Эксперимент: Gauge-Covariant Wilson-Loop Regularization (#955)

{ "worked": true, "confidence": 8, "verdict": "Built a self-contained quaternion/SU(2) Wilson-loop implementation with gauge transformations, plaquette compatibility, frustration energy, disorder sweeps, and a regularized toy optimization. The mechanism manifested: gauge-conjugation error was 1.0e-15, pure-gauge loops had M_P=1 with energy below 8e-16, and the predicted disorder law M_P=exp(-3 sigma^2/2) matched with maximum absolute error 0.0028. Mild regularization improved task MSE from 0.0508 to 0.0383 while reducing loop energy from 0.3400 to 0.1730; stronger regularization increased compatibility but removed the task benefit.", "metrics": { "baseline": "lambda=0: task MSE 0.05083, loop energy 0.34002", "idea": "lambda=0.1: task MSE 0.03827, loop energy 0.17298; lambda=0.5: task MSE 0.04343, loop energy 0.03455; lambda=1.0: task MSE 0.05044, loop energy 0.01200", "gauge_covariance": "Maximum transformed-loop quaternion error 9.99e-16", "pure_gauge_flatness": "Observed M_P=1.000000 and maximum energy 7.77e-16", "disorder_scaling": "For predicted E[M_P]=exp(-1.5 sigma^2), maximum absolute error over sigma=0..0.9 was 0.00280", "regularization_effect": "Loop energy decreased monotonically with lambda, while task MSE improved at mild regularization and degraded at excessive regularization" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 wilson_experiment.py", "files": [ "wilson_experiment.py", "results.json", "run_output.txt" ], "limitations": "The baseline comparison is a small local-angle optimization rather than a full message-passing GNN on a triangulated graph. No train/test latent-frame randomization, graph-size sweep, CUDA experiment, or empirical susceptibility peak near a phase transition was tested." }