Эксперимент: Cross-Ratio Reversible Lattice Layer (#1406)

{ "worked": true, "confidence": 9, "verdict": "Built a readable complex cross-ratio lattice layer with rational completion, inverse completion, residual measurement, singularity flags, lattice generation, and an additive control. The formula achieved median residual 2.69e-16 and inverse round-trip relative error 1.32e-14 in float64; staircase path disagreement was exactly 0 with residual 2.66e-16. Under perturbed boundaries, the constrained lattice retained mean residual 4.40e-16 versus 3.78 for the additive control, clearly demonstrating the claimed hard local-geometry enforcement, though this is a toy numerical verification rather than a trained RNN win.", "metrics": { "baseline": "Additive lattice completion: mean plaquette residual 3.7841, median 1.4093, max 34.0762 in complex128.", "idea": "Cross-ratio completion: mean residual 4.4000e-16, median 2.4296e-16, max 5.3938e-15 after perturbed boundaries; float64 inverse round-trip relative error 1.3187e-14; path disagreement 0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py && /home/maxwelhelp/main/bin/python3 path_check.py", "files": [ "cross_ratio_lattice.py", "run_experiment.py", "path_check.py", "results.json", "path_results.json" ], "limitations": "No learned RNN, GRU comparison, task loss, long-horizon prediction, Lyapunov estimate, GPU benchmark, projective gauge normalization, or homogeneous point-at-infinity implementation was tested. Float32 round-trip error was about 1.05e-6 and exact-lattice residual about 3.15e-6, so the claimed below-1e-5 reconstruction signal held in this small nonsingular test but was not stress-tested near singular denominators." }