{
  "deterministic": {
    "parameters": {
      "alpha_u": 3,
      "alpha_v": 3,
      "hill": 2,
      "protein_loss_rate": 1,
      "pulse_inhibition": 4
    },
    "equilibria": [
      {
        "point": [
          0.3819660112501048,
          2.6180339887498953
        ],
        "eigenvalues": [
          -0.3333333333333336,
          -1.666666666666666
        ],
        "stable": true,
        "residual": 2.220446049250313e-16
      },
      {
        "point": [
          1.2134116627622302,
          1.213411662762229
        ],
        "eigenvalues": [
          0.19105889149184674,
          -2.191058891491847
        ],
        "stable": false,
        "residual": 2.220446049250313e-16
      },
      {
        "point": [
          2.618033988749898,
          0.3819660112501044
        ],
        "eigenvalues": [
          -0.3333333333333346,
          -1.6666666666666654
        ],
        "stable": true,
        "residual": 1.7763568394002505e-15
      }
    ],
    "pulse_critical_duration": 1.0146882271102278,
    "pulses": [
      {
        "duration": 0.5073441135551139,
        "critical_fraction": 0.5,
        "end_of_pulse": [
          2.283459933387021,
          1.187986971890179
        ],
        "after_80_units": [
          2.6180339887332944,
          0.3819660112513339
        ],
        "solver_endpoint_difference": 3.125899539213606e-11
      },
      {
        "duration": 2.0293764542204555,
        "critical_fraction": 2.0,
        "end_of_pulse": [
          0.9694408499578708,
          2.429881734019867
        ],
        "after_80_units": [
          0.38196601124957863,
          2.6180339887394033
        ],
        "solver_endpoint_difference": 2.6216806503498447e-11
      }
    ],
    "asymmetric_folds_at_alpha_v_3": [
      {
        "alpha_u": 2.7007936383229905,
        "u": 1.8222611465394427,
        "v": 0.6943422722704393
      },
      {
        "alpha_u": 3.542407439828922,
        "u": 0.6671625825345062,
        "v": 2.075972408704097
      }
    ]
  },
  "stochastic": [
    {
      "omega": 5,
      "cap_factor": 6,
      "molecule_cap": 30,
      "states": 961,
      "iterations": 3433,
      "generator_drift_error": 5.684341886080802e-14,
      "stationary_residual_l1": 5.949565891889841e-12,
      "probability_sum": 1.0000000000000075,
      "boundary_probability": 6.316921964014462e-05,
      "first_passage_start": [
        13,
        2
      ],
      "first_passage_target": "N_v-N_u >= omega",
      "mean_first_passage_time": 21.715209932211973,
      "backward_equation_residual": 4.4164671919588727e-13
    },
    {
      "omega": 10,
      "cap_factor": 6,
      "molecule_cap": 60,
      "states": 3721,
      "iterations": 9952,
      "generator_drift_error": 1.4299672557172016e-13,
      "stationary_residual_l1": 1.1959616190208973e-11,
      "probability_sum": 1.0000000000000289,
      "boundary_probability": 6.914027900083624e-08,
      "first_passage_start": [
        26,
        4
      ],
      "first_passage_target": "N_v-N_u >= omega",
      "mean_first_passage_time": 49.90824046199234,
      "backward_equation_residual": 2.991606962154947e-12
    },
    {
      "omega": 20,
      "cap_factor": 6,
      "molecule_cap": 120,
      "states": 14641,
      "iterations": 28382,
      "generator_drift_error": 3.135269821541442e-13,
      "stationary_residual_l1": 2.4091961964926152e-11,
      "probability_sum": 1.0000000000001021,
      "boundary_probability": 1.4454053125534576e-13,
      "first_passage_start": [
        52,
        8
      ],
      "first_passage_target": "N_v-N_u >= omega",
      "mean_first_passage_time": 154.7178888983048,
      "backward_equation_residual": 2.4794388764348696e-11
    }
  ],
  "truncation_check": {
    "larger_cap": {
      "omega": 5,
      "cap_factor": 8,
      "molecule_cap": 40,
      "states": 1681,
      "iterations": 4527,
      "generator_drift_error": 1.127986593019159e-13,
      "stationary_residual_l1": 7.934435049986624e-12,
      "probability_sum": 1.000000000000007,
      "boundary_probability": 1.005884338442625e-08,
      "first_passage_start": [
        13,
        2
      ],
      "first_passage_target": "N_v-N_u >= omega",
      "mean_first_passage_time": 21.716562185472327,
      "backward_equation_residual": 6.10178574333986e-13
    },
    "mfpt_relative_difference": 6.227217073084823e-05
  },
  "scope": "Illustrative symmetric Hill model and separate finite-state birth/death process; no experimental fit.",
  "limits": [
    "No explicit mRNA, promoter switching, gene replication or cell division.",
    "Births beyond the stated molecule cap are suppressed; a cap convergence check is provided.",
    "A mean first-passage time is not assumed to imply exponential waiting times."
  ]
}