{
 "about": {
  "method": "two-phase dose-response (bell-shaped and biphasic)",
  "origin": "Original synthetic data (known curves plus a fixed noise vector), not experimental",
  "ruling": "CSO memo of 13 October 2026 (docs/board/memos/2026-10-13-cso-bell-and-biphasic.md)",
  "models": {
   "biphasic": "y = start + span*(f*L(h1*(x - m1)) + (1 - f)*L(h2*(x - m2)))",
   "bell": "y = dip + (p1 - dip)*(1 - L(h1*(x - m1))) + (p2 - dip)*L(h2*(x - m2))",
   "L": "L(z) = 1/(1 + 10^-z)",
   "vector": "[start, span, f | p1, dip, p2, m1, delta = m2 - m1, h1, h2]"
  },
  "tolerances": {
   "rss": "the engine's RSS at most the oracle's x (1 + 1e-6)",
   "parameters": "midpoints and Hill slopes within 1e-4 absolute; levels within 1e-4 of the response span; f within 1e-4",
   "comparison": "F, AICc within 1e-6 relative; p within 1e-4 relative",
   "status": "exact, with the reason"
  },
  "recordedOn": "2026-10-13",
  "script": "pipeline/assay-analyser/oracles/two_phase_dose_response.py",
  "scriptSha256": "571be525dcb42eab937047c8b1f0684d6bd80ffc112ddd41b81a42a7fe7687ff",
  "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 drc::drm with a user-defined fct (the seven-parameter forms)",
   "version": "R version 4.4.3 (2025-02-28)",
   "drc": "4.0-0",
   "script": "pipeline/assay-analyser/oracles/r/two_phase_drm.R",
   "scriptSha256": "666c3df1682b3cd67087451ff90b9af33b0785db75097c4a397daaecbe1ecef9",
   "ran": true,
   "settings": "drm on every well, started from the SciPy estimates; the model written in log10 of the dose inside fct",
   "tolerances": {
    "parameters": "1e-4 absolute on midpoints, Hill slopes and f; 1e-4 of the response span on levels",
    "rss": "R's RSS not below SciPy's by more than 1e-6 relative"
   },
   "twophase": {
    "exists": true,
    "source": "function (fixed = c(NA, NA, NA, NA, NA, NA, NA), names = c(\"b1\", \n    \"c1\", \"d1\", \"e1\", \"b2\", \"d2\", \"e2\"), fctName, fctText) \n{\n    numParm <- 7\n    if (!is.character(names) | !(length(names) == numParm)) {\n        stop(\"Not correct 'names' argument\")\n    }\n    if (!(length(fixed) == numParm)) {\n        stop(\"Not correct 'fixed' argument\")\n    }\n    notFixed <- is.na(fixed)\n    parmVec <- rep(0, numParm)\n    parmVec[!notFixed] <- fixed[!notFixed]\n    fct <- function(dose, parm) {\n        parmMat <- matrix(parmVec, nrow(parm), numParm, byrow = TRUE)\n        parmMat[, notFixed] <- parm\n        fixed1.4 <- fixed[1:4]\n        fixed5.7 <- fixed[5:7]\n        LL.4()$fct(dose, parmMat[, 1:4, drop = FALSE]) + LL.3()$fct(dose, \n            parmMat[, 5:7, drop = FALSE])\n    }\n    ssfct <- function(dframe) {\n        first4 <- llogistic.ssf(fixed = c(NA, NA, NA, NA, 1))(dframe)\n        c(first4[1:2], first4[3]/2, first4[4]/3, first4[1], first4[3], \n            first4[4])[is.na(fixed)]\n    }\n    deriv1 <- NULL\n    deriv2 <- NULL\n    derivx <- NULL\n    edfct <- NULL\n    returnList <- list(fct = fct, ssfct = ssfct, names = names[notFixed], \n        deriv1 = deriv1, deriv2 = deriv2, derivx = derivx, edfct = edfct, \n        name = ifelse(missing(fctName), as.character(match.call()[[1]]), \n            fctName), text = ifelse(missing(fctText), \"Two-phase\", \n            fctText), noParm = sum(is.na(fixed)))\n    class(returnList) <- \"two-phase\"\n    invisible(returnList)\n}"
   },
   "cases": 6,
   "agreeing": 6,
   "scipyOnly": [
    {
     "case": "seven-concentrations",
     "status": "refused",
     "reason": "concentrations"
    },
    {
     "case": "nine-wells",
     "status": "refused",
     "reason": "residual-df"
    }
   ],
   "result": [
    {
     "case": "bell-reported",
     "converged": true,
     "parameters": [
      0.123074689747569,
      100.011600765477,
      9.9677762367004,
      -8.99885529696307,
      2.49947230986841,
      1.50767133557859,
      1.4980858419917
     ],
     "rss": 7.61445001196885,
     "maxScaledDifference": 4.440892098500626e-15,
     "rssNotBelowScipy": true,
     "agrees": true
    },
    {
     "case": "biphasic-reported",
     "converged": true,
     "parameters": [
      100.116690243829,
      -100.131159512158,
      0.400138729948163,
      -9.00347473732438,
      2.50278152796135,
      1.48496604139162,
      1.19829226126624
     ],
     "rss": 7.62088264366421,
     "maxScaledDifference": 5.329070518200751e-15,
     "rssNotBelowScipy": true,
     "agrees": true
    },
    {
     "case": "bell-noiseless",
     "converged": true,
     "parameters": [
      4.87135754146946e-15,
      100,
      10,
      -9,
      2.5,
      1.5,
      1.5
     ],
     "rss": 4.03896783473158e-27,
     "maxScaledDifference": 2.220446049250313e-16,
     "rssNotBelowScipy": true,
     "agrees": true
    },
    {
     "case": "bell-bend",
     "converged": true,
     "parameters": [
      0.132356054654945,
      99.9044601742425,
      10.3799060449986,
      -8.00005194096685,
      2.99675564325417,
      1.20702193384274,
      1.52197147477543
     ],
     "rss": 6.71447296920908,
     "maxScaledDifference": 3.552713678800501e-15,
     "rssNotBelowScipy": true,
     "agrees": true
    },
    {
     "case": "biphasic-separation",
     "converged": true,
     "parameters": [
      100.013935799861,
      -100.009451717846,
      0.512311758322318,
      -8.1900830311527,
      0.696730162610164,
      1.97348426878675,
      2.01611594850668
     ],
     "rss": 0.29975114772672,
     "maxScaledDifference": 5.329070518200751e-15,
     "rssNotBelowScipy": true,
     "agrees": true
    },
    {
     "case": "biphasic-minor-phase",
     "converged": true,
     "parameters": [
      100.005874544631,
      -100.006586010207,
      0.0500313000977182,
      -9.00138468301519,
      2.50136386068241,
      1.49378855524837,
      1.19994871833006
     ],
     "rss": 0.0190505681253146,
     "maxScaledDifference": 4.4207081889572524e-15,
     "rssNotBelowScipy": true,
     "agrees": true
    }
   ]
  }
 },
 "oracle": {
  "engine": "scipy.optimize.least_squares",
  "method": "trf inside the box; the memo's gap-pair grid plus 300 seeded uniform starts; lowest RSS; the 4PL comparison by curve_fit lm from six starts"
 },
 "cases": [
  {
   "name": "bell-reported",
   "about": "a peak: rises from 0 by m1 = -9, h 1.5, falls to 10 by m2 = -6.5, h 1.5; 14 concentrations in duplicate, noise up to 0.9 percent of the span",
   "shape": "bell",
   "logConcentrations": [
    -11.0,
    -11.0,
    -10.5,
    -10.5,
    -10.0,
    -10.0,
    -9.5,
    -9.5,
    -9.0,
    -9.0,
    -8.5,
    -8.5,
    -8.0,
    -8.0,
    -7.5,
    -7.5,
    -7.0,
    -7.0,
    -6.5,
    -6.5,
    -6.0,
    -6.0,
    -5.5,
    -5.5,
    -5.0,
    -5.0,
    -4.5,
    -4.5
   ],
   "responses": [
    0.8998840953882528,
    -0.5001159046117474,
    0.9591067309734852,
    -0.34089326902651484,
    3.3648368988249113,
    3.7648368988249112,
    14.695109761235324,
    15.295109761235324,
    49.28399833085352,
    50.483998330853524,
    84.51213418895759,
    85.41213418895758,
    95.9313799390333,
    97.33137993903331,
    96.48199456626212,
    96.78199456626211,
    85.51193975108082,
    86.71193975108082,
    55.582220367615044,
    54.88222036761504,
    23.884997971355748,
    22.984997971355746,
    12.958246364691473,
    12.358246364691473,
    11.003177057895144,
    9.803177057895144,
    10.189892307119143,
    10.389892307119144
   ],
   "truth": [
    0.0,
    100.0,
    10.0,
    -9.0,
    2.5,
    1.5,
    1.5
   ],
   "direction": 1.0,
   "parameters": [
    0.12307468974756873,
    100.0116007654774,
    9.967776236700402,
    -8.99885529696307,
    2.4994723098684055,
    1.5076713355785922,
    1.4980858419916994
   ],
   "rss": 7.6144500119688265,
   "fourPL": {
    "top": 52.84174889399078,
    "bottom": 1.2518458604318041,
    "logMidpoint": -9.37835056215063,
    "hill": 3.6163930758102247,
    "rss": 24165.878263399325
   },
   "comparison": {
    "status": "computed",
    "rss4": 24165.878263399325,
    "rss7": 7.6144500119688265,
    "F": 22208.80647031606,
    "p": 6.480371964048119e-37,
    "df1": 3,
    "df2": 21,
    "aicc4": 202.02106042801955,
    "aicc7": -12.881441652148563,
    "dAicc": 214.90250208016812
   },
   "status": "reported",
   "phases": [
    {
     "logMidpoint": -8.99885529696307,
     "hill": 1.5076713355785922
    },
    {
     "logMidpoint": -6.499382987094664,
     "hill": -1.4980858419916994
    }
   ],
   "plateaus": [
    0.12307468974756873,
    100.0116007654774,
    9.967776236700402
   ],
   "df": 21,
   "extreme": {
    "kind": "peak",
    "logConcentration": -7.736764102048512,
    "response": 97.53396274018151,
    "before": 7,
    "beyond": 7
   },
   "correlation": [
    [
     1.0,
     -0.22693880366967617,
     0.04061048694485752,
     0.278169090133436,
     -0.0788249879613714,
     0.4992070923979209,
     0.11795678595259675
    ],
    [
     -0.2269388036696767,
     1.0,
     -0.2283658734627735,
     0.575048116881167,
     -0.7040820836884274,
     -0.6242754659568914,
     -0.625251187232146
    ],
    [
     0.04061048694485734,
     -0.22836587346277354,
     1.0,
     -0.12796276765440529,
     -0.10624047130885705,
     0.11846420312236412,
     0.5015609046700638
    ],
    [
     0.2781690901334351,
     0.5750481168811672,
     -0.12796276765440462,
     1.0,
     -0.79326794572777,
     -0.20626096425979132,
     -0.3536359873441979
    ],
    [
     -0.07882498796137022,
     -0.7040820836884281,
     -0.10624047130885629,
     -0.7932679457277699,
     1.0,
     0.34753431996233897,
     0.3372016367274788
    ],
    [
     0.4992070923979211,
     -0.6242754659568909,
     0.11846420312236411,
     -0.20626096425979054,
     0.34753431996233813,
     1.0,
     0.33950820676569127
    ],
    [
     0.1179567859525971,
     -0.6252511872321461,
     0.501560904670064,
     -0.3536359873441979,
     0.3372016367274785,
     0.3395082067656916,
     1.0
    ]
   ]
  },
  {
   "name": "biphasic-reported",
   "about": "falls from 100 to 0 in two phases (f 0.4 at m1 = -9, h 1.5; the rest at m2 = -6.5, h 1.2); 14 concentrations in duplicate",
   "shape": "biphasic",
   "logConcentrations": [
    -11.0,
    -11.0,
    -10.5,
    -10.5,
    -10.0,
    -10.0,
    -9.5,
    -9.5,
    -9.0,
    -9.0,
    -8.5,
    -8.5,
    -8.0,
    -8.0,
    -7.5,
    -7.5,
    -7.0,
    -7.0,
    -6.5,
    -6.5,
    -6.0,
    -6.0,
    -5.5,
    -5.5,
    -5.0,
    -5.0,
    -4.5,
    -4.5
   ],
   "responses": [
    100.75980109668856,
    99.35980109668857,
    100.17537038680221,
    98.8753703868022,
    99.07007729351373,
    99.47007729351374,
    93.54575017775137,
    94.14575017775138,
    79.24005994005994,
    80.44005994005994,
    65.5012651513038,
    66.40126515130379,
    59.79003746675885,
    61.190037466758845,
    56.46262210618733,
    56.76262210618734,
    47.19435950517393,
    48.394359505173924,
    30.607111852953985,
    29.90711185295398,
    12.34686540585145,
    11.44686540585145,
    3.7612815214312265,
    3.1612815214312264,
    1.4361397344697764,
    0.23613973446977643,
    0.33792425026550743,
    0.5379242502655075
   ],
   "truth": [
    100.0,
    -100.0,
    0.4,
    -9.0,
    2.5,
    1.5,
    1.2
   ],
   "direction": -1.0,
   "parameters": [
    100.11669024382941,
    -100.13115951215802,
    0.4001387299481631,
    -9.003474737324375,
    2.502781527961348,
    1.4849660413916212,
    1.198292261266237
   ],
   "rss": 7.620882643664166,
   "fourPL": {
    "top": -18.428806131592328,
    "bottom": 109.10815821417184,
    "logMidpoint": -7.227010930496683,
    "hill": 0.32894657071394234,
    "rss": 584.7548731403728
   },
   "comparison": {
    "status": "computed",
    "rss4": 584.7548731403728,
    "rss7": 7.620882643664166,
    "F": 530.1141773696878,
    "p": 6.071770654705556e-20,
    "df1": 3,
    "df2": 21,
    "aicc4": 97.81894313843999,
    "aicc7": -12.857797442698914,
    "dAicc": 110.6767405811389
   },
   "status": "reported",
   "phases": [
    {
     "logMidpoint": -9.003474737324375,
     "hill": -1.4849660413916212
    },
    {
     "logMidpoint": -6.5006932093630265,
     "hill": -1.198292261266237
    }
   ],
   "plateaus": [
    100.11669024382941,
    -0.014469268328610951
   ],
   "df": 21,
   "correlation": [
    [
     1.0,
     -0.6371135999597778,
     0.46849549952544167,
     -0.22519769849475205,
     0.35770505050859386,
     -0.5099360023678465,
     0.13667295515957195
    ],
    [
     -0.6371135999597781,
     1.0,
     0.03967906943837616,
     0.2975648436594219,
     -0.536445943965272,
     0.223150820027522,
     0.36127331732903467
    ],
    [
     0.46849549952544073,
     0.03967906943837696,
     1.0,
     0.5131469951413886,
     -0.08698101769710241,
     -0.7094320978577089,
     0.7328565645570728
    ],
    [
     -0.22519769849475166,
     0.29756484365942126,
     0.5131469951413882,
     1.0,
     -0.6743649912845053,
     -0.28768516335932787,
     0.43376615075466524
    ],
    [
     0.357705050508593,
     -0.5364459439652711,
     -0.0869810176971022,
     -0.674364991284505,
     1.0,
     -0.05499491916605521,
     -0.2118164350737197
    ],
    [
     -0.5099360023678462,
     0.22315082002752176,
     -0.709432097857709,
     -0.28768516335932814,
     -0.054994919166055055,
     1.0,
     -0.3880033912861439
    ],
    [
     0.13667295515957092,
     0.3612733173290354,
     0.7328565645570724,
     0.4337661507546655,
     -0.21181643507372006,
     -0.3880033912861436,
     1.0
    ]
   ]
  },
  {
   "name": "bell-noiseless",
   "about": "the reported bell without noise: parameters recovered; the comparison withheld at the exact fit, so the rule withholds (not-preferred)",
   "shape": "bell",
   "logConcentrations": [
    -11.0,
    -11.0,
    -10.5,
    -10.5,
    -10.0,
    -10.0,
    -9.5,
    -9.5,
    -9.0,
    -9.0,
    -8.5,
    -8.5,
    -8.0,
    -8.0,
    -7.5,
    -7.5,
    -7.0,
    -7.0,
    -6.5,
    -6.5,
    -6.0,
    -6.0,
    -5.5,
    -5.5,
    -5.0,
    -5.0,
    -4.5,
    -4.5
   ],
   "responses": [
    0.09988409538825266,
    0.09988409538825266,
    0.5591067309734852,
    0.5591067309734852,
    3.0648368988249115,
    3.0648368988249115,
    15.095109761235324,
    15.095109761235324,
    49.983998330853524,
    49.983998330853524,
    84.81213418895759,
    84.81213418895759,
    96.4313799390333,
    96.4313799390333,
    96.68199456626212,
    96.68199456626212,
    86.31193975108081,
    86.31193975108081,
    54.98222036761504,
    54.98222036761504,
    23.584997971355747,
    23.584997971355747,
    12.758246364691473,
    12.758246364691473,
    10.503177057895144,
    10.503177057895144,
    10.089892307119143,
    10.089892307119143
   ],
   "truth": [
    0.0,
    100.0,
    10.0,
    -9.0,
    2.5,
    1.5,
    1.5
   ],
   "direction": 1.0,
   "parameters": [
    4.871357541476553e-15,
    100.0,
    10.000000000000004,
    -9.0,
    2.5,
    1.5000000000000002,
    1.5000000000000002
   ],
   "rss": 0.0,
   "fourPL": {
    "top": 52.82036182556066,
    "bottom": 1.1410987108003565,
    "logMidpoint": -9.381583088197333,
    "hill": 3.6518671017900246,
    "rss": 24117.510456165866
   },
   "comparison": {
    "status": "not-available",
    "reason": "zero-residual"
   },
   "status": "withheld",
   "reason": "not-preferred"
  },
  {
   "name": "bell-bend",
   "about": "a clean bell whose high plateau's bend point has one tested concentration beyond it: withheld (bend)",
   "shape": "bell",
   "logConcentrations": [
    -10.0,
    -10.0,
    -9.5,
    -9.5,
    -9.0,
    -9.0,
    -8.5,
    -8.5,
    -8.0,
    -8.0,
    -7.5,
    -7.5,
    -7.0,
    -7.0,
    -6.5,
    -6.5,
    -6.0,
    -6.0,
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