{
 "about": {
  "method": "relationships",
  "origin": "Original synthetic values, not experimental data; Anscombe's quartet and R's stackloss as published",
  "ruling": "CSO memos of 13 October 2026 (docs/board/memos/2026-10-13-cso-correlation.md, -linear-regression.md, -nonlinear-families.md, -model-comparison.md, -method-comparison.md); roadmap A-2 family 3",
  "settings": {
   "correlation": "cor.test(method = 'pearson', conf.level = L); cor.test(method = 'spearman') with R's defaults; Bonett-Wright written in R",
   "regression": "lm, summary.lm, confint, predict.lm(interval = 'confidence' | 'prediction'), hatvalues, rstandard, cooks.distance, car::vif, anova(lm(y ~ x), lm(y ~ factor(x)))",
   "nonlinear": "nls(algorithm = 'port') from this script's start grid and boxes; SciPy least_squares (trf) second; SciPy direct profile (least_squares refits, brentq) for intervals; polynomials in exact fractions",
   "comparison": "anova between pairs; AIC(); AICc on the RSS form n ln(RSS/n) + 2K + 2K(K + 1)/(n - K - 1), K = parameters + 1",
   "method comparison": "Deming by the eigen route and a numpy closed form; ODR point estimates; delete-one jackknife in R; Bland-Altman with mean, sd, qt, qnorm; lm for the proportional line; shapiro.test"
  },
  "coverage": {
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    "gate": "every untied cell in [0.93, 0.97] at nominal 0.95",
    "cleared": true
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  "spearmanIntervalCleared": true,
  "tolerances": {
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   "regression": "1e-9 relative; p 1e-8 relative",
   "nonlinear": "noiseless 1e-8; noisy RSS 1e-8 relative, linear parameters 1e-6 x max(|value|, span), ln parameters 1e-6 absolute; profile bounds 1e-3 in ln or scaled units; polynomials 1e-9 relative",
   "comparison": "linear RSS 1e-10, F and p 1e-8, delta AICc 1e-8 absolute; nonlinear RSS 1e-6, F 1e-5, p 1e-4, delta AICc 1e-4 absolute",
   "method comparison": "hand cases 1e-12; Deming 1e-10; jackknife 1e-9; Bland-Altman 1e-9; t quantiles 1e-8",
   "codes, counts and order": "exact"
  },
  "recordedOn": "2026-10-13",
  "script": "pipeline/assay-analyser/oracles/relationships.py",
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   "image": "ghcr.io/biotechmat/drybench/oracle-env:11b8a5e4456df7eb@sha256:7e69891ca1d9f24838660e0a9887bdb654ce7771d2f2ac7e7275e9b1eb3b6a09",
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   "recordedOn": "2026-10-13",
   "cpu": "AMD EPYC 7763 64-Core Processor",
   "cpuClass": "x86-64-v3",
   "simd": [
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   "openblasCore": "Haswell",
   "threads": 1
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  "crossCheck": {
   "tool": "SciPy (pearsonr, spearmanr, linregress, least_squares, odr)",
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   "cases": 105,
   "agreeing": 105,
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    {
     "what": "nl-7-decay-plateau-0 RSS (R nls port vs SciPy trf)",
     "r": 38.9009774645385,
     "scipy": 38.9009774645385,
     "agrees": true
    },
    {
     "what": "nl-9-y0-extrapolated RSS (R nls port vs SciPy trf)",
     "r": 274.178177983393,
     "scipy": 274.17817798338353,
     "agrees": true
    },
    {
     "what": "nl-10-two-phase-noiseless RSS (R nls port vs SciPy trf)",
     "r": 6.07422897020179e-29,
     "scipy": 5.127595883936577e-29,
     "agrees": true
    },
    {
     "what": "nl-10-two-phase-noisy RSS (R nls port vs SciPy trf)",
     "r": 21.5256749894105,
     "scipy": 21.52567498941044,
     "agrees": true
    },
    {
     "what": "nl-17-power-noiseless RSS (R nls port vs SciPy trf)",
     "r": 0,
     "scipy": 0.0,
     "agrees": true
    },
    {
     "what": "nl-17-power-noisy RSS (R nls port vs SciPy trf)",
     "r": 0.688076687855827,
     "scipy": 0.6880766878558264,
     "agrees": true
    },
    {
     "what": "nl-19-boltzmann-noiseless RSS (R nls port vs SciPy trf)",
     "r": 0,
     "scipy": 0.0,
     "agrees": true
    },
    {
     "what": "nl-19-boltzmann-falling RSS (R nls port vs SciPy trf)",
     "r": 150853.495530229,
     "scipy": 150853.4955302283,
     "agrees": true
    },
    {
     "what": "nl-22-serial RSS (R nls port vs SciPy trf)",
     "r": 274.178177983392,
     "scipy": 274.17817798338854,
     "agrees": true
    },
    {
     "what": "nl-22-undeclared RSS (R nls port vs SciPy trf)",
     "r": 274.178177983392,
     "scipy": 274.17817798338854,
     "agrees": true
    },
    {
     "what": "mc-1-hand Deming slope (R eigen vs ODR)",
     "r": 1.5,
     "scipy": 1.4999999590770394,
     "agrees": true
    },
    {
     "what": "mc-1-hand Deming slope (R eigen vs numpy closed form)",
     "r": 1.5,
     "scipy": 1.4999999999999998,
     "agrees": true
    },
    {
     "what": "mc-1-hand-lambda-4 Deming slope (R eigen vs ODR)",
     "r": 1.33333333333333,
     "scipy": 1.3333333274267833,
     "agrees": true
    },
    {
     "what": "mc-1-hand-lambda-4 Deming slope (R eigen vs numpy closed form)",
     "r": 1.33333333333333,
     "scipy": 1.3333333333333333,
     "agrees": true
    },
    {
     "what": "mc-2-swapped Deming slope (R eigen vs ODR)",
     "r": 0.75,
     "scipy": 0.7500000013464762,
     "agrees": true
    },
    {
     "what": "mc-2-swapped Deming slope (R eigen vs numpy closed form)",
     "r": 0.75,
     "scipy": 0.75,
     "agrees": true
    },
    {
     "what": "mc-3-n40-lambda-4 Deming slope (R eigen vs ODR)",
     "r": 1.03890858727959,
     "scipy": 1.0389085874968977,
     "agrees": true
    },
    {
     "what": "mc-3-n40-lambda-4 Deming slope (R eigen vs numpy closed form)",
     "r": 1.03890858727959,
     "scipy": 1.0389085872795936,
     "agrees": true
    },
    {
     "what": "mc-3-n40-lambda-1 Deming slope (R eigen vs ODR)",
     "r": 1.04518574520756,
     "scipy": 1.0451857458698193,
     "agrees": true
    },
    {
     "what": "mc-3-n40-lambda-1 Deming slope (R eigen vs numpy closed form)",
     "r": 1.04518574520756,
     "scipy": 1.0451857452075628,
     "agrees": true
    },
    {
     "what": "mc-3-n40-lambda-1e-06 Deming slope (R eigen vs ODR)",
     "r": 1.05498592209235,
     "scipy": 1.05498592166205,
     "agrees": true
    },
    {
     "what": "mc-3-n40-lambda-1e-06 Deming slope (R eigen vs numpy closed form)",
     "r": 1.05498592209235,
     "scipy": 1.0549859220923525,
     "agrees": true
    },
    {
     "what": "mc-3-n40-lambda-1e+06 Deming slope (R eigen vs ODR)",
     "r": 1.03458845218074,
     "scipy": 1.0345884535640908,
     "agrees": true
    },
    {
     "what": "mc-3-n40-lambda-1e+06 Deming slope (R eigen vs numpy closed form)",
     "r": 1.03458845218074,
     "scipy": 1.0345884521930557,
     "agrees": true
    },
    {
     "what": "mc-7-negative Deming slope (R eigen vs ODR)",
     "r": -1.19966470036191,
     "scipy": -1.1996646997104525,
     "agrees": true
    },
    {
     "what": "mc-7-negative Deming slope (R eigen vs numpy closed form)",
     "r": -1.19966470036191,
     "scipy": -1.1996647003619094,
     "agrees": true
    },
    {
     "what": "mc-8-ba-hand Deming slope (R eigen vs ODR)",
     "r": 1.12079514021763,
     "scipy": 1.1207951460909367,
     "agrees": true
    },
    {
     "what": "mc-8-ba-hand Deming slope (R eigen vs numpy closed form)",
     "r": 1.12079514021763,
     "scipy": 1.1207951402176308,
     "agrees": true
    },
    {
     "what": "mc-15-ba-against-a Deming slope (R eigen vs ODR)",
     "r": 1.12079514021763,
     "scipy": 1.1207951460909367,
     "agrees": true
    },
    {
     "what": "mc-15-ba-against-a Deming slope (R eigen vs numpy closed form)",
     "r": 1.12079514021763,
     "scipy": 1.1207951402176308,
     "agrees": true
    },
    {
     "what": "mc-9-proportional-raw Deming slope (R eigen vs ODR)",
     "r": 1.11074620198525,
     "scipy": 1.110746202110571,
     "agrees": true
    },
    {
     "what": "mc-9-proportional-raw Deming slope (R eigen vs numpy closed form)",
     "r": 1.11074620198525,
     "scipy": 1.1107462019852503,
     "agrees": true
    },
    {
     "what": "mc-9-proportional-percent Deming slope (R eigen vs ODR)",
     "r": 1.11074620198525,
     "scipy": 1.110746202110571,
     "agrees": true
    },
    {
     "what": "mc-9-proportional-percent Deming slope (R eigen vs numpy closed form)",
     "r": 1.11074620198525,
     "scipy": 1.1107462019852503,
     "agrees": true
    },
    {
     "what": "mc-9-proportional-log Deming slope (R eigen vs ODR)",
     "r": 1.11074620198525,
     "scipy": 1.110746202110571,
     "agrees": true
    },
    {
     "what": "mc-9-proportional-log Deming slope (R eigen vs numpy closed form)",
     "r": 1.11074620198525,
     "scipy": 1.1107462019852503,
     "agrees": true
    },
    {
     "what": "mc-10-nonpositive Deming slope (R eigen vs ODR)",
     "r": 1.11104529704478,
     "scipy": 1.111045296644052,
     "agrees": true
    },
    {
     "what": "mc-10-nonpositive Deming slope (R eigen vs numpy closed form)",
     "r": 1.11104529704478,
     "scipy": 1.111045297044777,
     "agrees": true
    },
    {
     "what": "mc-11-n3 Deming slope (R eigen vs ODR)",
     "r": 1.69167655732069,
     "scipy": 1.6916765060577903,
     "agrees": true
    },
    {
     "what": "mc-11-n3 Deming slope (R eigen vs numpy closed form)",
     "r": 1.69167655732069,
     "scipy": 1.6916765573206922,
     "agrees": true
    },
    {
     "what": "mc-11-n9 Deming slope (R eigen vs ODR)",
     "r": 1.06838461594857,
     "scipy": 1.0683846138415878,
     "agrees": true
    },
    {
     "what": "mc-11-n9 Deming slope (R eigen vs numpy closed form)",
     "r": 1.06838461594857,
     "scipy": 1.0683846159485697,
     "agrees": true
    },
    {
     "what": "mc-11-n10 Deming slope (R eigen vs ODR)",
     "r": 1.1150546385031,
     "scipy": 1.11505464048509,
     "agrees": true
    },
    {
     "what": "mc-11-n10 Deming slope (R eigen vs numpy closed form)",
     "r": 1.1150546385031,
     "scipy": 1.1150546385030973,
     "agrees": true
    },
    {
     "what": "mc-12-plus-five Deming slope (R eigen vs ODR)",
     "r": 1,
     "scipy": 1.0,
     "agrees": true
    },
    {
     "what": "mc-12-plus-five Deming slope (R eigen vs numpy closed form)",
     "r": 1,
     "scipy": 1.0,
     "agrees": true
    },
    {
     "what": "mc-13-undeclared Deming slope (R eigen vs ODR)",
     "r": 1.12079514021763,
     "scipy": 1.1207951460909367,
     "agrees": true
    },
    {
     "what": "mc-13-undeclared Deming slope (R eigen vs numpy closed form)",
     "r": 1.12079514021763,
     "scipy": 1.1207951402176308,
     "agrees": true
    },
    {
     "what": "mc-16-offset Deming slope (R eigen vs ODR)",
     "r": 1.11505463850641,
     "scipy": 1.1150546347792973,
     "agrees": true
    },
    {
     "what": "mc-16-offset Deming slope (R eigen vs numpy closed form)",
     "r": 1.11505463850641,
     "scipy": 1.1150546385064075,
     "agrees": true
    }
   ],
   "r": {
    "tool": "R stats, car, jsonlite",
    "version": "R version 4.4.3 (2025-02-28)",
    "car": "3.1.5",
    "script": "pipeline/assay-analyser/oracles/r/relationships.R",
    "scriptSha256": "32d840544bab9b9664ca4f5b268fcdc1eb4f3365019b9eede4b0d87ac12fa5cd",
    "jobs": 153
   }
  }
 },
 "oracle": {
  "engine": "R (relationships.R) and SciPy, as above",
  "method": "the withholding policy from the memos, applied here"
 },
 "cases": [
  {
   "name": "cor-1-hand",
   "kind": "correlation",
   "input": {
    "x": [
     1,
     2,
     3,
     4,
     5
    ],
    "y": [
     2,
     4,
     5,
     4,
     5
    ]
   },
   "settings": {
    "unit": "rows",
    "level": 0.95
   },
   "expected": {
    "n": 5,
    "pearson": {
     "r": 0.774596669241483,
     "r2": 0.5999999999999993,
     "inference": {
      "t": 2.12132034355964,
      "df": 3,
      "p": 0.124027062657555,
      "interval": {
       "lower": -0.34008203518751,
       "upper": 0.984235755150727
      }
     }
    },
    "spearman": {
     "rho": 0.737864787372622,
     "inference": {
      "s": 5.24270425254756,
      "p": 0.154618523128449,
      "path": "t-ties",
      "rMethod": "Spearman's rank correlation rho"
     },
     "interval": {
      "withheld": "SPEARMAN_CI_N"
     }
    }
   }
  },
  {
   "name": "cor-2-n3",
   "kind": "correlation",
   "input": {
    "x": [
     1,
     2,
     3
    ],
    "y": [
     1,
     3,
     2
    ]
   },
   "settings": {
    "unit": "rows",
    "level": 0.95
   },
   "expected": {
    "n": 3,
    "pearson": {
     "r": 0.5,
     "r2": 0.25,
     "inference": {
      "t": 0.577350269189626,
      "df": 1,
      "p": 0.666666666666667,
      "interval": {
       "withheld": "N_TOO_SMALL"
      }
     }
    },
    "spearman": {
     "rho": 0.5,
     "inference": {
      "s": 2,
      "p": 1,
      "path": "exact",
      "rMethod": "Spearman's rank correlation rho"
     },
     "interval": {
      "withheld": "SPEARMAN_CI_N"
     }
    }
   }
  },
  {
   "name": "cor-3-n4",
   "kind": "correlation",
   "input": {
    "x": [
     1,
     2,
     3,
     4
    ],
    "y": [
     1.2,
     1.9,
     3.4,
     3.8
    ]
   },
   "settings": {
    "unit": "rows",
    "level": 0.95
   },
   "expected": {
    "n": 4,
    "pearson": {
     "r": 0.977324354259651,
     "r2": 0.9551628934290438,
     "inference": {
      "t": 6.52732037899543,
      "df": 2,
      "p": 0.0226756457403486,
      "interval": {
       "lower": 0.267473091752099,
       "upper": 0.999545001626387
      }
     }
    },
    "spearman": {
     "rho": 1,
     "inference": {
      "s": 0,
      "p": 0.0833333333333333,
      "path": "exact",
      "rMethod": "Spearman's rank correlation rho"
     },
     "interval": {
      "withheld": "SPEARMAN_CI_N"
     }
    }
   }
  },
  {
   "name": "cor-4-cubic",
   "kind": "correlation",
   "input": {
    "x": [
     1,
     2,
     3,
     4,
     5
    ],
    "y": [
     1,
     8,
     27,
     64,
     125
    ]
   },
   "settings": {
    "unit": "rows",
    "level": 0.95
   },
   "expected": {
    "n": 5,
    "pearson": {
     "r": 0.9431175138077,
     "r2": 0.8894706448508173,
     "inference": {
      "t": 4.91346219714779,
      "df": 3,
      "p": 0.0161458552886304,
      "interval": {
       "lower": 0.36238340124087,
       "upper": 0.996344605553194
      }
     }
    },
    "spearman": {
     "rho": 1,
     "inference": {
      "s": 4.44089209850063e-15,
      "p": 0.0166666666666667,
      "path": "exact",
      "rMethod": "Spearman's rank correlation rho"
     },
     "interval": {
      "withheld": "SPEARMAN_CI_N"
     }
    }
   }
  },
  {
   "name": "cor-5-untied-n6",
   "kind": "correlation",
   "input": {
    "x": [
     1,
     2,
     3,
     4,
     5,
     6
    ],
    "y": [
     3.0,
     5.1,
     2.2,
     4.3,
     0.4,
     1.5
    ]
   },
   "settings": {
    "unit": "rows",
    "level": 0.95
   },
   "expected": {
    "n": 6,
    "pearson": {
     "r": -0.594398943916976,
     "r2": 0.35331010452961636,
     "inference": {
      "t": -1.47829118497886,
      "df": 4,
      "p": 0.213405160628336,
      "interval": {
       "lower": -0.948440771807233,
       "upper": 0.419549128014309
      }
     }
    },
    "spearman": {
     "rho": -0.657142857142857,
     "inference": {
      "s": 58,
      "p": 0.175,
      "path": "exact",
      "rMethod": "Spearman's rank correlation rho"
     },
     "interval": {
      "withheld": "SPEARMAN_CI_N"
     }
    }
   }
  },
  {
   "name": "cor-5-untied-n9",
   "kind": "correlation",
   "input": {
    "x": [
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     8,
     9
    ],
    "y": [
     8.0,
     6.1,
     0.2,
     2.3,
     3.4,
     7.5,
     1.6,
     4.7,
     5.8
    ]
   },
   "settings": {
    "unit": "rows",
    "level": 0.95
   },
   "expected": {
    "n": 9,
    "pearson": {
     "r": -0.0844671722999357,
     "r2": 0.007134703196347024,
     "inference": {
      "t": -0.224280652008128,
      "df": 7,
      "p": 0.82894469501086,
      "interval": {
       "lower": -0.708826222288439,
       "upper": 0.614103586883896
      }
     }
    },
    "spearman": {
     "rho": -0.183333333333333,
     "inference": {
      "s": 142,
      "p": 0.643639770723104,
      "path": "exact",
      "rMethod": "Spearman's rank correlation rho"
     },
     "interval": {
      "withheld": "SPEARMAN_CI_N"
     }
    }
   }
  },
  {
   "name": "cor-5-untied-n10",
   "kind": "correlation",
   "input": {
    "x": [
     1,
     2,
     3,
     4,
     5,
     6,
     7,
     8,
     9,
     10
    ],
    "y": [
     9.0,
     1.1,
     5.2,
     8.3,
     6.4,
     3.5,
     4.6,
     7.7,
     2.8,
     0.9
    ]
   },
   "settings": {
    "unit": "rows",
    "level": 0.95
   },
   "expected": {
    "n": 10,
    "pearson": {
     "r": -0.396155224682662,
     "r2": 0.15693896204337043,
     "inference": {
      "t": -1.22034007122587,
      "df": 8,
      "p": 0.257084263453751,
      "interval": {
       "lower": -0.820999761135353,
       "upper": 0.311058259021026
      }
     }
    },
    "spearman": {
     "rho": -0.478787878787879,
     "inference": {
      "s": 244,
      "p": 0.166058037179348,
      "path": "edgeworth",
      "rMethod": "Spearman's rank correlation rho"
     },
     "interval": {
      "bonettWright": [
       -0.862624135490043,
       0.254940348056775
      ],
      "cleared": true
     }
    }
   }
  },
  {
   "name": "cor-6-untied-n1290",
   "kind": "correlation",
   "input": {
    "x": [
     -1.326845718992183,
     -0.0591249801781126,
     0.8578762971283299,
     1.242858573988545,
     -0.46595789402479376,
     -1.642018312033111,
     0.524686342967008,
     -0.18543347316086575,
     0.8450814379240136,
     0.5435385112502609,
     -1.185585736689123,
     0.2289468439077422,
     -0.20601017738333594,
     -0.01168085671225311,
     -1.274711244409505,
     -0.5626896571601413,
     -0.018768254108354067,
     -1.3418803750675552,
     0.29097446512145503,
     -0.8573908692065237,
     0.6565356308817121,
     -0.38361192735295185,
     1.0828174719721522,
     0.890010851383488,
     0.6260252879765339,
     -0.28651526161173085,
     1.8997448920337188,
     0.9424449627360274,
     0.34775100498635036,
     -0.3842135177861412,
     1.1436279192522214,
     0.028965977962503917,
     0.12280508670585995,
     0.9638471857199772,
     0.8910269694895707,
     2.258211763725124,
     0.17028850129817133,
     -0.12429737325254978,
     0.014996516593362668,
     1.681822734736798,
     -1.4099005227421069,
     -2.222034741038179,
     0.19289425525126067,
     0.7104184671159105,
     -0.5899992829544807,
     0.8699988004518435,
     0.1956116112428933,
     0.3077532869959915,
     0.45056706906564875,
     -0.2520881418336967,
     -1.475703386422339,
     -0.5331930403518943,
     1.8333873056877514,
     0.8919469002177441,
     -0.39927530962959346,
     -1.071525186682448,
     0.625808065961649,
     1.047736238306207,
     1.1885196991153624,
     -0.4628401533178935,
     0.2834664780613271,
     -0.14987672232637578,
     0.26314919335888165,
     1.1926297841610356,
     -0.7156258518512988,
     -1.4487464102734027,
     -0.11882340803653331,
     -1.585941463158036,
     -1.5617850920081557,
     -1.0369898581243318,
     2.0649884253687976,
     0.015030039732195374,
     0.7516710134353045,
     -1.385467074431284,
     1.8386103209404414,
     2.6326428348746176,
     -0.0019756684489033506,
     -0.5692125843421283,
     0.11889781793372887,
     -0.619334885505735,
     0.3216161192155525,
     -1.3812067735578324,
     1.9156815259871431,
     0.26445463026204463,
     -1.072948536068192,
     0.7606747916004639,
     0.019298544527248516,
     -0.7301992964638461,
     0.053012682000941704,
     0.0239931366742388,
     1.0419815250618336,
     -0.7246246540177667,
     0.023593001225548103,
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