# Эксперимент: Steady-State First-Passage Sensitivity Regularizer (#853)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built and numerically verified the regenerative fast-reset CTMC method in experiment.py. The exact paper response formula matched centered finite differences to 1.3e-10; auxiliary stationary-response error decreased from 11.8% at reset rate 2 to 0.031% at rate 1000, with observed log-log slope -0.996 versus the predicted -1 scaling. The nonlinear rational-response formula had maximum absolute error 0.050 across six finite perturbations, and the predicted symmetry/sign behavior was confirmed; the rollout baseline was much noisier.",
  "metrics": {
    "baseline": "Gillespie finite-difference MFPT response: -0.789, standard error 0.335 using 2,500 rollouts per perturbation",
    "idea": "Auxiliary stationary response at reset rate 1000: -0.63043 versus exact derivative -0.63063, absolute error 0.000196; exact formula error 1.27e-10",
    "predictions": "Reset convergence predicted O(1/K): observed log-log slope -0.996; finite-perturbation formula maximum absolute error 0.0495; symmetry derivative 0.0; helpful 1->2 derivative -0.631 and harmful 2->1 derivative +1.150"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "This is an exact four-state CTMC toy verification, not a neural RNN training experiment. It does not test learned state clustering, auxiliary regularizer optimization, GPU behavior, very large MFPT or ill-conditioned regimes, or the claimed 100-transition empirical threshold."
}