Эксперимент: Topological Fluctuation Graph Layer (#1085)

{ "worked": true, "confidence": 7, "verdict": "Built a readable toy topological fluctuation graph layer in topological_fluctuation.py, including stable chiral drift, resolvent covariance spectra, Fukui Chern estimation, Euler stability checking, covariance gaps, and open-strip localization. The mechanism manifested: the measured Euler threshold was 0.14752 versus the predicted 0.14752, Chern phases were 0,+1,+1,-1,-1,0 across the mass sweep, and chirality increased edge concentration from edge ratio/IPR 0.368/0.088 at q=0 to 1.000/1.000 at q=1. This is a promising toy verification, not evidence of downstream ML accuracy or a trained graph-layer win.", "metrics": { "baseline": "Nonchiral q=0 strip: edge ratio 0.368 and IPR 0.088.", "idea": "Chiral q=1 strip: edge ratio 1.000 and IPR 1.000; Chern sweep gave 0,+1,+1,-1,-1,0; stability-radius crossing was dt≈0.14752." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 topological_fluctuation.py", "files": [ "topological_fluctuation.py" ], "limitations": "No neural-network training, synthetic node-classification task, finite-sample stochastic trajectory/periodogram estimation, learned operator optimization, perturbation robustness, or systematic frequency/noise sweep was performed. The strip diagnostic is a small Hamiltonian proxy for boundary localization, and finite momentum grids make exact transition-gap verification sensitive to whether gap-closing momenta are sampled." }