{
  "status": "Exact finite model extension: capture observed before provider action",
  "baseline_passed_assertions": 173,
  "additional_passed_assertions": 140,
  "total_passed_assertions": 313,
  "parameters": {
    "base": "2/5",
    "success_payment": "1/5",
    "prior": "9/10",
    "capture": "1/2",
    "detection": "4/5",
    "false_positive": "1/10",
    "consequence_cap": "1/5",
    "false_harm_cap": "1/100",
    "outside": "0",
    "current_budget": "3/4",
    "review_unit_cost": "1/20"
  },
  "visible_capture_feasible_frontier": {
    "frontier": "4/5",
    "vertices": [
      [
        "0",
        "0"
      ],
      [
        "0",
        "1/5"
      ],
      [
        "3/5",
        "0"
      ],
      [
        "3/5",
        "1/5"
      ],
      [
        "4/5",
        "0"
      ],
      [
        "4/5",
        "1/5"
      ]
    ]
  },
  "hidden_capture_reference_frontier": "19/15",
  "lambda1_Konefifth": [
    {
      "states": [
        {
          "group": "E",
          "captured": 0,
          "probability": "1/4",
          "action": "high",
          "utility": "43/200",
          "all_action_utilities": {
            "reject": "0",
            "low": "21/100",
            "high": "43/200"
          }
        },
        {
          "group": "E",
          "captured": 1,
          "probability": "1/4",
          "action": "high",
          "utility": "39/200",
          "all_action_utilities": {
            "reject": "-4/25",
            "low": "19/100",
            "high": "39/200"
          }
        },
        {
          "group": "H",
          "captured": 0,
          "probability": "1/4",
          "action": "reject",
          "utility": "0",
          "all_action_utilities": {
            "reject": "0",
            "low": "-7/100",
            "high": "-3/100"
          }
        },
        {
          "group": "H",
          "captured": 1,
          "probability": "1/4",
          "action": "high",
          "utility": "-1/20",
          "all_action_utilities": {
            "reject": "-4/25",
            "low": "-9/100",
            "high": "-1/20"
          }
        }
      ],
      "eligible_completion": "3/4",
      "success_per_eligible": "5/8",
      "selected_success": "5/6",
      "ex_ante_provider_payoff": "9/100",
      "service_payment": "17/40",
      "effort_resource_cost": "3/10",
      "review_cost": "1/40",
      "gross_current_spend": "9/20",
      "false_penalty_per_eligible": "1/100",
      "false_penalty_per_accepted": "1/75",
      "group_false_penalty_per_accepted": {
        "E": "1/100",
        "H": "1/50"
      }
    }
  ],
  "boundary_policy_correspondence": {
    "lambda=4/5,K=0": [
      {
        "states": [
          {
            "group": "E",
            "captured": 0,
            "probability": "1/4",
            "action": "low",
            "utility": "11/50",
            "all_action_utilities": {
              "reject": "0",
              "low": "11/50",
              "high": "21/100"
            }
          },
          {
            "group": "E",
            "captured": 1,
            "probability": "1/4",
            "action": "low",
            "utility": "11/50",
            "all_action_utilities": {
              "reject": "0",
              "low": "11/50",
              "high": "21/100"
            }
          },
          {
            "group": "H",
            "captured": 0,
            "probability": "1/4",
            "action": "reject",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-1/50",
              "high": "0"
            }
          },
          {
            "group": "H",
            "captured": 1,
            "probability": "1/4",
            "action": "reject",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-1/50",
              "high": "0"
            }
          }
        ],
        "eligible_completion": "1/2",
        "success_per_eligible": "2/5",
        "selected_success": "4/5",
        "ex_ante_provider_payoff": "11/100",
        "service_payment": "7/25",
        "effort_resource_cost": "3/20",
        "review_cost": "1/40",
        "gross_current_spend": "61/200",
        "false_penalty_per_eligible": "0",
        "false_penalty_per_accepted": "0",
        "group_false_penalty_per_accepted": {
          "E": "0",
          "H": null
        }
      },
      {
        "states": [
          {
            "group": "E",
            "captured": 0,
            "probability": "1/4",
            "action": "low",
            "utility": "11/50",
            "all_action_utilities": {
              "reject": "0",
              "low": "11/50",
              "high": "21/100"
            }
          },
          {
            "group": "E",
            "captured": 1,
            "probability": "1/4",
            "action": "low",
            "utility": "11/50",
            "all_action_utilities": {
              "reject": "0",
              "low": "11/50",
              "high": "21/100"
            }
          },
          {
            "group": "H",
            "captured": 0,
            "probability": "1/4",
            "action": "reject",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-1/50",
              "high": "0"
            }
          },
          {
            "group": "H",
            "captured": 1,
            "probability": "1/4",
            "action": "high",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-1/50",
              "high": "0"
            }
          }
        ],
        "eligible_completion": "3/4",
        "success_per_eligible": "11/20",
        "selected_success": "11/15",
        "ex_ante_provider_payoff": "11/100",
        "service_payment": "41/100",
        "effort_resource_cost": "1/4",
        "review_cost": "1/40",
        "gross_current_spend": "87/200",
        "false_penalty_per_eligible": "0",
        "false_penalty_per_accepted": "0",
        "group_false_penalty_per_accepted": {
          "E": "0",
          "H": "0"
        }
      },
      {
        "states": [
          {
            "group": "E",
            "captured": 0,
            "probability": "1/4",
            "action": "low",
            "utility": "11/50",
            "all_action_utilities": {
              "reject": "0",
              "low": "11/50",
              "high": "21/100"
            }
          },
          {
            "group": "E",
            "captured": 1,
            "probability": "1/4",
            "action": "low",
            "utility": "11/50",
            "all_action_utilities": {
              "reject": "0",
              "low": "11/50",
              "high": "21/100"
            }
          },
          {
            "group": "H",
            "captured": 0,
            "probability": "1/4",
            "action": "high",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-1/50",
              "high": "0"
            }
          },
          {
            "group": "H",
            "captured": 1,
            "probability": "1/4",
            "action": "reject",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-1/50",
              "high": "0"
            }
          }
        ],
        "eligible_completion": "3/4",
        "success_per_eligible": "11/20",
        "selected_success": "11/15",
        "ex_ante_provider_payoff": "11/100",
        "service_payment": "41/100",
        "effort_resource_cost": "1/4",
        "review_cost": "1/40",
        "gross_current_spend": "87/200",
        "false_penalty_per_eligible": "0",
        "false_penalty_per_accepted": "0",
        "group_false_penalty_per_accepted": {
          "E": "0",
          "H": "0"
        }
      },
      {
        "states": [
          {
            "group": "E",
            "captured": 0,
            "probability": "1/4",
            "action": "low",
            "utility": "11/50",
            "all_action_utilities": {
              "reject": "0",
              "low": "11/50",
              "high": "21/100"
            }
          },
          {
            "group": "E",
            "captured": 1,
            "probability": "1/4",
            "action": "low",
            "utility": "11/50",
            "all_action_utilities": {
              "reject": "0",
              "low": "11/50",
              "high": "21/100"
            }
          },
          {
            "group": "H",
            "captured": 0,
            "probability": "1/4",
            "action": "high",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-1/50",
              "high": "0"
            }
          },
          {
            "group": "H",
            "captured": 1,
            "probability": "1/4",
            "action": "high",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-1/50",
              "high": "0"
            }
          }
        ],
        "eligible_completion": "1",
        "success_per_eligible": "7/10",
        "selected_success": "7/10",
        "ex_ante_provider_payoff": "11/100",
        "service_payment": "27/50",
        "effort_resource_cost": "7/20",
        "review_cost": "1/40",
        "gross_current_spend": "113/200",
        "false_penalty_per_eligible": "0",
        "false_penalty_per_accepted": "0",
        "group_false_penalty_per_accepted": {
          "E": "0",
          "H": "0"
        }
      }
    ],
    "lambda=4/5,K=1/5": [
      {
        "states": [
          {
            "group": "E",
            "captured": 0,
            "probability": "1/4",
            "action": "low",
            "utility": "11/50",
            "all_action_utilities": {
              "reject": "0",
              "low": "11/50",
              "high": "21/100"
            }
          },
          {
            "group": "E",
            "captured": 1,
            "probability": "1/4",
            "action": "low",
            "utility": "1/5",
            "all_action_utilities": {
              "reject": "-4/25",
              "low": "1/5",
              "high": "19/100"
            }
          },
          {
            "group": "H",
            "captured": 0,
            "probability": "1/4",
            "action": "reject",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-1/50",
              "high": "0"
            }
          },
          {
            "group": "H",
            "captured": 1,
            "probability": "1/4",
            "action": "high",
            "utility": "-1/50",
            "all_action_utilities": {
              "reject": "-4/25",
              "low": "-1/25",
              "high": "-1/50"
            }
          }
        ],
        "eligible_completion": "3/4",
        "success_per_eligible": "11/20",
        "selected_success": "11/15",
        "ex_ante_provider_payoff": "1/10",
        "service_payment": "41/100",
        "effort_resource_cost": "1/4",
        "review_cost": "1/40",
        "gross_current_spend": "87/200",
        "false_penalty_per_eligible": "1/100",
        "false_penalty_per_accepted": "1/75",
        "group_false_penalty_per_accepted": {
          "E": "1/100",
          "H": "1/50"
        }
      },
      {
        "states": [
          {
            "group": "E",
            "captured": 0,
            "probability": "1/4",
            "action": "low",
            "utility": "11/50",
            "all_action_utilities": {
              "reject": "0",
              "low": "11/50",
              "high": "21/100"
            }
          },
          {
            "group": "E",
            "captured": 1,
            "probability": "1/4",
            "action": "low",
            "utility": "1/5",
            "all_action_utilities": {
              "reject": "-4/25",
              "low": "1/5",
              "high": "19/100"
            }
          },
          {
            "group": "H",
            "captured": 0,
            "probability": "1/4",
            "action": "high",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-1/50",
              "high": "0"
            }
          },
          {
            "group": "H",
            "captured": 1,
            "probability": "1/4",
            "action": "high",
            "utility": "-1/50",
            "all_action_utilities": {
              "reject": "-4/25",
              "low": "-1/25",
              "high": "-1/50"
            }
          }
        ],
        "eligible_completion": "1",
        "success_per_eligible": "7/10",
        "selected_success": "7/10",
        "ex_ante_provider_payoff": "1/10",
        "service_payment": "27/50",
        "effort_resource_cost": "7/20",
        "review_cost": "1/40",
        "gross_current_spend": "113/200",
        "false_penalty_per_eligible": "1/100",
        "false_penalty_per_accepted": "1/100",
        "group_false_penalty_per_accepted": {
          "E": "1/100",
          "H": "1/100"
        }
      }
    ],
    "lambda=1,K=0": [
      {
        "states": [
          {
            "group": "E",
            "captured": 0,
            "probability": "1/4",
            "action": "high",
            "utility": "43/200",
            "all_action_utilities": {
              "reject": "0",
              "low": "21/100",
              "high": "43/200"
            }
          },
          {
            "group": "E",
            "captured": 1,
            "probability": "1/4",
            "action": "high",
            "utility": "43/200",
            "all_action_utilities": {
              "reject": "0",
              "low": "21/100",
              "high": "43/200"
            }
          },
          {
            "group": "H",
            "captured": 0,
            "probability": "1/4",
            "action": "reject",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-7/100",
              "high": "-3/100"
            }
          },
          {
            "group": "H",
            "captured": 1,
            "probability": "1/4",
            "action": "reject",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-7/100",
              "high": "-3/100"
            }
          }
        ],
        "eligible_completion": "1/2",
        "success_per_eligible": "19/40",
        "selected_success": "19/20",
        "ex_ante_provider_payoff": "43/400",
        "service_payment": "59/200",
        "effort_resource_cost": "1/5",
        "review_cost": "1/40",
        "gross_current_spend": "8/25",
        "false_penalty_per_eligible": "0",
        "false_penalty_per_accepted": "0",
        "group_false_penalty_per_accepted": {
          "E": "0",
          "H": null
        }
      }
    ],
    "lambda=1,K=1/5": [
      {
        "states": [
          {
            "group": "E",
            "captured": 0,
            "probability": "1/4",
            "action": "high",
            "utility": "43/200",
            "all_action_utilities": {
              "reject": "0",
              "low": "21/100",
              "high": "43/200"
            }
          },
          {
            "group": "E",
            "captured": 1,
            "probability": "1/4",
            "action": "high",
            "utility": "39/200",
            "all_action_utilities": {
              "reject": "-4/25",
              "low": "19/100",
              "high": "39/200"
            }
          },
          {
            "group": "H",
            "captured": 0,
            "probability": "1/4",
            "action": "reject",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-7/100",
              "high": "-3/100"
            }
          },
          {
            "group": "H",
            "captured": 1,
            "probability": "1/4",
            "action": "high",
            "utility": "-1/20",
            "all_action_utilities": {
              "reject": "-4/25",
              "low": "-9/100",
              "high": "-1/20"
            }
          }
        ],
        "eligible_completion": "3/4",
        "success_per_eligible": "5/8",
        "selected_success": "5/6",
        "ex_ante_provider_payoff": "9/100",
        "service_payment": "17/40",
        "effort_resource_cost": "3/10",
        "review_cost": "1/40",
        "gross_current_spend": "9/20",
        "false_penalty_per_eligible": "1/100",
        "false_penalty_per_accepted": "1/75",
        "group_false_penalty_per_accepted": {
          "E": "1/100",
          "H": "1/50"
        }
      }
    ],
    "lambda=19/15,K=0": [
      {
        "states": [
          {
            "group": "E",
            "captured": 0,
            "probability": "1/4",
            "action": "high",
            "utility": "133/600",
            "all_action_utilities": {
              "reject": "0",
              "low": "59/300",
              "high": "133/600"
            }
          },
          {
            "group": "E",
            "captured": 1,
            "probability": "1/4",
            "action": "high",
            "utility": "133/600",
            "all_action_utilities": {
              "reject": "0",
              "low": "59/300",
              "high": "133/600"
            }
          },
          {
            "group": "H",
            "captured": 0,
            "probability": "1/4",
            "action": "reject",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-41/300",
              "high": "-7/100"
            }
          },
          {
            "group": "H",
            "captured": 1,
            "probability": "1/4",
            "action": "reject",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-41/300",
              "high": "-7/100"
            }
          }
        ],
        "eligible_completion": "1/2",
        "success_per_eligible": "19/40",
        "selected_success": "19/20",
        "ex_ante_provider_payoff": "133/1200",
        "service_payment": "59/200",
        "effort_resource_cost": "1/5",
        "review_cost": "1/40",
        "gross_current_spend": "8/25",
        "false_penalty_per_eligible": "0",
        "false_penalty_per_accepted": "0",
        "group_false_penalty_per_accepted": {
          "E": "0",
          "H": null
        }
      }
    ],
    "lambda=19/15,K=1/5": [
      {
        "states": [
          {
            "group": "E",
            "captured": 0,
            "probability": "1/4",
            "action": "high",
            "utility": "133/600",
            "all_action_utilities": {
              "reject": "0",
              "low": "59/300",
              "high": "133/600"
            }
          },
          {
            "group": "E",
            "captured": 1,
            "probability": "1/4",
            "action": "high",
            "utility": "121/600",
            "all_action_utilities": {
              "reject": "-4/25",
              "low": "53/300",
              "high": "121/600"
            }
          },
          {
            "group": "H",
            "captured": 0,
            "probability": "1/4",
            "action": "reject",
            "utility": "0",
            "all_action_utilities": {
              "reject": "0",
              "low": "-41/300",
              "high": "-7/100"
            }
          },
          {
            "group": "H",
            "captured": 1,
            "probability": "1/4",
            "action": "high",
            "utility": "-9/100",
            "all_action_utilities": {
              "reject": "-4/25",
              "low": "-47/300",
              "high": "-9/100"
            }
          }
        ],
        "eligible_completion": "3/4",
        "success_per_eligible": "5/8",
        "selected_success": "5/6",
        "ex_ante_provider_payoff": "1/12",
        "service_payment": "17/40",
        "effort_resource_cost": "3/10",
        "review_cost": "1/40",
        "gross_current_spend": "9/20",
        "false_penalty_per_eligible": "1/100",
        "false_penalty_per_accepted": "1/75",
        "group_false_penalty_per_accepted": {
          "E": "1/100",
          "H": "1/50"
        }
      }
    ]
  },
  "protection_interpretation": "q*f*K is the ex-ante false-penalty amount per opportunity if everyone accepts. A capture-contingent policy changes conditioning. Actual false penalties divided by accepted opportunities need not be bounded by q*f*K. Neither this arithmetic nor epsilon is a clinical safety guarantee.",
  "sha256": {
    "exact_solver.py": "cd129004c7cff564581fec99502b46d9eddd448f4a8421bf279ec679d3e0dfce",
    "visible_capture.py": "028b7b93ae36a8c6bddad4f83c563869ca4a2e4e637cc69329a69994eefaf71f"
  }
}