Эксперимент: Observability-Gated Spectral Phase Initialization (#1358)

{ "worked": true, "confidence": 8, "verdict": "Built a NumPy MVP for Hermitian connection-matrix spectral phase initialization, reference-node gauge fixing, centered-Jacobian observability margin, MAD-based eta estimation, and gated refinement. The math check reproduced an exact gauge nullspace (||J1||=0) and matched the constrained margin to the smallest nonzero singular value (rho=1.608038). Across 40 fixed-seed trials per noise level, spectral initialization had lower phase RMSE than random in 100%, 100%, 100%, and 87.5% of trials for noise 0.15, 0.35, 0.70, and 1.10 respectively; the effect weakened at high noise but remained positive. The promised initialization benefit is observed, while the full GNN adaptation claim was not tested.", "metrics": { "baseline": "Random initialization: phase RMSE 1.560 mean across noise levels; after 100-step refinement, RMSE was 0.413, 0.487, 0.819, and 1.241 for noise 0.15, 0.35, 0.70, and 1.10.", "idea": "Spectral initialization RMSE was 0.115, 0.271, 0.607, and 1.156; gated refinement RMSE was 0.115, 0.269, 0.593, and 1.076 for the same noise levels. Spectral beat random after refinement in 95%, 90%, 75%, and 70% of trials respectively." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 spectral_phase_experiment.py", "files": [ "spectral_phase_experiment.py", "results.json" ], "limitations": "This is a small NumPy graph synchronization experiment rather than the planned two-layer GCN or differentiable PyTorch layer. The Jacobian is the exact pairwise-difference Jacobian, weights are uniform, eta uses K=1, and no wall-clock/FLOP, classification-accuracy, CUDA, or learned downstream observation-map evaluation was performed." }