, observed slope=+0.194905, amplitude ratio=1.2152", "idea": "q=3, mode=1, shaped weights [1.1092, 1.1991, 0.7752, -0.4158]: mu=+0.113278, observed slope=-0.113170, amplitude ratio=0.8930; analytic Euler hcrit=0.345107 versus observed 0.349421" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 fourier_stability.py", "files": [ "fourier_stability.py", "results.json" ], "limitations": "This MVP tests phase-ring dynamics and perturbation stability, not a trained copy-memory or delayed-sine neural task. Weight shaping uses offline bounded optimization rather than an integrated optimizer barrier during end-to-end training, and the finite-step boundary was estimated on a grid." }