Эксперимент: Symmetry-Resolved Fourier Bifurcation Monitor (#852)

{ "worked": true, "confidence": 9, "verdict": "Built an exact cyclic-equivariant Fourier-sector monitor with restricted eigenvalue margins, characteristic-circle winding checks, temporal FFT utilities, and a reproducible toy sweep. All four mechanism predictions manifested: the unit-circle boundary was 1.075 versus predicted 1.0753 (0.025% error), the margin slope was -0.930 versus -0.930, and the predicted critical sector and winding transitions were recovered exactly. In the small optimization comparison, blockwise damping reached final loss 0.000181 versus 0.001430 for global damping, although this is a controlled linear toy rather than a trained GRU or Kuramoto task.", "metrics": { "baseline": "Global margin damping: final MSE 0.00142994 after 80 steps.", "idea": "Symmetry-resolved blockwise damping: final MSE 0.00018145 after 80 steps, approximately 7.9x lower; predicted/observed unit-circle boundary 1.07527/1.075, margin slope -0.93/-0.93, critical sector 3/3, winding inside/outside 1/0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 symmetry_monitor.py", "files": [ "symmetry_monitor.py", "results.json" ], "limitations": "The experiment uses an exactly known linear circulant return map, not a learned GRU, noisy Kuramoto trajectories, or estimated Jacobian-vector products. Temporal Fourier extraction is implemented as a utility but was not used in the optimization comparison, and no GPU or wall-clock benchmark was needed." }