Эксперимент: Harmonic-Mode Branch for Topological Memory (#987)

{ "worked": true, "confidence": 9, "verdict": "Built a fixed-seed harmonic-branch simulation with a 2D nullspace and positive Hodge-like spectrum. All three quantitative predictions manifested: harmonic drift stayed at 1.05e-14, decay slopes matched -nulambda_1+ within 0.0025, and the observed Euler stability transition matched the predicted boundary dt=2/(nulambda_max)=0.1818. The split branch retained 1.0 of harmonic memory while the fully damped baseline retained 0.000293, with comparable dissipative residuals.", "metrics": { "baseline": "Fully damped branch: harmonic retention 0.0002926; final norm 0.0584579", "idea": "Harmonic-decoupled split: harmonic retention 1.0000000; maximum harmonic drift 1.05e-14; final dissipative norm 0.0584564; decay-sweep max slope error 0.00246; Euler boundary classification 4/4 correct" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 harmonic_experiment.py", "files": [ "harmonic_experiment.py", "results.json" ], "limitations": "This is a synthetic orthogonally rotated PSD operator rather than an explicitly constructed disk, annulus, or two-hole cell complex. It tests the linear zero-interaction branch, not a learned GNN, nonlinear harmonic-conditioned interaction, GPU behavior, or prediction accuracy on a real trajectory dataset." }