{
 "about": {
  "method": "calibration-blank-limits and dilution linearity",
  "ruling": "docs/board/memos/2026-10-13-cso-lod-loq-linearity-recovery.md",
  "origin": "Self-constructed readings; 4PL standards noiseless from the stated parameters",
  "tolerances": {
   "blank mean and SD": "1e-12 relative",
   "limits on linear curves, original concentrations, percents, CV, slope and its bounds": "1e-9 relative (1e-9 absolute for a zero slope, CV or bound)",
   "limits on 4PL curves": "1e-6 relative (the engine fits the noiseless standards)",
   "states, reasons, n and notes": "exact"
  },
  "thresholds": {
   "minBlanks": 6,
   "k": {
    "lod": 3,
    "loq": 10
   },
   "minDilutions": 2,
   "minForTrend": 3
  },
  "recordedOn": "2026-10-13",
  "script": "pipeline/assay-analyser/oracles/calibration_limits.py",
  "scriptSha256": "ae067271c2c2332296a9abe9210205f8afed5a723cc06a2b88b08422401863cb",
  "helper": {
   "script": "pipeline/assay-analyser/oracles/stage_a_oracle.py",
   "sha256": "492d85ca2fa6750db80b1c64214fd4a0b13cd4c588267244f6262c504c73e3e8"
  },
  "environment": {
   "image": "ghcr.io/biotechmat/drybench/oracle-env:11b8a5e4456df7eb@sha256:7e69891ca1d9f24838660e0a9887bdb654ce7771d2f2ac7e7275e9b1eb3b6a09",
   "r": "R version 4.4.3 (2025-02-28)",
   "packages": {
    "jsonlite": "2.0.0"
   },
   "python": "3.11.15",
   "numpy": "2.0.2",
   "scipy": "1.13.1",
   "recordedOn": "2026-10-13",
   "cpu": "AMD EPYC 7763 64-Core Processor",
   "cpuClass": "x86-64-v3",
   "simd": [
    "SSSE3",
    "SSE41",
    "POPCNT",
    "SSE42",
    "AVX",
    "F16C",
    "FMA3",
    "AVX2"
   ],
   "openblasCore": "Haswell",
   "threads": 1
  },
  "crossCheck": {
   "tool": "R stats mean, sd and confint(lm(log10Original ~ log10Dilution))",
   "version": "R version 4.4.3 (2025-02-28)",
   "script": "pipeline/assay-analyser/oracles/r/calibration_limits.R",
   "scriptSha256": "547ab965a172112a421d2cae4bdbaac72d2387436223292a04a1ff13fb8384b3",
   "ran": true,
   "agreement": "blank mean and SD within 1e-12 relative; every trend's slope and 95 percent bounds within 1e-9; the script stops otherwise"
  }
 },
 "oracle": {
  "engine": "Python fractions and decimal (exact linear least squares, limits, series), closed-form 4PL inverse, scipy.stats.t for the quantile"
 },
 "cases": [
  {
   "name": "L01-linear",
   "about": "Linear rising, 8 blanks: both limits in range; one unknown noted below the limit of quantification, one below the limit of detection",
   "model": "linear",
   "blankCorrection": "none",
   "readings": [
    {
     "role": "standard",
     "label": "S0",
     "concentration": "0",
     "response": "0.051",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S50",
     "concentration": "50",
     "response": "0.149",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S100",
     "concentration": "100",
     "response": "0.252",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S200",
     "concentration": "200",
     "response": "0.448",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S400",
     "concentration": "400",
     "response": "0.853",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S800",
     "concentration": "800",
     "response": "1.648",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 1",
     "concentration": null,
     "response": "0.050",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 2",
     "concentration": null,
     "response": "0.053",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 3",
     "concentration": null,
     "response": "0.047",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 4",
     "concentration": null,
     "response": "0.052",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 5",
     "concentration": null,
     "response": "0.049",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 6",
     "concentration": null,
     "response": "0.051",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 7",
     "concentration": null,
     "response": "0.048",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 8",
     "concentration": null,
     "response": "0.054",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "unknown",
     "label": "Sample A",
     "concentration": null,
     "response": "0.30",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "unknown",
     "label": "Trace",
     "concentration": null,
     "response": "0.060",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "unknown",
     "label": "Faint",
     "concentration": null,
     "response": "0.055",
     "dilutionFactor": "1",
     "excluded": false
    }
   ],
   "expected": {
    "blank": {
     "n": 8,
     "mean": 0.0505,
     "sd": 0.0024494897427831783
    },
    "testedRange": [
     0.0,
     800.0
    ],
    "lod": {
     "status": "computed",
     "threshold": 0.05784846922834953,
     "concentration": 3.5849789709289723
    },
    "loq": {
     "status": "computed",
     "threshold": 0.07499489742783177,
     "concentration": 12.166814453781901
    },
    "unknowns": [
     {
      "label": "Sample A",
      "dilutionFactor": 1.0,
      "status": "interpolated",
      "concentration": 124.78250039209898,
      "originalConcentration": 124.78250039209898,
      "note": null
     },
     {
      "label": "Trace",
      "dilutionFactor": 1.0,
      "status": "interpolated",
      "concentration": 4.661826166379128,
      "originalConcentration": 4.661826166379128,
      "note": "loq"
     },
     {
      "label": "Faint",
      "dilutionFactor": 1.0,
      "status": "interpolated",
      "concentration": 2.159312120009964,
      "originalConcentration": 2.159312120009964,
      "note": "lod"
     }
    ],
    "series": []
   }
  },
  {
   "name": "L02-linear-subtracted",
   "about": "L01 with mean-blank subtraction: the same limits",
   "model": "linear",
   "blankCorrection": "mean-blank",
   "readings": [
    {
     "role": "standard",
     "label": "S0",
     "concentration": "0",
     "response": "0.051",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S50",
     "concentration": "50",
     "response": "0.149",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S100",
     "concentration": "100",
     "response": "0.252",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S200",
     "concentration": "200",
     "response": "0.448",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S400",
     "concentration": "400",
     "response": "0.853",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S800",
     "concentration": "800",
     "response": "1.648",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 1",
     "concentration": null,
     "response": "0.050",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 2",
     "concentration": null,
     "response": "0.053",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 3",
     "concentration": null,
     "response": "0.047",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 4",
     "concentration": null,
     "response": "0.052",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 5",
     "concentration": null,
     "response": "0.049",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 6",
     "concentration": null,
     "response": "0.051",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 7",
     "concentration": null,
     "response": "0.048",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 8",
     "concentration": null,
     "response": "0.054",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "unknown",
     "label": "Sample A",
     "concentration": null,
     "response": "0.30",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "unknown",
     "label": "Trace",
     "concentration": null,
     "response": "0.060",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "unknown",
     "label": "Faint",
     "concentration": null,
     "response": "0.055",
     "dilutionFactor": "1",
     "excluded": false
    }
   ],
   "expected": {
    "blank": {
     "n": 8,
     "mean": 0.0505,
     "sd": 0.0024494897427831783
    },
    "testedRange": [
     0.0,
     800.0
    ],
    "lod": {
     "status": "computed",
     "threshold": 0.007348469228349534,
     "concentration": 3.5849789709289723
    },
    "loq": {
     "status": "computed",
     "threshold": 0.024494897427831782,
     "concentration": 12.166814453781901
    },
    "unknowns": [
     {
      "label": "Sample A",
      "dilutionFactor": 1.0,
      "status": "interpolated",
      "concentration": 124.78250039209898,
      "originalConcentration": 124.78250039209898,
      "note": null
     },
     {
      "label": "Trace",
      "dilutionFactor": 1.0,
      "status": "interpolated",
      "concentration": 4.661826166379128,
      "originalConcentration": 4.661826166379128,
      "note": "loq"
     },
     {
      "label": "Faint",
      "dilutionFactor": 1.0,
      "status": "interpolated",
      "concentration": 2.159312120009964,
      "originalConcentration": 2.159312120009964,
      "note": "lod"
     }
    ],
    "series": []
   }
  },
  {
   "name": "L03-4pl-falling",
   "about": "Falling 4PL (competitive format), noiseless standards: thresholds at mean - k SD, both in range",
   "model": "4pl",
   "blankCorrection": "none",
   "readings": [
    {
     "role": "standard",
     "label": "S0.01",
     "concentration": "0.01",
     "response": "1.9811881188118812",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S0.1",
     "concentration": "0.1",
     "response": "1.8272727272727272",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S1",
     "concentration": "1",
     "response": "1.05",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S10",
     "concentration": "10",
     "response": "0.2727272727272727",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S100",
     "concentration": "100",
     "response": "0.11881188118811882",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 1",
     "concentration": null,
     "response": "1.995",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 2",
     "concentration": null,
     "response": "2.005",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 3",
     "concentration": null,
     "response": "1.990",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 4",
     "concentration": null,
     "response": "2.010",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 5",
     "concentration": null,
     "response": "2.000",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 6",
     "concentration": null,
     "response": "1.985",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 7",
     "concentration": null,
     "response": "2.015",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 8",
     "concentration": null,
     "response": "2.000",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "unknown",
     "label": "Serum 1",
     "concentration": null,
     "response": "1.2",
     "dilutionFactor": "1",
     "excluded": false
    }
   ],
   "parameters": {
    "bottom": 0.1,
    "top": 2.0,
    "logMidpoint": 0.0,
    "hill": -1.0
   },
   "expected": {
    "blank": {
     "n": 8,
     "mean": 2.0,
     "sd": 0.01
    },
    "testedRange": [
     0.01,
     100.0
    ],
    "lod": {
     "status": "computed",
     "threshold": 1.97,
     "concentration": 0.01604278074866312
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    "loq": {
     "status": "computed",
     "threshold": 1.9,
     "concentration": 0.05555555555555562
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    "unknowns": [
     {
      "label": "Serum 1",
      "dilutionFactor": 1.0,
      "status": "interpolated",
      "concentration": 0.7272727272727274,
      "originalConcentration": 0.7272727272727274,
      "note": null
     }
    ],
    "series": []
   }
  },
  {
   "name": "L04a-one-blank",
   "about": "One blank: both limits withheld",
   "model": "linear",
   "blankCorrection": "none",
   "readings": [
    {
     "role": "standard",
     "label": "S0",
     "concentration": "0",
     "response": "0.051",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S50",
     "concentration": "50",
     "response": "0.149",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S100",
     "concentration": "100",
     "response": "0.252",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S200",
     "concentration": "200",
     "response": "0.448",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S400",
     "concentration": "400",
     "response": "0.853",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S800",
     "concentration": "800",
     "response": "1.648",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 1",
     "concentration": null,
     "response": "0.050",
     "dilutionFactor": "1",
     "excluded": false
    }
   ],
   "expected": {
    "blank": {
     "n": 1
    },
    "testedRange": [
     0.0,
     800.0
    ],
    "lod": {
     "status": "withheld",
     "reason": "too-few-blanks"
    },
    "loq": {
     "status": "withheld",
     "reason": "too-few-blanks"
    },
    "unknowns": [],
    "series": []
   }
  },
  {
   "name": "L04b-five-blanks",
   "about": "Five blanks: both limits withheld, the count shown",
   "model": "linear",
   "blankCorrection": "none",
   "readings": [
    {
     "role": "standard",
     "label": "S0",
     "concentration": "0",
     "response": "0.051",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S50",
     "concentration": "50",
     "response": "0.149",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S100",
     "concentration": "100",
     "response": "0.252",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S200",
     "concentration": "200",
     "response": "0.448",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S400",
     "concentration": "400",
     "response": "0.853",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S800",
     "concentration": "800",
     "response": "1.648",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 1",
     "concentration": null,
     "response": "0.050",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 2",
     "concentration": null,
     "response": "0.053",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 3",
     "concentration": null,
     "response": "0.047",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 4",
     "concentration": null,
     "response": "0.052",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 5",
     "concentration": null,
     "response": "0.049",
     "dilutionFactor": "1",
     "excluded": false
    }
   ],
   "expected": {
    "blank": {
     "n": 5,
     "mean": 0.0502,
     "sd": 0.0023874672772626645
    },
    "testedRange": [
     0.0,
     800.0
    ],
    "lod": {
     "status": "withheld",
     "reason": "too-few-blanks"
    },
    "loq": {
     "status": "withheld",
     "reason": "too-few-blanks"
    },
    "unknowns": [],
    "series": []
   }
  },
  {
   "name": "L05-no-spread",
   "about": "Six identical blanks: SD 0, both limits withheld",
   "model": "linear",
   "blankCorrection": "none",
   "readings": [
    {
     "role": "standard",
     "label": "S0",
     "concentration": "0",
     "response": "0.051",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S50",
     "concentration": "50",
     "response": "0.149",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S100",
     "concentration": "100",
     "response": "0.252",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S200",
     "concentration": "200",
     "response": "0.448",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S400",
     "concentration": "400",
     "response": "0.853",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "standard",
     "label": "S800",
     "concentration": "800",
     "response": "1.648",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 1",
     "concentration": null,
     "response": "0.050",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 2",
     "concentration": null,
     "response": "0.050",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 3",
     "concentration": null,
     "response": "0.050",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 4",
     "concentration": null,
     "response": "0.050",
     "dilutionFactor": "1",
     "excluded": false
    },
    {
     "role": "blank",
     "label": "Blank 5",
     "concentration": null,
     "response": "0.050",
     "dilutionFactor": "1",
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    {
     "role": "blank",
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   ],
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     "mean": 0.05,
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     "status": "withheld",
     "reason": "no-spread"
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     "status": "withheld",
     "reason": "no-spread"
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  },
  {
   "name": "L06-below-lowest",
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     "role": "standard",
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     "role": "standard",
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     "role": "blank",
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    {
     "role": "blank",
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     "role": "blank",
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     "role": "blank",
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     "role": "blank",
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     "role": "blank",
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     "role": "blank",
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     "role": "blank",
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     "role": "blank",
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     "role": "blank",
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     "role": "blank",
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     "role": "blank",
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     "role": "blank",
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     "role": "standard",
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     "role": "standard",
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     "role": "blank",
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     "role": "blank",
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     "role": "blank",
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     "role": "blank",
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     "role": "blank",
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     "role": "unknown",
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     "role": "standard",
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    {
     "role": "standard",
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 ]
}