Эксперимент: Braid-Monodromy Set State (#1428)

{ "worked": true, "confidence": 7, "verdict": "Built a compact Braid-Monodromy set-state module using skew-symmetric generators and Cayley transport, plus a DeepSets-GRU baseline on independently permuted 5-object trajectories. The Cayley update preserved fiber norms to 2.4e-7 error versus 0.0535 for an Euler control, and permutation changes altered logits by only 3.7e-8. In the toy exchange-direction task, the monodromy model reached 100% accuracy at both 12 and 24 frames, versus 79.1% and 68.4% for the baseline; this is a promising signal, though not yet a definitive general result.", "metrics": { "baseline": "DeepSets-GRU, 6,354 parameters: accuracy_T12=0.7906, accuracy_T24=0.6844", "idea": "Braid monodromy, 9,371 parameters: accuracy_T12=1.0000, accuracy_T24=1.0000; max skew residual=0, max Cayley norm error=2.38e-7, max permutation logit difference=3.73e-8" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only one random seed and one synthetic trajectory family were tested. The models were not matched exactly for parameter count or FLOPs, no explicit rollout prediction metric was evaluated, and the CUDA attempt failed due to a shared-environment cuDNN allocation error so the completed run used CPU." }