{
  "benchmark_id": "hall-2010-measurement-dependent-singlet",
  "cases": [
    {
      "correlation": -0.8910065241883678,
      "joint": {
        "-1,-1": 0.027248368952908025,
        "-1,1": 0.47275163104709195,
        "1,-1": 0.47275163104709195,
        "1,1": 0.027248368952908025
      },
      "marginal_A": {
        "-1": 0.5,
        "1": 0.5
      },
      "marginal_B": {
        "-1": 0.5,
        "1": 0.5
      },
      "max_probability_error": 0.0,
      "phi_rad": 0.47123889803846897,
      "target": {
        "-1,-1": 0.027248368952908025,
        "-1,1": 0.47275163104709195,
        "1,-1": 0.47275163104709195,
        "1,1": 0.027248368952908025
      }
    },
    {
      "correlation": -0.7071067811865475,
      "joint": {
        "-1,-1": 0.0732233047033631,
        "-1,1": 0.4267766952966368,
        "1,-1": 0.42677669529663687,
        "1,1": 0.0732233047033631
      },
      "marginal_A": {
        "-1": 0.4999999999999999,
        "1": 0.5
      },
      "marginal_B": {
        "-1": 0.5,
        "1": 0.4999999999999999
      },
      "max_probability_error": 5.551115123125783e-17,
      "phi_rad": 0.7853981633974483,
      "target": {
        "-1,-1": 0.0732233047033631,
        "-1,1": 0.42677669529663687,
        "1,-1": 0.42677669529663687,
        "1,1": 0.0732233047033631
      }
    },
    {
      "correlation": -0.5000000000000004,
      "joint": {
        "-1,-1": 0.12499999999999992,
        "-1,1": 0.3750000000000001,
        "1,-1": 0.3750000000000001,
        "1,1": 0.12499999999999992
      },
      "marginal_A": {
        "-1": 0.5,
        "1": 0.5
      },
      "marginal_B": {
        "-1": 0.5,
        "1": 0.5
      },
      "max_probability_error": 1.1102230246251565e-16,
      "phi_rad": 1.0471975511965976,
      "target": {
        "-1,-1": 0.12499999999999997,
        "-1,1": 0.375,
        "1,-1": 0.375,
        "1,1": 0.12499999999999997
      }
    },
    {
      "correlation": -5.551115123125783e-17,
      "joint": {
        "-1,-1": 0.24999999999999997,
        "-1,1": 0.25,
        "1,-1": 0.25,
        "1,1": 0.24999999999999997
      },
      "marginal_A": {
        "-1": 0.5,
        "1": 0.5
      },
      "marginal_B": {
        "-1": 0.5,
        "1": 0.5
      },
      "max_probability_error": 0.0,
      "phi_rad": 1.5707963267948966,
      "target": {
        "-1,-1": 0.24999999999999997,
        "-1,1": 0.25,
        "1,-1": 0.25,
        "1,1": 0.24999999999999997
      }
    },
    {
      "correlation": 0.7071067811865475,
      "joint": {
        "-1,-1": 0.4267766952966368,
        "-1,1": 0.07322330470336313,
        "1,-1": 0.07322330470336313,
        "1,1": 0.42677669529663687
      },
      "marginal_A": {
        "-1": 0.49999999999999994,
        "1": 0.5
      },
      "marginal_B": {
        "-1": 0.49999999999999994,
        "1": 0.5
      },
      "max_probability_error": 5.551115123125783e-17,
      "phi_rad": 2.356194490192345,
      "target": {
        "-1,-1": 0.42677669529663687,
        "-1,1": 0.07322330470336313,
        "1,-1": 0.07322330470336313,
        "1,1": 0.42677669529663687
      }
    },
    {
      "correlation": 0.9510565162951536,
      "joint": {
        "-1,-1": 0.4877641290737884,
        "-1,1": 0.012235870926211617,
        "1,-1": 0.012235870926211617,
        "1,1": 0.4877641290737884
      },
      "marginal_A": {
        "-1": 0.5,
        "1": 0.5
      },
      "marginal_B": {
        "-1": 0.5,
        "1": 0.5
      },
      "max_probability_error": 0.0,
      "phi_rad": 2.827433388230814,
      "target": {
        "-1,-1": 0.4877641290737884,
        "-1,1": 0.012235870926211617,
        "1,-1": 0.012235870926211617,
        "1,1": 0.4877641290737884
      }
    }
  ],
  "measurement_dependence": {
    "M_numeric": 0.2764337057326622,
    "absolute_error": 2.94267337830334e-07,
    "erratum_target": 0.276434,
    "original_incorrect_value": 0.276142,
    "phi_star_over_pi": 0.25798070556045627,
    "phi_star_rad": 0.8104702893566409
  },
  "ok": true,
  "ontology_contract_sha256": "b749348b619769f3b4bf2d5e7cd3a50a6b38c9aaad22983846c893dab09b8d24",
  "physical_mechanism_status": "not supplied by this adapter",
  "q1_q5": {
    "Q1": "singlet correlation represented by an explicit objective-variable model after relaxing measurement independence",
    "Q2": "exact joint law is the adapter target",
    "Q3": "joint probabilities and marginals tested",
    "Q4": "this is a Bell model, not a unified physical theory",
    "Q5": "not earned"
  },
  "schema": "classical-reconstruction-receipt/v1",
  "scope_exclusion": "The adapter demonstrates mathematical representation and no-signalling marginals. It does not supply a microscopic physical mechanism for the setting-lambda dependence.",
  "sources": [
    {
      "arxiv": "1007.5518v4",
      "doi": "10.1103/PhysRevLett.105.250404",
      "id": "hall2010",
      "role": "model equations 5-8"
    },
    {
      "doi": "10.1103/PhysRevLett.116.219902",
      "id": "hall2016erratum",
      "role": "corrected M_singlet about 0.276434"
    }
  ],
  "verified_properties": [
    "deterministic local response functions",
    "setting-dependent hidden-state density",
    "singlet joint probabilities",
    "singlet correlation",
    "one-half local marginals / no-signalling at tested settings"
  ],
  "worst_errors": {
    "correlation": 3.3306690738754696e-16,
    "joint_probability": 1.1102230246251565e-16,
    "marginal": 1.1102230246251565e-16
  }
}