{
 "about": {
  "method": "binding-equilibrium",
  "origin": "Original synthetic binding data from known constants with recorded noise vectors (NumPy default_rng seeds named per case); no published dataset",
  "ruling": "CSO memo of 13 October 2026, binding rulings 1 to 9 (docs/board/memos/2026-10-13-cso-binding.md)",
  "models": {
   "saturation": "specific = Bmax L/(Kd + L), or the sum of two; NS subtracted by the mean at each concentration, or fitted as ns L (+ c)",
   "competition": "y = Bottom + (Top - Bottom)/(1 + (x/IC50)^nH), nH = 1 unless freed; two sites with F on the logit scale",
   "ki": "Cheng-Prusoff IC50/(1 + L/Kd); Munson-Rodbard IC50/(1 + L (y0 + 2)/(2 Kd (y0 + 1)) + y0) - Kd y0/(y0 + 2)"
  },
  "minimum": {
   "oneSite": 6,
   "twoSite": 10,
   "twoSiteDecades": 3,
   "twoSiteRatio": 10,
   "nsFitted": 3
  },
  "munsonRodbard": [
   {
    "receptor": 0.09761904761904762,
    "L": 1.0,
    "kd": 1.0,
    "trueKi": 0.5,
    "ic50": 1.0625145180023225,
    "y0": 0.05,
    "munsonRodbard": 0.4999999999999999,
    "chengPrusoff": 0.5312572590011613,
    "relativeError": 2.220446049250313e-16,
    "passes": true
   },
   {
    "receptor": 0.5307692307692308,
    "L": 1.0,
    "kd": 1.0,
    "trueKi": 0.5,
    "ic50": 1.377257525083613,
    "y0": 0.29999999999999993,
    "munsonRodbard": 0.5000000000000004,
    "chengPrusoff": 0.6886287625418065,
    "relativeError": 8.881784197001252e-16,
    "passes": true
   },
   {
    "receptor": 1.5,
    "L": 1.0,
    "kd": 1.0,
    "trueKi": 0.5,
    "ic50": 2.291666666666666,
    "y0": 1.0,
    "munsonRodbard": 0.49999999999999983,
    "chengPrusoff": 1.145833333333333,
    "relativeError": 3.3306690738754696e-16,
    "passes": true
   },
   {
    "case": "not-resolved",
    "inputs": {
     "ic50": 0.5,
     "L": 1.0,
     "kd": 1.0,
     "y0": 1.0
    },
    "munsonRodbard": {
     "status": "withheld",
     "reason": "not-resolved"
    }
   },
   {
    "case": "hand",
    "inputs": {
     "ic50": 10.0,
     "L": 1.0,
     "kd": 1.0,
     "y0": 1.0
    },
    "expected": 3.3030303030303028,
    "munsonRodbard": {
     "status": "computed",
     "ki": 3.3030303030303028
    }
   }
  ],
  "coverage": {
   "range": [
    93.5,
    96.5
   ],
   "runs": [
    {
     "quantity": "Kd",
     "design": "fitted",
     "seed": 20261023,
     "replicates": 2000,
     "resolved": 2000,
     "contained": 1891,
     "percent": 94.55,
     "passes": true
    },
    {
     "quantity": "Bmax",
     "design": "fitted",
     "seed": 20261023,
     "replicates": 2000,
     "resolved": 2000,
     "contained": 1879,
     "percent": 93.95,
     "passes": true
    },
    {
     "quantity": "Kd",
     "design": "subtracted",
     "seed": 20261024,
     "replicates": 2000,
     "resolved": 2000,
     "contained": 1793,
     "percent": 89.65,
     "passes": false
    },
    {
     "quantity": "Bmax",
     "design": "subtracted",
     "seed": 20261024,
     "replicates": 2000,
     "resolved": 2000,
     "contained": 1802,
     "percent": 90.1,
     "passes": false
    },
    {
     "quantity": "IC50",
     "design": "competition",
     "seed": 20261025,
     "replicates": 2000,
     "resolved": 2000,
     "contained": 1899,
     "percent": 94.95,
     "passes": true
    }
   ],
   "shown": [
    "fitted",
    "competition"
   ],
   "passes": true,
   "subtracted": "the subtracted route's intervals treat the NS mean as exact; they are computed here for the record and not given by the engine ('ns-subtracted')"
  },
  "tolerances": {
   "statuses, refusals, reasons, the parameters at the box, flags and counts": "exact",
   "constants": "within 1e-5 relative; hand values within 1e-9 relative",
   "rss": "within 1e-6 relative, or both at the readings' numeric resolution",
   "correlations": "within 1e-4 absolute",
   "interval bounds": "within 1e-3 in ln; side states exact",
   "aicc, dAicc": "within 1e-6 absolute",
   "F": "within 1e-5 relative",
   "p": "within 1e-4 relative or 1e-10 absolute",
   "Ki": "within 1e-9 relative of the same equation on the fixture's IC50 (hand cases 1e-9 of the true value)"
  },
  "recordedOn": "2026-10-13",
  "script": "pipeline/assay-analyser/oracles/binding.py",
  "scriptSha256": "b93bb8aa14acb1cfb33a32cd9a905821b1c8b619c79e9431cd333e9b417f246f",
  "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",
    "drc": "4.0-0"
   },
   "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::nls (port) and drc::drm LL.4 with b fixed at 1",
   "version": "R version 4.4.3 (2025-02-28)",
   "script": "pipeline/assay-analyser/oracles/r/binding_nls.R",
   "scriptSha256": "c4a97d2166792d6b9edd820a41bb55c8cc94ea926c59616c0ef898e4812c441e",
   "ran": true,
   "tolerances": {
    "parameters": "1e-5 relative"
   },
   "cases": 20,
   "agreeing": 20,
   "result": [
    {
     "case": "saturation-hand-subtracted/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "bmax": 1000,
      "kd": 2
     },
     "relativeDifferences": {
      "bmax": 0.0,
      "kd": 2.2204460492503126e-16
     },
     "agrees": true
    },
    {
     "case": "saturation-hand-fitted/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "bmax": 1000,
      "kd": 2,
      "ns": 30
     },
     "relativeDifferences": {
      "bmax": 1.1368683772161603e-16,
      "kd": 2.2204460492503126e-16,
      "ns": 0.0
     },
     "agrees": true
    },
    {
     "case": "saturation-noisy-fitted/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "bmax": 1004.30730599092,
      "kd": 2.0694724309433,
      "ns": 30.1163077862254
     },
     "relativeDifferences": {
      "bmax": 7.456403163973132e-10,
      "kd": 2.4440626710179124e-09,
      "ns": 2.951886077284336e-11
     },
     "agrees": true
    },
    {
     "case": "saturation-noisy-subtracted/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "bmax": 1005.76037144328,
      "kd": 2.14434683742136
     },
     "relativeDifferences": {
      "bmax": 3.2780355913166e-15,
      "kd": 1.2425859532614422e-15
     },
     "agrees": true
    },
    {
     "case": "saturation-metamorphic-pM/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "bmax": 1004.30730524207,
      "kd": 2069.47242588538,
      "ns": 0.0301163077871144
     },
     "relativeDifferences": {
      "bmax": 2.0375865716677765e-15,
      "kd": 2.1974071516894469e-16,
      "ns": 1.1520160361218172e-16
     },
     "agrees": true
    },
    {
     "case": "saturation-metamorphic-counts/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "bmax": 60258.4383541467,
      "kd": 2.06947243040127,
      "ns": 1806.97846714377
     },
     "relativeDifferences": {
      "bmax": 4.82983483337001e-16,
      "kd": 8.58362166755618e-16,
      "ns": 5.033234863116749e-16
     },
     "agrees": true
    },
    {
     "case": "saturation-metamorphic-row-order/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "bmax": 1004.30730559656,
      "kd": 2.06947242849614,
      "ns": 30.1163077919273
     },
     "relativeDifferences": {
      "bmax": 1.560623778694323e-10,
      "kd": 6.079307137230662e-10,
      "ns": 8.996227043629655e-11
     },
     "agrees": true
    },
    {
     "case": "saturation-constant-freed/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "bmax": 1000,
      "kd": 2,
      "ns": 30,
      "constant": 50
     },
     "relativeDifferences": {
      "bmax": 1.13686837721616e-16,
      "kd": 2.2204460492503126e-16,
      "ns": 1.1842378929335005e-16,
      "constant": 0.0
     },
     "agrees": true
    },
    {
     "case": "saturation-depletion-flag/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "bmax": 0.5,
      "kd": 2
     },
     "relativeDifferences": {
      "bmax": 0.0,
      "kd": 2.2204460492503126e-16
     },
     "agrees": true
    },
    {
     "case": "saturation-extrapolated/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "bmax": 1000,
      "kd": 20
     },
     "relativeDifferences": {
      "bmax": 1.1368683772161603e-16,
      "kd": 1.7763568394002508e-16
     },
     "agrees": true
    },
    {
     "case": "saturation-two-site-hand/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "bmax": 934.646483704374,
      "kd": 12.4385130555343
     },
     "relativeDifferences": {
      "bmax": 2.1226826521631645e-09,
      "kd": 2.0012022103614193e-08
     },
     "agrees": true
    },
    {
     "case": "saturation-two-site-hand/twoSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "bmax1": 300.000000000002,
      "kd1": 0.500000000000006,
      "bmax2": 700.000000000002,
      "kd2": 50.0000000000009
     },
     "relativeDifferences": {
      "bmax1": 1.3263464400855133e-15,
      "kd1": 2.442490654175321e-15,
      "bmax2": 1.6240976817373674e-16,
      "kd2": 0.0
     },
     "agrees": true
    },
    {
     "case": "saturation-two-site-on-one-site/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "bmax": 996.460983505909,
      "kd": 2.0229615702561
     },
     "relativeDifferences": {
      "bmax": 4.563624250359499e-16,
      "kd": 4.3904858735783323e-16
     },
     "agrees": true
    },
    {
     "case": "saturation-two-site-narrow/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "bmax": 449.426922725695,
      "kd": 1.13158163717376
     },
     "relativeDifferences": {
      "bmax": 5.059191248807502e-16,
      "kd": 1.4901162555176367e-08
     },
     "agrees": true
    },
    {
     "case": "competition-hand/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "top": 1000,
      "bottom": 100,
      "ic50": 2
     },
     "relativeDifferences": {
      "top": 0.0,
      "bottom": 1.4210854715202006e-16,
      "ic50": 2.2204460492503126e-16
     },
     "agrees": true
    },
    {
     "case": "competition-noisy/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "top": 996.554212996192,
      "bottom": 102.738255575619,
      "ic50": 2.06291634382241
     },
     "relativeDifferences": {
      "top": 3.4223979861510203e-16,
      "bottom": 3.043061243183478e-15,
      "ic50": 1.0763626241556728e-15
     },
     "agrees": true
    },
    {
     "case": "competition-bottom-ns/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "top": 1000,
      "ic50": 2
     },
     "relativeDifferences": {
      "top": 0.0,
      "ic50": 2.2204460492503126e-16
     },
     "agrees": true
    },
    {
     "case": "competition-hill-free/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "top": 1000,
      "bottom": 100,
      "ic50": 2,
      "hill": 1.5
     },
     "relativeDifferences": {
      "top": 0.0,
      "bottom": 1.4210854715202006e-16,
      "ic50": 2.2204460492503126e-16,
      "hill": 1.480297366166875e-16
     },
     "agrees": true
    },
    {
     "case": "competition-two-site/oneSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "top": 907.413178878585,
      "bottom": 99.8474229578234,
      "ic50": 6.96437788265051
     },
     "relativeDifferences": {
      "top": 5.01146954299758e-16,
      "bottom": 2.846514070013569e-16,
      "ic50": 1.4901160900300992e-08
     },
     "agrees": true
    },
    {
     "case": "competition-two-site/twoSite",
     "converged": true,
     "tool": "nls",
     "parameters": {
      "top": 1000,
      "bottom": 50,
      "ic50High": 0.05,
      "ic50Low": 20,
      "fraction": 0.3
     },
     "relativeDifferences": {
      "top": 0.0,
      "bottom": 2.8421709430404e-16,
      "ic50High": 9.71445146547013e-16,
      "ic50Low": 3.552713678800502e-16,
      "fraction": 0.0
     },
     "agrees": true
    }
   ]
  }
 },
 "oracle": {
  "engine": "scipy.optimize.least_squares",
  "method": "trf with bounds, log constants, three starts per model, lowest RSS; profiles by least_squares refits and brentq; AICc and F by hand, p from scipy.stats.f.sf; the mass balance by brentq"
 },
 "cases": [
  {
   "name": "saturation-hand-subtracted",
   "about": "One site, Kd 2 nM, Bmax 1000 cpm, NS 30 cpm/nM, 8 concentrations, NS subtracted: the hand values exactly",
   "analysis": "saturation",
   "rows": [
    {
     "x": 0.1,
     "kind": "total",
     "y": 50.61904761904762
    },
    {
     "x": 0.1,
     "kind": "ns",
     "y": 3.0
    },
    {
     "x": 0.25,
     "kind": "total",
     "y": 118.61111111111111
    },
    {
     "x": 0.25,
     "kind": "ns",
     "y": 7.5
    },
    {
     "x": 0.5,
     "kind": "total",
     "y": 215.0
    },
    {
     "x": 0.5,
     "kind": "ns",
     "y": 15.0
    },
    {
     "x": 1.0,
     "kind": "total",
     "y": 363.3333333333333
    },
    {
     "x": 1.0,
     "kind": "ns",
     "y": 30.0
    },
    {
     "x": 2.0,
     "kind": "total",
     "y": 560.0
    },
    {
     "x": 2.0,
     "kind": "ns",
     "y": 60.0
    },
    {
     "x": 4.0,
     "kind": "total",
     "y": 786.6666666666666
    },
    {
     "x": 4.0,
     "kind": "ns",
     "y": 120.0
    },
    {
     "x": 8.0,
     "kind": "total",
     "y": 1040.0
    },
    {
     "x": 8.0,
     "kind": "ns",
     "y": 240.0
    },
    {
     "x": 16.0,
     "kind": "total",
     "y": 1368.888888888889
    },
    {
     "x": 16.0,
     "kind": "ns",
     "y": 480.0
    }
   ],
   "options": {
    "route": "subtracted",
    "freeConstant": false,
    "boundToConcentration": null,
    "sites": 1
   },
   "concentrationUnit": "nM",
   "readingUnit": "cpm",
   "expected": {
    "oneSite": {
     "status": "estimated",
     "bmax": 1000.0,
     "kd": 2.0000000000000004,
     "rss": 1.2820511432266637e-26,
     "df": 6,
     "order": [
      "bmax",
      "kd"
     ],
     "correlation": [
      [
       1.0,
       0.8306655869786923
      ],
      [
       0.8306655869786924,
       1.0
      ]
     ],
     "kdInterval": {
      "status": "not-available",
      "reason": "ns-subtracted"
     },
     "bmaxInterval": {
      "status": "not-available",
      "reason": "ns-subtracted"
     },
     "extrapolated": false,
     "depletion": null,
     "n": 8,
     "concentrations": 8
    }
   },
   "hand": {
    "kd": 2.0,
    "bmax": 1000.0
   }
  },
  {
   "name": "saturation-hand-fitted",
   "about": "The same rows with NS fitted as a line: Kd, Bmax and the NS slope exactly",
   "analysis": "saturation",
   "rows": [
    {
     "x": 0.1,
     "kind": "total",
     "y": 50.61904761904762
    },
    {
     "x": 0.1,
     "kind": "ns",
     "y": 3.0
    },
    {
     "x": 0.25,
     "kind": "total",
     "y": 118.61111111111111
    },
    {
     "x": 0.25,
     "kind": "ns",
     "y": 7.5
    },
    {
     "x": 0.5,
     "kind": "total",
     "y": 215.0
    },
    {
     "x": 0.5,
     "kind": "ns",
     "y": 15.0
    },
    {
     "x": 1.0,
     "kind": "total",
     "y": 363.3333333333333
    },
    {
     "x": 1.0,
     "kind": "ns",
     "y": 30.0
    },
    {
     "x": 2.0,
     "kind": "total",
     "y": 560.0
    },
    {
     "x": 2.0,
     "kind": "ns",
     "y": 60.0
    },
    {
     "x": 4.0,
     "kind": "total",
     "y": 786.6666666666666
    },
    {
     "x": 4.0,
     "kind": "ns",
     "y": 120.0
    },
    {
     "x": 8.0,
     "kind": "total",
     "y": 1040.0
    },
    {
     "x": 8.0,
     "kind": "ns",
     "y": 240.0
    },
    {
     "x": 16.0,
     "kind": "total",
     "y": 1368.888888888889
    },
    {
     "x": 16.0,
     "kind": "ns",
     "y": 480.0
    }
   ],
   "options": {
    "route": "fitted",
    "freeConstant": false,
    "boundToConcentration": null,
    "sites": 1
   },
   "concentrationUnit": "nM",
   "readingUnit": "cpm",
   "expected": {
    "oneSite": {
     "status": "estimated",
     "bmax": 999.9999999999999,
     "kd": 2.0000000000000004,
     "rss": 1.5157803428378243e-26,
     "df": 13,
     "order": [
      "bmax",
      "kd",
      "ns"
     ],
     "correlation": [
      [
       1.0000000000000002,
       0.8307769184727913,
       -0.626349531820358
      ],
      [
       0.8307769184727913,
       1.0,
       -0.36311291064606255
      ],
      [
       -0.6263495318203579,
       -0.3631129106460624,
       1.0
      ]
     ],
     "kdInterval": {
      "status": "not-available",
      "reason": "zero-residual"
     },
     "bmaxInterval": {
      "status": "not-available",
      "reason": "zero-residual"
     },
     "extrapolated": false,
     "depletion": null,
     "n": 16,
     "concentrations": 8,
     "ns": 30.0
    }
   },
   "hand": {
    "kd": 2.0,
    "bmax": 1000.0,
    "ns": 30.0
   }
  },
  {
   "name": "saturation-noisy-fitted",
   "about": "Triplicates with additive noise SD 15 cpm (seed 20261020), NS fitted",
   "analysis": "saturation",
   "rows": [
    {
     "x": 0.1,
     "kind": "total",
     "y": 21.875432840302704
    },
    {
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   "name": "saturation-two-site-narrow",
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 ]
}