{
  "status": "exact finite-model derivation; no Monte Carlo, clinical evidence, RL, or Lean proof",
  "arithmetic": "fractions.Fraction",
  "passed_assertions": 173,
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    "success_payment": "1/5",
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      {
        "policy": {
          "E": "high",
          "H": "reject"
        },
        "eligible_completion": "1/2",
        "success_per_eligible": "19/40",
        "success_per_completed": "19/20",
        "effort_resource_cost": "1/5",
        "current_service_payment": "59/200",
        "provider_expected_payoff": "8/75",
        "current_service_and_review_spend": "8/25",
        "current_budget_slack": "43/100"
      }
    ],
    "lambda=14/15,K=1/5": [
      {
        "policy": {
          "E": "low",
          "H": "high"
        },
        "eligible_completion": "1",
        "success_per_eligible": "7/10",
        "success_per_completed": "7/10",
        "effort_resource_cost": "7/20",
        "current_service_payment": "27/50",
        "provider_expected_payoff": "13/150",
        "current_service_and_review_spend": "113/200",
        "current_budget_slack": "37/200"
      },
      {
        "policy": {
          "E": "high",
          "H": "high"
        },
        "eligible_completion": "1",
        "success_per_eligible": "31/40",
        "success_per_completed": "31/40",
        "effort_resource_cost": "2/5",
        "current_service_payment": "111/200",
        "provider_expected_payoff": "13/150",
        "current_service_and_review_spend": "29/50",
        "current_budget_slack": "17/100"
      }
    ],
    "lambda=1,K=0": [
      {
        "policy": {
          "E": "high",
          "H": "reject"
        },
        "eligible_completion": "1/2",
        "success_per_eligible": "19/40",
        "success_per_completed": "19/20",
        "effort_resource_cost": "1/5",
        "current_service_payment": "59/200",
        "provider_expected_payoff": "43/400",
        "current_service_and_review_spend": "8/25",
        "current_budget_slack": "43/100"
      }
    ],
    "lambda=1,K=1/5": [
      {
        "policy": {
          "E": "high",
          "H": "high"
        },
        "eligible_completion": "1",
        "success_per_eligible": "31/40",
        "success_per_completed": "31/40",
        "effort_resource_cost": "2/5",
        "current_service_payment": "111/200",
        "provider_expected_payoff": "33/400",
        "current_service_and_review_spend": "29/50",
        "current_budget_slack": "17/100"
      }
    ],
    "lambda=19/15,K=0": [
      {
        "policy": {
          "E": "high",
          "H": "reject"
        },
        "eligible_completion": "1/2",
        "success_per_eligible": "19/40",
        "success_per_completed": "19/20",
        "effort_resource_cost": "1/5",
        "current_service_payment": "59/200",
        "provider_expected_payoff": "133/1200",
        "current_service_and_review_spend": "8/25",
        "current_budget_slack": "43/100"
      }
    ],
    "lambda=19/15,K=1/5": [
      {
        "policy": {
          "E": "high",
          "H": "reject"
        },
        "eligible_completion": "1/2",
        "success_per_eligible": "19/40",
        "success_per_completed": "19/20",
        "effort_resource_cost": "1/5",
        "current_service_payment": "59/200",
        "provider_expected_payoff": "79/1200",
        "current_service_and_review_spend": "8/25",
        "current_budget_slack": "43/100"
      },
      {
        "policy": {
          "E": "high",
          "H": "high"
        },
        "eligible_completion": "1",
        "success_per_eligible": "31/40",
        "success_per_completed": "31/40",
        "effort_resource_cost": "2/5",
        "current_service_payment": "111/200",
        "provider_expected_payoff": "79/1200",
        "current_service_and_review_spend": "29/50",
        "current_budget_slack": "17/100"
      }
    ],
    "lambda=13/10,K=0": [
      {
        "policy": {
          "E": "high",
          "H": "reject"
        },
        "eligible_completion": "1/2",
        "success_per_eligible": "19/40",
        "success_per_completed": "19/20",
        "effort_resource_cost": "1/5",
        "current_service_payment": "59/200",
        "provider_expected_payoff": "89/800",
        "current_service_and_review_spend": "8/25",
        "current_budget_slack": "43/100"
      }
    ],
    "lambda=13/10,K=1/5": [
      {
        "policy": {
          "E": "high",
          "H": "reject"
        },
        "eligible_completion": "1/2",
        "success_per_eligible": "19/40",
        "success_per_completed": "19/20",
        "effort_resource_cost": "1/5",
        "current_service_payment": "59/200",
        "provider_expected_payoff": "53/800",
        "current_service_and_review_spend": "8/25",
        "current_budget_slack": "43/100"
      }
    ]
  },
  "post_type_costless_exit": {
    "lambda=0,K=0": {
      "E": [
        "low"
      ],
      "H": [
        "low"
      ]
    },
    "lambda=0,K=1/5": {
      "E": [
        "low"
      ],
      "H": [
        "low"
      ]
    },
    "lambda=3/5,K=0": {
      "E": [
        "low"
      ],
      "H": [
        "low",
        "high"
      ]
    },
    "lambda=3/5,K=1/5": {
      "E": [
        "low"
      ],
      "H": [
        "low",
        "high"
      ]
    },
    "lambda=11/15,K=0": {
      "E": [
        "low"
      ],
      "H": [
        "high"
      ]
    },
    "lambda=11/15,K=1/5": {
      "E": [
        "low"
      ],
      "H": [
        "exit",
        "high"
      ]
    },
    "lambda=4/5,K=0": {
      "E": [
        "low"
      ],
      "H": [
        "exit",
        "reject",
        "high"
      ]
    },
    "lambda=4/5,K=1/5": {
      "E": [
        "low"
      ],
      "H": [
        "exit"
      ]
    },
    "lambda=14/15,K=0": {
      "E": [
        "low",
        "high"
      ],
      "H": [
        "exit",
        "reject"
      ]
    },
    "lambda=14/15,K=1/5": {
      "E": [
        "low",
        "high"
      ],
      "H": [
        "exit"
      ]
    },
    "lambda=1,K=0": {
      "E": [
        "high"
      ],
      "H": [
        "exit",
        "reject"
      ]
    },
    "lambda=1,K=1/5": {
      "E": [
        "high"
      ],
      "H": [
        "exit"
      ]
    },
    "lambda=19/15,K=0": {
      "E": [
        "high"
      ],
      "H": [
        "exit",
        "reject"
      ]
    },
    "lambda=19/15,K=1/5": {
      "E": [
        "high"
      ],
      "H": [
        "exit"
      ]
    },
    "lambda=13/10,K=0": {
      "E": [
        "high"
      ],
      "H": [
        "exit",
        "reject"
      ]
    },
    "lambda=13/10,K=1/5": {
      "E": [
        "high"
      ],
      "H": [
        "exit"
      ]
    }
  },
  "script_sha256": "cd129004c7cff564581fec99502b46d9eddd448f4a8421bf279ec679d3e0dfce",
  "budget_scope": "Current service payment plus capture probability times review cost is compared with B1=3/4. Review unit cost=1/20. Sanctions are not rebated into the care budget. Enrollment transfer F=0. Outside option is normalized to the rejected-case continuation baseline. Continuation opportunities and their funding are not modeled."
}