Эксперимент: Characteristic-Invariant BT Monitor (#980)

{ "worked": true, "confidence": 8, "verdict": "Built a readable 2D continuous-time BT monitor with characteristic invariants, differentiable directional derivatives, finite-difference validation, and a baseline comparison. The three toy predictions manifested exactly: over 81 unfolding points delta=-mu and tau=nu with maximum error 0, and across four coefficient settings autodiff recovered a=alpha and b=beta with zero error; the candidate grid isolated delta=tau=0 at (mu,nu)=(0,0). The monitor optimization reached invariant loss 1.09e-12 versus 2.03 for the spectral-abscissa baseline, although this is a deliberately simple canonical system rather than evidence of a neural-network training win.", "metrics": { "baseline": "Spectral-abscissa penalty: final mu=-0.351995, nu=-1.379715, delta=0.351995, tau=-1.379715, delta^2+tau^2=2.027515.", "idea": "Invariant target penalty: final mu=-9.59e-7, nu=4.18e-7, delta=9.59e-7, tau=4.18e-7, delta^2+tau^2=1.094e-12. Identity sweep and coefficient sweep maximum errors were both 0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 bt_monitor_experiment.py", "files": [ "bt_monitor_experiment.py", "results.json" ], "limitations": "Only a 2D analytic canonical BT family was tested; no learned neural ODE or continuous-time RNN, equilibrium solver, noisy Jacobian estimation, higher-dimensional principal-minor implementation, trajectory-fit validation, GPU path, or runtime/FLOP comparison was evaluated. The n=2 transverse invariant is trivially e0=1, so transverse-block conditioning was not meaningfully stressed." }