{
  "what": "Exact TESTS of the centring identity, the symmetry, the discretisation lemma (E >= L with the verifier's own L), the bathtub constants, and an exact count of monochromatic 3-APs of the PRS colouring. Tests, not proofs.",
  "decidedOn": "2026-10-05",
  "node": "v24.14.1",
  "identity": {
    "cases": 1400,
    "identityHolds": 1400,
    "symmetryHolds": 1400
  },
  "discretisation": {
    "cases": 4200,
    "holds": 4200,
    "ENonnegative": 4200,
    "smallestGapEminusL": 0,
    "smallestE": 0.0000014271252749594696,
    "byGenerator": {
      "random": {
        "cases": 600,
        "holds": 600,
        "minGap": 3.737709053465278e-7,
        "trivial": 4
      },
      "bathtub": {
        "cases": 600,
        "holds": 600,
        "minGap": 0,
        "trivial": 7
      },
      "cells": {
        "cases": 600,
        "holds": 600,
        "minGap": 0,
        "trivial": 7
      },
      "breakpoints": {
        "cases": 600,
        "holds": 600,
        "minGap": 0,
        "trivial": 0
      },
      "cutpair": {
        "cases": 600,
        "holds": 600,
        "minGap": 0,
        "trivial": 0
      },
      "colouring": {
        "cases": 600,
        "holds": 600,
        "minGap": 0.0000014568570515211253,
        "trivial": 0
      },
      "constant": {
        "cases": 600,
        "holds": 600,
        "minGap": 0.00012388487998827856,
        "trivial": 40
      }
    }
  },
  "bathtub": {
    "cases": 4416,
    "holds": 4416,
    "smallestSlack": 0,
    "singlePieceReading": {
      "cases": 2432,
      "violations": 1358,
      "example": {
        "cell": [
          24,
          40
        ],
        "y": "1/64",
        "F": "385/115316736",
        "bSingle": "2/18769",
        "bSummed": "2/56307"
      }
    }
  },
  "counts": [
    {
      "k": 1,
      "n": 548,
      "mono": 15756,
      "ratio": "3939/75076",
      "ratioDecimal": "0.0524668336",
      "minus117over2192": "-9.0908e-4",
      "timesN": "-0.498175"
    },
    {
      "k": 2,
      "n": 1096,
      "mono": 63568,
      "ratio": "29/548",
      "ratioDecimal": "0.0529197080",
      "minus117over2192": "-4.5620e-4",
      "timesN": "-0.500000"
    },
    {
      "k": 4,
      "n": 2192,
      "mono": 255368,
      "ratio": "233/4384",
      "ratioDecimal": "0.0531478102",
      "minus117over2192": "-2.2810e-4",
      "timesN": "-0.500000"
    },
    {
      "k": 8,
      "n": 4384,
      "mono": 1023664,
      "ratio": "467/8768",
      "ratioDecimal": "0.0532618613",
      "minus117over2192": "-1.1405e-4",
      "timesN": "-0.500000"
    },
    {
      "k": 16,
      "n": 8768,
      "mono": 4099040,
      "ratio": "935/17536",
      "ratioDecimal": "0.0533188869",
      "minus117over2192": "-5.7026e-5",
      "timesN": "-0.500000"
    },
    {
      "k": 32,
      "n": 17536,
      "mono": 16404928,
      "ratio": "1871/35072",
      "ratioDecimal": "0.0533473996",
      "minus117over2192": "-2.8513e-5",
      "timesN": "-0.500000"
    },
    {
      "k": 64,
      "n": 35072,
      "mono": 65637248,
      "ratio": "3743/70144",
      "ratioDecimal": "0.0533616560",
      "minus117over2192": "-1.4256e-5",
      "timesN": "-0.500000"
    }
  ],
  "landscape": {
    "N": 1096,
    "starts": 400,
    "best4N2Q": -175360,
    "bestQ": -0.0364963503649635,
    "targetQ": -0.0364963503649635,
    "below": 0,
    "atPhiStar": 108
  },
  "seconds": 16,
  "allPass": true
}