{
 "about": {
  "method": "calibration-inverse-prediction",
  "version": 2,
  "origin": "Original synthetic data, not experimental or manufacturer validation; the coverage replicates from a seeded NumPy generator",
  "ruling": "the CSO's Stage A exit memo of 13 October 2026 (docs/board/memos/2026-10-13-cso-stage-a-exit.md), the inverse-prediction defect, SCI-123: the pooled reading variance; otherwise the CSO memo of 11 October 2026, item 4 (docs/board/memos/2026-10-11-cso-assay-depth-stage.md)",
  "basedOn": {
   "file": "pipeline/assay-analyser/oracles/fixtures/calibration-inverse.json",
   "sha256": "4708f632a365985bf3244f50cf8bf46c2022a10908e0f421c15868c0fb4896cc",
   "script": "pipeline/assay-analyser/oracles/calibration_inverse_scipy.py",
   "scriptSha256": "07883124ef9edf5693f3c13d52355a40b44d5ba3340a7305cda5e1cd0f362ffb",
   "changed": "SCI-123: s^2 pooled over the individual standard readings on N - p degrees of freedom, the curve term (s^2/r)(J'J)^-1 and, for linear, r/m in the Fieller radicand; unequal replicate counts withheld ('unequal-replicates'); replicated, unequal and singlicate cases added; investr over the individual readings; a coverage simulation"
  },
  "level": 0.95,
  "minimumResidualDf": 3,
  "slopeFraction": 0.1,
  "judgements": "the 10 percent slope rule is the CSO's judgement; three residual degrees of freedom on the concentration levels for every model (five standards for linear, as the CSO set) is the builder's; the coverage gates are the CSO's",
  "tolerances": {
   "linear": "bounds within 1e-9 relative",
   "logistic": "bounds within 1e-6 relative; concentrations within 5e-5 relative",
   "status": "exact"
  },
  "uncorrected": "each unknown's `uncorrected` is the first method (calibration-inverse.json, Assay 0.6.0 to 0.12.0) on the same data: s^2 = RSS of the means / (n - p), t on n - p, the unknown's term s^2/m; recorded to document SCI-123, not a target",
  "recordedOn": "2026-10-14",
  "script": "pipeline/assay-analyser/oracles/calibration_inverse_v2.py",
  "scriptSha256": "49a2b5463df23420a4654b3e920a3672c205eb077dd1a2a1950d0fa04432603f",
  "helper": {
   "script": "pipeline/assay-analyser/oracles/stage_a_oracle.py",
   "sha256": "492d85ca2fa6750db80b1c64214fd4a0b13cd4c588267244f6262c504c73e3e8"
  },
  "environment": {
   "image": "ghcr.io/biotechmat/drybench/oracle-env:d6cd987911c17af3@sha256:52c2da8b4a62b2a916a0a44ef276834f8c473115a3d4d73b9809ce4cbd4c8e2c",
   "r": "R version 4.4.3 (2025-02-28)",
   "packages": {
    "jsonlite": "2.0.0",
    "investr": "1.4.2"
   },
   "python": "3.11.15",
   "numpy": "2.0.2",
   "scipy": "1.13.1",
   "recordedOn": "2026-10-14",
   "cpu": "AMD EPYC 9V74 80-Core Processor",
   "cpuClass": "x86-64-v3",
   "simd": [
    "SSSE3",
    "SSE41",
    "POPCNT",
    "SSE42",
    "AVX",
    "F16C",
    "FMA3",
    "AVX2"
   ],
   "openblasCore": "Haswell",
   "threads": 1
  },
  "crossCheck": {
   "tool": "R investr::invest",
   "version": "R version 4.4.3 (2025-02-28)",
   "investr": "1.4.2",
   "script": "pipeline/assay-analyser/oracles/r/calibration_invest_v2.R",
   "scriptSha256": "4e3ef8f54b5adc3f3bfa74a39167e733b93d1c0e3c6f21d3002d7535eb60891f",
   "ran": true,
   "settings": "lm(y ~ c) or nls of the 4PL or 5PL in x = log10 c (from this script's estimates; nls at tol 1e-10, then 1e-8) fitted to the individual standard readings, not their means; interval 'inversion' for the linear fit (the Fieller interval; uniroot at tol 1e-12 over (0, 3 x the highest standard)), 'Wald' for the logistic fits (the delta method; uniroot at tol 1e-12 over the standards' log range +- 2); level 0.95; unknowns read once only; cases with replicated standards of unequal number, and the weighted case, not run",
   "tolerances": {
    "linear": "bounds and the pooled s^2 (R's sigma^2) within 1e-9 relative, degrees of freedom N - p exact",
    "logistic": "bounds and the pooled s^2 within 1e-6 relative, degrees of freedom N - p exact"
   },
   "cases": 11,
   "agreeing": 11,
   "notCompared": [
    {
     "case": "linear-replicates",
     "unknown": "sample-a",
     "m": 3,
     "reason": "investr counts an unknown's m readings in its degrees of freedom (n + m - p - 1) and, for lm, pools their scatter into the variance: a different estimator for m > 1"
    },
    {
     "case": "four-pl",
     "unknown": "sample-a",
     "m": 2,
     "reason": "investr counts an unknown's m readings in its degrees of freedom (n + m - p - 1) and, for lm, pools their scatter into the variance: a different estimator for m > 1"
    },
    {
     "case": "five-pl",
     "unknown": "sample-a",
     "m": 2,
     "reason": "investr counts an unknown's m readings in its degrees of freedom (n + m - p - 1) and, for lm, pools their scatter into the variance: a different estimator for m > 1"
    },
    {
     "case": "linear-singlicate",
     "unknown": "sample-b",
     "m": 2,
     "reason": "investr counts an unknown's m readings in its degrees of freedom (n + m - p - 1) and, for lm, pools their scatter into the variance: a different estimator for m > 1"
    },
    {
     "case": "linear-triplicate",
     "unknown": "sample-b",
     "m": 3,
     "reason": "investr counts an unknown's m readings in its degrees of freedom (n + m - p - 1) and, for lm, pools their scatter into the variance: a different estimator for m > 1"
    },
    {
     "case": "linear-triplicate",
     "unknown": "sample-c",
     "m": 2,
     "reason": "investr counts an unknown's m readings in its degrees of freedom (n + m - p - 1) and, for lm, pools their scatter into the variance: a different estimator for m > 1"
    },
    {
     "case": "four-pl-duplicate",
     "unknown": "sample-a",
     "m": 2,
     "reason": "investr counts an unknown's m readings in its degrees of freedom (n + m - p - 1) and, for lm, pools their scatter into the variance: a different estimator for m > 1"
    },
    {
     "case": "four-pl-triplicate",
     "unknown": "sample-a",
     "m": 3,
     "reason": "investr counts an unknown's m readings in its degrees of freedom (n + m - p - 1) and, for lm, pools their scatter into the variance: a different estimator for m > 1"
    },
    {
     "case": "five-pl-duplicate",
     "unknown": "sample-a",
     "m": 2,
     "reason": "investr counts an unknown's m readings in its degrees of freedom (n + m - p - 1) and, for lm, pools their scatter into the variance: a different estimator for m > 1"
    },
    {
     "case": "five-pl-triplicate",
     "unknown": "sample-a",
     "m": 3,
     "reason": "investr counts an unknown's m readings in its degrees of freedom (n + m - p - 1) and, for lm, pools their scatter into the variance: a different estimator for m > 1"
    }
   ],
   "result": [
    {
     "case": "linear-replicates",
     "unknown": "sample-b",
     "interval": "inversion",
     "readings": 14,
     "df": 12,
     "lower": 5.0178830740942,
     "upper": 5.14319259731675,
     "lowRelativeDifference": 2.1771321493543066e-14,
     "highRelativeDifference": 2.0722811434209506e-14,
     "s2RelativeDifference": 1.7268709130428486e-14,
     "agrees": true
    },
    {
     "case": "linear-replicates",
     "unknown": "near-bottom",
     "interval": "inversion",
     "readings": 14,
     "df": 12,
     "lower": 0.447000584389631,
     "upper": 0.577898111570208,
     "lowRelativeDifference": 2.662544801866391e-13,
     "highRelativeDifference": 1.9672470881197325e-13,
     "s2RelativeDifference": 1.7268709130428486e-14,
     "agrees": true
    },
    {
     "case": "four-pl",
     "unknown": "sample-b",
     "interval": "Wald",
     "readings": 9,
     "df": 5,
     "lower": 3.26106046025327,
     "upper": 3.38295697508065,
     "lowRelativeDifference": 1.9159350117835472e-11,
     "highRelativeDifference": 1.9050658602687794e-11,
     "s2RelativeDifference": 1.2629607824698657e-15,
     "agrees": true
    },
    {
     "case": "five-pl",
     "unknown": "sample-b",
     "interval": "Wald",
     "readings": 9,
     "df": 4,
     "lower": 1.26082396011732,
     "upper": 1.34017773347446,
     "lowRelativeDifference": 2.779319205775464e-09,
     "highRelativeDifference": 2.7793378310376738e-09,
     "s2RelativeDifference": 4.655085877728704e-16,
     "agrees": true
    },
    {
     "case": "linear-singlicate",
     "unknown": "sample-a",
     "interval": "inversion",
     "readings": 7,
     "df": 5,
     "lower": 5.00519072051374,
     "upper": 5.16057733288882,
     "lowRelativeDifference": 1.5970631737446838e-15,
     "highRelativeDifference": 6.884333766609294e-16,
     "s2RelativeDifference": 1.2144134371841299e-14,
     "agrees": true
    },
    {
     "case": "linear-triplicate",
     "unknown": "sample-a",
     "interval": "inversion",
     "readings": 21,
     "df": 19,
     "lower": 5.02405311343021,
     "upper": 5.13687262165661,
     "lowRelativeDifference": 1.767852368689858e-16,
     "highRelativeDifference": 6.9161023456617755e-16,
     "s2RelativeDifference": 4.409934204994688e-15,
     "agrees": true
    },
    {
     "case": "four-pl-duplicate",
     "unknown": "sample-b",
     "interval": "Wald",
     "readings": 18,
     "df": 14,
     "lower": 3.28903776520331,
     "upper": 3.37799419222587,
     "lowRelativeDifference": 1.4936523999844006e-10,
     "highRelativeDifference": 1.4947795057966556e-10,
     "s2RelativeDifference": 4.473846474500543e-16,
     "agrees": true
    },
    {
     "case": "four-pl-triplicate",
     "unknown": "sample-b",
     "interval": "Wald",
     "readings": 27,
     "df": 23,
     "lower": 3.28951782523241,
     "upper": 3.36900216665239,
     "lowRelativeDifference": 7.686299484095753e-12,
     "highRelativeDifference": 7.5787749182443e-12,
     "s2RelativeDifference": 1.3053697279849279e-14,
     "agrees": true
    },
    {
     "case": "four-pl-triplicate",
     "unknown": "sample-c",
     "interval": "Wald",
     "readings": 27,
     "df": 23,
     "lower": 0.511013237481394,
     "upper": 0.53111524972387,
     "lowRelativeDifference": 2.1847819280824378e-10,
     "highRelativeDifference": 2.1851659688001167e-10,
     "s2RelativeDifference": 1.3053697279849279e-14,
     "agrees": true
    },
    {
     "case": "five-pl-duplicate",
     "unknown": "sample-b",
     "interval": "Wald",
     "readings": 18,
     "df": 13,
     "lower": 1.27891554095898,
     "upper": 1.32966257386084,
     "lowRelativeDifference": 3.452193103709023e-09,
     "highRelativeDifference": 3.452180248556674e-09,
     "s2RelativeDifference": 1.8441186015678945e-15,
     "agrees": true
    },
    {
     "case": "five-pl-triplicate",
     "unknown": "sample-b",
     "interval": "Wald",
     "readings": 27,
     "df": 22,
     "lower": 1.27951782154036,
     "upper": 1.32428632614234,
     "lowRelativeDifference": 6.201897968066821e-10,
     "highRelativeDifference": 6.202112063945598e-10,
     "s2RelativeDifference": 1.4169688805998473e-14,
     "agrees": true
    }
   ]
  }
 },
 "oracle": {
  "engine": "Python fractions (linear, to the square root and the t quantile); SciPy curve_fit and central finite differences (4PL, 5PL)",
  "t": "scipy.stats.t.ppf"
 },
 "cases": [
  {
   "name": "linear-replicates",
   "model": "linear",
   "about": "seven standards in duplicate; unknowns read three times, once, twice and once, the last two placed so that a bound leaves the standards",
   "levels": [
    0.5,
    1,
    2,
    4,
    6,
    8,
    10
   ],
   "standardReadings": [
    [
     0.114,
     0.108
    ],
    [
     0.167,
     0.175
    ],
    [
     0.292,
     0.291
    ],
    [
     0.526,
     0.529
    ],
    [
     0.773,
     0.765
    ],
    [
     1.011,
     1.014
    ],
    [
     1.248,
     1.252
    ]
   ],
   "unknowns": [
    {
     "label": "sample-a",
     "readings": [
      0.41,
      0.418,
      0.405
     ],
     "m": 3,
     "dilutionFactor": 2,
     "concentration": 3.0049261729384407,
     "df": 12,
     "t": 2.1788128296634177,
     "s2": 1.1085336178496509e-05,
     "g": 2.2997441094627983e-05,
     "low": 2.965757521211659,
     "high": 3.04402605733921,
     "status": "computed",
     "interval": {
      "low": 2.965757521211659,
      "high": 3.04402605733921,
      "originalLow": 5.931515042423318,
      "originalHigh": 6.08805211467842
     },
     "uncorrected": {
      "status": "computed",
      "low": 2.977035669045177,
      "high": 3.0327587818420163,
      "df": 5
     }
    },
    {
     "label": "sample-b",
     "readings": [
      0.66
     ],
     "m": 1,
     "dilutionFactor": 1,
     "concentration": 5.080524484820797,
     "df": 12,
     "t": 2.1788128296634177,
     "s2": 1.1085336178496509e-05,
     "g": 2.2997441094627983e-05,
     "low": 5.01788307409431,
     "high": 5.143192597316643,
     "status": "computed",
     "interval": {
      "low": 5.01788307409431,
      "high": 5.143192597316643,
      "originalLow": 5.01788307409431,
      "originalHigh": 5.143192597316643
     },
     "uncorrected": {
      "status": "computed",
      "low": 5.038515566767015,
      "high": 5.122555883007971,
      "df": 5
     }
    },
    {
     "label": "near-top",
     "readings": [
      1.2475,
      1.248
     ],
     "m": 2,
     "dilutionFactor": 1,
     "concentration": 9.97985343184431,
     "df": 12,
     "t": 2.1788128296634177,
     "s2": 1.1085336178496509e-05,
     "g": 2.2997441094627983e-05,
     "low": 9.9272523578464,
     "high": 10.032706556851759,
     "status": "upper-bound-outside",
     "interval": null,
     "uncorrected": {
      "status": "upper-bound-outside",
      "low": 9.940324213489278,
      "high": 10.019594851130282,
      "df": 5
     }
    },
    {
     "label": "near-bottom",
     "readings": [
      0.112
     ],
     "m": 1,
     "dilutionFactor": 5,
     "concentration": 0.5125410514411537,
     "df": 12,
     "t": 2.1788128296634177,
     "s2": 1.1085336178496509e-05,
     "g": 2.2997441094627983e-05,
     "low": 0.44700058438975,
     "high": 0.5778981115700943,
     "status": "lower-bound-outside",
     "interval": null,
     "uncorrected": {
      "status": "lower-bound-outside",
      "low": 0.4669992939148262,
      "high": 0.5579283992717663,
      "df": 5
     }
    }
   ],
   "fit": {
    "intercept": 0.05051280323450135,
    "slope": 0.11996540880503144,
    "rssOfMeans": 1.676201707097891e-05,
    "n": 7,
    "r": 2,
    "N": 14,
    "levelDf": 5,
    "df": 12,
    "withinStandardsSS": 9.950000000000029e-05,
    "pooledS2": 1.1085336178496509e-05
   }
  },
  {
   "name": "linear-four-standards",
   "model": "linear",
   "about": "four standards: residual df 2, below the three the interval needs",
   "levels": [
    1,
    2,
    4,
    8
   ],
   "standardReadings": [
    [
     0.17
    ],
    [
     0.29
    ],
    [
     0.53
    ],
    [
     1.01
    ]
   ],
   "unknowns": [
    {
     "label": "sample-a",
     "readings": [
      0.4
     ],
     "m": 1,
     "dilutionFactor": 1,
     "concentration": 2.916666666666667,
     "status": "standard-count",
     "interval": null,
     "uncorrected": {
      "status": "standard-count"
     }
    }
   ],
   "fit": {
    "intercept": 0.05,
    "slope": 0.12,
    "rssOfMeans": 1.071821882093766e-33,
    "n": 4,
    "r": 1,
    "N": 4,
    "levelDf": 2,
    "df": 2,
    "withinStandardsSS": 0.0,
    "pooledS2": 5.35910941046883e-34
   }
  },
  {
   "name": "linear-weak-slope",
   "model": "linear",
   "about": "five standards whose scatter swamps the slope: g >= 1, no bounded interval",
   "levels": [
    1,
    2,
    3,
    4,
    5
   ],
   "standardReadings": [
    [
     0.5
    ],
    [
     0.2
    ],
    [
     0.75
    ],
    [
     0.3
    ],
    [
     0.8
    ]
   ],
   "unknowns": [
    {
     "label": "sample-a",
     "readings": [
      0.5
     ],
     "m": 1,
     "dilutionFactor": 1,
     "concentration": 2.857142857142857,
     "df": 3,
     "t": 3.182446305284263,
     "s2": 0.07766666666666668,
     "g": 16.053168198925626,
     "status": "unbounded",
     "interval": null,
     "uncorrected": {
      "status": "unbounded"
     }
    }
   ],
   "fit": {
    "intercept": 0.3,
    "slope": 0.07,
    "rssOfMeans": 0.233,
    "n": 5,
    "r": 1,
    "N": 5,
    "levelDf": 3,
    "df": 3,
    "withinStandardsSS": 0.0,
    "pooledS2": 0.07766666666666668
   }
  },
  {
   "name": "four-pl",
   "model": "4pl",
   "about": "nine standards read once on a rising 4PL with noise; unknowns read twice, once and three times, the last near the upper asymptote",
   "levels": [
    0.01,
    0.03162277660168379,
    0.1,
    0.31622776601683794,
    1.0,
    3.1622776601683795,
    10.0,
    31.622776601683793,
    100.0
   ],
   "standardReadings": [
    [
     0.126955
    ],
    [
     0.133665
    ],
    [
     0.185113
    ],
    [
     0.342294
    ],
    [
     0.813826
    ],
    [
     1.571215
    ],
    [
     2.10906
    ],
    [
     2.322119
    ],
    [
     2.378394
    ]
   ],
   "unknowns": [
    {
     "label": "sample-a",
     "readings": [
      0.9,
      0.93
     ],
     "m": 2,
     "dilutionFactor": 1,
     "concentration": 1.1838706671214005,
     "slopeRatio": 0.9082727372372463,
     "df": 5,
     "t": 2.570581835636314,
     "s2": 1.2072103316431515e-05,
     "seLog10": 0.0025563197965572963,
     "low": 1.1660925773559163,
     "high": 1.2019197992396509,
     "status": "computed",
     "interval": {
      "low": 1.1660925773559163,
      "high": 1.2019197992396509,
      "originalLow": 1.1660925773559163,
      "originalHigh": 1.2019197992396509
     },
     "uncorrected": {
      "status": "computed",
      "low": 1.1660925773559163,
      "high": 1.2019197992396509,
      "df": 5
     }
    },
    {
     "label": "sample-b",
     "readings": [
      1.6
     ],
     "m": 1,
     "dilutionFactor": 10,
     "concentration": 3.3214495676093465,
     "slopeRatio": 0.9107903198777308,
     "df": 5,
     "t": 2.570581835636314,
     "s2": 1.2072103316431515e-05,
     "seLog10": 0.003100003173398525,
     "low": 3.26106046019079,
     "high": 3.3829569751450976,
     "status": "computed",
     "interval": {
      "low": 3.26106046019079,
      "high": 3.3829569751450976,
      "originalLow": 32.6106046019079,
      "originalHigh": 33.829569751450975
     },
     "uncorrected": {
      "status": "computed",
      "low": 3.26106046019079,
      "high": 3.3829569751450976,
      "df": 5
     }
    },
    {
     "label": "near-asymptote",
     "readings": [
      2.355,
      2.36,
      2.352
     ],
     "m": 3,
     "dilutionFactor": 1,
     "concentration": 53.096840948366584,
     "slopeRatio": 0.07401320388876088,
     "status": "asymptote",
     "interval": null,
     "uncorrected": {
      "status": "asymptote"
     }
    }
   ],
   "fit": {
    "parameters": [
     0.12114845999353095,
     2.3986173648206477,
     0.2989765317155362,
     1.203438128747598
    ],
    "rssOfMeans": 6.0360516582157575e-05,
    "n": 9,
    "r": 1,
    "N": 9,
    "levelDf": 5,
    "df": 5,
    "withinStandardsSS": 0.0,
    "pooledS2": 1.2072103316431515e-05
   }
  },
  {
   "name": "four-pl-weighted",
   "model": "4pl",
   "weighting": "1/y2",
   "about": "the same standards fitted with 1/y2 weighting: no inference",
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 }
}