Эксперимент: Lie-Poisson Hamiltonian latent block (#503)

{ "worked": true, "confidence": 8, "verdict": "Built a self-contained SO(3) Lie-Poisson rigid-body experiment with explicit coadjoint coupling, implicit midpoint integration, Euler baseline, and no-coadjoint ablation. The core predictions were confirmed: antisymmetry and energy conservation held to machine precision, the coadjoint effect vanished at p=0, momentum scaling was 2.06 versus predicted 2, and nonlinear midpoint state error showed approximately second-order timestep scaling.", "metrics": { "baseline": "Explicit Euler had maximum energy error 0.1004 at T=10 and fitted timestep drift exponent 1.09.", "idea": "Implicit midpoint had maximum free-system energy error 6.33e-15; zero-momentum ablation difference 0; momentum exponent 2.06; nonlinear refined convergence approximately O(dt^2); terminal full-versus-ablated momentum error 0.373." }, "how_to_run": "cd /home/maxwelhelp/all/math2nn/experiments/exp1255_lie-poisson-hamiltonian-latent-block && /home/maxwelhelp/main/bin/python3 experiment.py && /home/maxwelhelp/main/bin/python3 nonlinear_check.py", "files": [ "experiment.py", "nonlinear_check.py", "results.json", "nonlinear_results.json" ], "limitations": "This was a toy analytic rigid-body test, not a learned latent neural block. No GRU, neural ODE, encoder, parameter matching, dataset benchmark, GPU benchmark, or wall-clock/FLOP comparison was tested." }