{
  "about": {
    "method": "standard-curve-interpolation (linear)",
    "recordedOn": "2026-10-10",
    "script": "pipeline/assay-analyser/oracles/calibration_linear_exact.py",
    "scriptSha256": "21780ddf62e4a6d6f6205fa1c67dba788fb620b08b46d0890f474e42b16c9740",
    "origin": "Self-generated readings, not experimental, kit or manufacturer data",
    "tolerances": {
      "values": "within 1e-9 relative (nine significant figures)",
      "status and refusal": "exact"
    }
  },
  "oracle": {
    "engine": "Python fractions (exact rational ordinary least squares)",
    "python": "3.11.15"
  },
  "cases": [
    {
      "name": "bradford-style-rising",
      "about": "Self-generated Bradford-style series (BSA standards in µg/mL, A595); duplicates; a 1:5 diluted sample; one unknown each side of the tested range",
      "unit": "µg/mL",
      "blankCorrection": "none",
      "readings": [
        {
          "role": "standard",
          "label": "S1",
          "concentration": "125",
          "response": "0.141",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S1",
          "concentration": "125",
          "response": "0.147",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S2",
          "concentration": "250",
          "response": "0.262",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S2",
          "concentration": "250",
          "response": "0.270",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S3",
          "concentration": "500",
          "response": "0.502",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S3",
          "concentration": "500",
          "response": "0.494",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S4",
          "concentration": "750",
          "response": "0.721",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S4",
          "concentration": "750",
          "response": "0.737",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S5",
          "concentration": "1000",
          "response": "0.941",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S5",
          "concentration": "1000",
          "response": "0.951",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "lysate A",
          "concentration": null,
          "response": "0.388",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "lysate A",
          "concentration": null,
          "response": "0.396",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "lysate B",
          "concentration": null,
          "response": "0.612",
          "dilutionFactor": "5",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "lysate B",
          "concentration": null,
          "response": "0.604",
          "dilutionFactor": "5",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "too dilute",
          "concentration": null,
          "response": "0.090",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "too concentrated",
          "concentration": null,
          "response": "1.204",
          "dilutionFactor": "1",
          "excluded": false
        }
      ],
      "expected": {
        "status": "fitted",
        "blankSubtracted": 0.0,
        "slope": 0.0009174146341463414,
        "intercept": 0.034957317073170735,
        "testedRange": [
          125.0,
          1000.0
        ],
        "standards": [
          {
            "concentration": 125.0,
            "n": 2,
            "meanResponse": 0.144,
            "fittedResponse": 0.1496341463414634,
            "residual": -0.0056341463414634144,
            "recoveredConcentration": 118.85866964428138
          },
          {
            "concentration": 250.0,
            "n": 2,
            "meanResponse": 0.266,
            "fittedResponse": 0.2643109756097561,
            "residual": 0.0016890243902439024,
            "recoveredConcentration": 251.8410698144308
          },
          {
            "concentration": 500.0,
            "n": 2,
            "meanResponse": 0.498,
            "fittedResponse": 0.4936646341463415,
            "residual": 0.004335365853658537,
            "recoveredConcentration": 504.72563407241984
          },
          {
            "concentration": 750.0,
            "n": 2,
            "meanResponse": 0.729,
            "fittedResponse": 0.7230182926829268,
            "residual": 0.005981707317073171,
            "recoveredConcentration": 756.5201786568831
          },
          {
            "concentration": 1000.0,
            "n": 2,
            "meanResponse": 0.946,
            "fittedResponse": 0.9523719512195122,
            "residual": -0.006371951219512195,
            "recoveredConcentration": 993.0544478119849
          }
        ],
        "rSquared": 0.9996992309401701,
        "unknowns": [
          {
            "label": "lysate A",
            "dilutionFactor": 1.0,
            "n": 2,
            "meanResponse": 0.392,
            "status": "interpolated",
            "concentration": 389.18354867868345,
            "originalConcentration": 389.18354867868345
          },
          {
            "label": "lysate B",
            "dilutionFactor": 5.0,
            "n": 2,
            "meanResponse": 0.608,
            "status": "interpolated",
            "concentration": 624.6277981602594,
            "originalConcentration": 3123.1389908012975
          },
          {
            "label": "too dilute",
            "dilutionFactor": 1.0,
            "n": 1,
            "meanResponse": 0.09,
            "status": "below-range",
            "concentration": null,
            "originalConcentration": null
          },
          {
            "label": "too concentrated",
            "dilutionFactor": 1.0,
            "n": 1,
            "meanResponse": 1.204,
            "status": "above-range",
            "concentration": null,
            "originalConcentration": null
          }
        ]
      }
    },
    {
      "name": "bca-style-blank-subtracted",
      "about": "Self-generated BCA-style series (BSA standards in µg/mL, A562); the zero-protein standard assigned as blanks and subtracted; one excluded standard well with a reason; unequal replicate counts",
      "unit": "µg/mL",
      "blankCorrection": "mean-blank",
      "readings": [
        {
          "role": "blank",
          "label": "zero protein",
          "concentration": null,
          "response": "0.095",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "blank",
          "label": "zero protein",
          "concentration": null,
          "response": "0.101",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "blank",
          "label": "zero protein",
          "concentration": null,
          "response": "0.098",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S1",
          "concentration": "25",
          "response": "0.121",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S1",
          "concentration": "25",
          "response": "0.125",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S2",
          "concentration": "125",
          "response": "0.208",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S2",
          "concentration": "125",
          "response": "0.216",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S2",
          "concentration": "125",
          "response": "0.212",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S3",
          "concentration": "250",
          "response": "0.329",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S3",
          "concentration": "250",
          "response": "0.337",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S3",
          "concentration": "250",
          "response": "0.912",
          "dilutionFactor": "1",
          "excluded": true,
          "exclusionReason": "Pipetting error noted at the bench"
        },
        {
          "role": "standard",
          "label": "S4",
          "concentration": "500",
          "response": "0.561",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S4",
          "concentration": "500",
          "response": "0.555",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S5",
          "concentration": "1000",
          "response": "1.020",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S5",
          "concentration": "1000",
          "response": "1.034",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S6",
          "concentration": "2000",
          "response": "1.902",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "sample 1",
          "concentration": null,
          "response": "0.402",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "sample 1",
          "concentration": null,
          "response": "0.410",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "sample 2",
          "concentration": null,
          "response": "0.700",
          "dilutionFactor": "10",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "below the lowest standard",
          "concentration": null,
          "response": "0.110",
          "dilutionFactor": "1",
          "excluded": false
        }
      ],
      "expected": {
        "status": "fitted",
        "blankSubtracted": 0.098,
        "slope": 0.0009027561521252796,
        "intercept": 0.007708501118568233,
        "testedRange": [
          25.0,
          2000.0
        ],
        "standards": [
          {
            "concentration": 25.0,
            "n": 2,
            "meanResponse": 0.025,
            "fittedResponse": 0.030277404921700224,
            "residual": -0.005277404921700223,
            "recoveredConcentration": 19.154119128098888
          },
          {
            "concentration": 125.0,
            "n": 3,
            "meanResponse": 0.114,
            "fittedResponse": 0.1205530201342282,
            "residual": -0.006553020134228188,
            "recoveredConcentration": 117.74109612124937
          },
          {
            "concentration": 250.0,
            "n": 2,
            "meanResponse": 0.235,
            "fittedResponse": 0.23339753914988814,
            "residual": 0.0016024608501118568,
            "recoveredConcentration": 251.77507607822923
          },
          {
            "concentration": 500.0,
            "n": 2,
            "meanResponse": 0.46,
            "fittedResponse": 0.45908657718120804,
            "residual": 0.0009134228187919464,
            "recoveredConcentration": 501.0118156676546
          },
          {
            "concentration": 1000.0,
            "n": 2,
            "meanResponse": 0.929,
            "fittedResponse": 0.9104646532438478,
            "residual": 0.018535346756152125,
            "recoveredConcentration": 1020.5319528562791
          },
          {
            "concentration": 2000.0,
            "n": 1,
            "meanResponse": 1.804,
            "fittedResponse": 1.8132208053691274,
            "residual": -0.009220805369127517,
            "recoveredConcentration": 1989.7859401484889
          }
        ],
        "rSquared": 0.9997792241329846,
        "unknowns": [
          {
            "label": "sample 1",
            "dilutionFactor": 1.0,
            "n": 2,
            "meanResponse": 0.308,
            "status": "interpolated",
            "concentration": 332.638551589465,
            "originalConcentration": 332.638551589465
          },
          {
            "label": "sample 2",
            "dilutionFactor": 10.0,
            "n": 1,
            "meanResponse": 0.602,
            "status": "interpolated",
            "concentration": 658.3078913196475,
            "originalConcentration": 6583.078913196475
          },
          {
            "label": "below the lowest standard",
            "dilutionFactor": 1.0,
            "n": 1,
            "meanResponse": 0.012,
            "status": "below-range",
            "concentration": null,
            "originalConcentration": null
          }
        ]
      }
    },
    {
      "name": "falling-competitive-style",
      "about": "A falling linear series (competitive format): the range is read in concentration direction, so a response above the lowest standard's fitted response is below range",
      "unit": "ng/mL",
      "blankCorrection": "none",
      "readings": [
        {
          "role": "standard",
          "label": "S1",
          "concentration": "0.5",
          "response": "1.84",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S2",
          "concentration": "1",
          "response": "1.71",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S3",
          "concentration": "2",
          "response": "1.47",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S4",
          "concentration": "4",
          "response": "0.98",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S5",
          "concentration": "8",
          "response": "0.12",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "plasma 1",
          "concentration": null,
          "response": "1.20",
          "dilutionFactor": "2",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "above the top response",
          "concentration": null,
          "response": "1.95",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "below the bottom response",
          "concentration": null,
          "response": "0.05",
          "dilutionFactor": "1",
          "excluded": false
        }
      ],
      "expected": {
        "status": "fitted",
        "blankSubtracted": 0.0,
        "slope": -0.22908602150537635,
        "intercept": 1.9341666666666666,
        "testedRange": [
          0.5,
          8.0
        ],
        "standards": [
          {
            "concentration": 0.5,
            "n": 1,
            "meanResponse": 1.84,
            "fittedResponse": 1.8196236559139785,
            "residual": 0.020376344086021507,
            "recoveredConcentration": 0.41105374325275756
          },
          {
            "concentration": 1.0,
            "n": 1,
            "meanResponse": 1.71,
            "fittedResponse": 1.7050806451612903,
            "residual": 0.004919354838709677,
            "recoveredConcentration": 0.978526167566299
          },
          {
            "concentration": 2.0,
            "n": 1,
            "meanResponse": 1.47,
            "fittedResponse": 1.475994623655914,
            "residual": -0.005994623655913979,
            "recoveredConcentration": 2.026167566298991
          },
          {
            "concentration": 4.0,
            "n": 1,
            "meanResponse": 0.98,
            "fittedResponse": 1.0178225806451613,
            "residual": -0.03782258064516129,
            "recoveredConcentration": 4.16510208871157
          },
          {
            "concentration": 8.0,
            "n": 1,
            "meanResponse": 0.12,
            "fittedResponse": 0.10147849462365591,
            "residual": 0.018521505376344085,
            "recoveredConcentration": 7.9191504341703824
          }
        ],
        "rSquared": 0.9988493723619186,
        "unknowns": [
          {
            "label": "plasma 1",
            "dilutionFactor": 2.0,
            "n": 1,
            "meanResponse": 1.2,
            "status": "interpolated",
            "concentration": 3.2047641398732694,
            "originalConcentration": 6.409528279746539
          },
          {
            "label": "above the top response",
            "dilutionFactor": 1.0,
            "n": 1,
            "meanResponse": 1.95,
            "status": "below-range",
            "concentration": null,
            "originalConcentration": null
          },
          {
            "label": "below the bottom response",
            "dilutionFactor": 1.0,
            "n": 1,
            "meanResponse": 0.05,
            "status": "above-range",
            "concentration": null,
            "originalConcentration": null
          }
        ]
      }
    },
    {
      "name": "boundary-at-highest-standard",
      "about": "An unknown whose mean equals the fitted response at the highest standard exactly (an exactly linear series) is interpolated to that standard, not flagged",
      "unit": "mg/mL",
      "blankCorrection": "none",
      "readings": [
        {
          "role": "standard",
          "label": "S1",
          "concentration": "0.25",
          "response": "0.30",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S2",
          "concentration": "0.5",
          "response": "0.55",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S3",
          "concentration": "1",
          "response": "1.05",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S4",
          "concentration": "2",
          "response": "2.05",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "at the top",
          "concentration": null,
          "response": "2.05",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "at the bottom",
          "concentration": null,
          "response": "0.30",
          "dilutionFactor": "1",
          "excluded": false
        }
      ],
      "expected": {
        "status": "fitted",
        "blankSubtracted": 0.0,
        "slope": 1.0,
        "intercept": 0.05,
        "testedRange": [
          0.25,
          2.0
        ],
        "standards": [
          {
            "concentration": 0.25,
            "n": 1,
            "meanResponse": 0.3,
            "fittedResponse": 0.3,
            "residual": 0.0,
            "recoveredConcentration": 0.25
          },
          {
            "concentration": 0.5,
            "n": 1,
            "meanResponse": 0.55,
            "fittedResponse": 0.55,
            "residual": 0.0,
            "recoveredConcentration": 0.5
          },
          {
            "concentration": 1.0,
            "n": 1,
            "meanResponse": 1.05,
            "fittedResponse": 1.05,
            "residual": 0.0,
            "recoveredConcentration": 1.0
          },
          {
            "concentration": 2.0,
            "n": 1,
            "meanResponse": 2.05,
            "fittedResponse": 2.05,
            "residual": 0.0,
            "recoveredConcentration": 2.0
          }
        ],
        "rSquared": 1.0,
        "unknowns": [
          {
            "label": "at the top",
            "dilutionFactor": 1.0,
            "n": 1,
            "meanResponse": 2.05,
            "status": "interpolated",
            "concentration": 2.0,
            "originalConcentration": 2.0
          },
          {
            "label": "at the bottom",
            "dilutionFactor": 1.0,
            "n": 1,
            "meanResponse": 0.3,
            "status": "interpolated",
            "concentration": 0.25,
            "originalConcentration": 0.25
          }
        ]
      }
    },
    {
      "name": "refused-two-concentrations",
      "about": "Two distinct standard concentrations (replicated) do not support a linear calibration; no unknown receives a value",
      "unit": "µg/mL",
      "blankCorrection": "none",
      "readings": [
        {
          "role": "standard",
          "label": "S1",
          "concentration": "100",
          "response": "0.20",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S1",
          "concentration": "100",
          "response": "0.21",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S2",
          "concentration": "200",
          "response": "0.40",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S2",
          "concentration": "200",
          "response": "0.41",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S3",
          "concentration": "300",
          "response": "0.62",
          "dilutionFactor": "1",
          "excluded": true,
          "exclusionReason": "Pipetting error noted at the bench"
        },
        {
          "role": "unknown",
          "label": "u",
          "concentration": null,
          "response": "0.30",
          "dilutionFactor": "1",
          "excluded": false
        }
      ],
      "expected": {
        "status": "refused",
        "refusal": "standardCount"
      }
    },
    {
      "name": "refused-flat",
      "about": "Standards with no slope identify no calibration",
      "unit": "µg/mL",
      "blankCorrection": "none",
      "readings": [
        {
          "role": "standard",
          "label": "S1",
          "concentration": "100",
          "response": "0.50",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S2",
          "concentration": "200",
          "response": "0.50",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S3",
          "concentration": "300",
          "response": "0.50",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "u",
          "concentration": null,
          "response": "0.50",
          "dilutionFactor": "1",
          "excluded": false
        }
      ],
      "expected": {
        "status": "refused",
        "refusal": "flat"
      }
    },
    {
      "name": "refused-no-blank",
      "about": "Blank subtraction chosen with no retained blank (the only blank excluded) is refused rather than run without it",
      "unit": "µg/mL",
      "blankCorrection": "mean-blank",
      "readings": [
        {
          "role": "blank",
          "label": "zero protein",
          "concentration": null,
          "response": "0.10",
          "dilutionFactor": "1",
          "excluded": true,
          "exclusionReason": "Pipetting error noted at the bench"
        },
        {
          "role": "standard",
          "label": "S1",
          "concentration": "100",
          "response": "0.20",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S2",
          "concentration": "200",
          "response": "0.40",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "standard",
          "label": "S3",
          "concentration": "300",
          "response": "0.60",
          "dilutionFactor": "1",
          "excluded": false
        },
        {
          "role": "unknown",
          "label": "u",
          "concentration": null,
          "response": "0.30",
          "dilutionFactor": "1",
          "excluded": false
        }
      ],
      "expected": {
        "status": "refused",
        "refusal": "blank"
      }
    }
  ]
}