# Эксперимент: OSL-QIB Contractive State Observer (#1128)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a scalar OSL-QIB contractive observer MVP with exact bounds for phi(x)=gamma*tanh(x), Lyapunov certificate evaluation, parameter sweeps, and noisy tracking comparison. The sampled OSL/QIB maxima stayed below theoretical rho=1.7 and alpha=2.89; the certificate sign boundary was observed at gamma=0.8 versus predicted 0.75 with grid spacing 0.1, and the gain required for kappa=0.8 was observed at 1.8, exactly matching prediction. The certificate upper bound held at every rate-sweep point, while the observer reduced noisy MSE from 1.298e-3 to 2.416e-5, approximately 54x.",
  "metrics": {
    "baseline": "No observer correction: noisy tracking MSE 0.0012980 ± 0.0000000",
    "idea": "Certified observer: noisy tracking MSE 0.00002416 ± 0.00001099; certificate boundary predicted 0.75 and observed grid transition 0.8; gain threshold predicted and observed at 1.8"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 observer_experiment.py",
  "files": [
    "observer_experiment.py",
    "results.json"
  ],
  "limitations": "This is a scalar analytic toy rather than a trained neural ODE or Duffing model, and it uses hand-specified OSL/QIB constants instead of minibatch estimates or an SDP. The exact nonlinear stability boundary was analytically identified but not independently localized with a dense empirical sweep; disturbance-floor behavior was tested only with fixed observation noise and one input trajectory."
}