{
  "table": "T468",
  "checked_document": "before",
  "exact_entries_passed": 13,
  "decimal_entries_passed": 5,
  "working_bits": 768,
  "rows": [
    {
      "region": "equilateral-triangle",
      "n": 3,
      "exact": "1",
      "passed": true
    },
    {
      "region": "equilateral-triangle",
      "n": 4,
      "exact": "2/3",
      "passed": true
    },
    {
      "region": "equilateral-triangle",
      "n": 5,
      "exact": "11/36",
      "passed": true
    },
    {
      "region": "equilateral-triangle",
      "n": 6,
      "exact": "91/900",
      "passed": true
    },
    {
      "region": "equilateral-triangle",
      "n": 7,
      "exact": "17/675",
      "passed": true
    },
    {
      "region": "equilateral-triangle",
      "n": 8,
      "exact": "323/66150",
      "passed": true
    },
    {
      "region": "unit-square",
      "n": 3,
      "exact": "1",
      "passed": true
    },
    {
      "region": "unit-square",
      "n": 4,
      "exact": "25/36",
      "passed": true
    },
    {
      "region": "unit-square",
      "n": 5,
      "exact": "49/144",
      "passed": true
    },
    {
      "region": "unit-square",
      "n": 6,
      "exact": "49/400",
      "passed": true
    },
    {
      "region": "unit-square",
      "n": 7,
      "exact": "121/3600",
      "passed": true
    },
    {
      "region": "unit-square",
      "n": 8,
      "exact": "20449/2822400",
      "passed": true
    },
    {
      "region": "unit-disk",
      "n": 3,
      "exact": "1",
      "passed": true
    },
    {
      "region": "unit-disk",
      "n": 4,
      "passed": true,
      "absolute_discrepancy_ulps": "[0.0639821291554168211323545841954274814728556591408793728529304726953929692872749382152841900974960213287929713707240941344658427846 +/- 4.74e-131]",
      "independent_ball_radius": "1.5171225e-231",
      "generator_ball_radius": "1.0046560e-124"
    },
    {
      "region": "unit-disk",
      "n": 5,
      "passed": true,
      "absolute_discrepancy_ulps": "[0.0322467813743009317526296298543241560658641145569157765724556726578203973758489725404405569981163321805846876290774907929434432092 +/- 6.78e-131]",
      "independent_ball_radius": "1.8443992e-231",
      "generator_ball_radius": "2.1122944e-124"
    },
    {
      "region": "unit-disk",
      "n": 6,
      "passed": true,
      "absolute_discrepancy_ulps": "[0.0819145575152513487463824922510233489480805736083918367981222136711558862407396920340325544485207789585644052002048234510044584652 +/- 8.10e-131]",
      "independent_ball_radius": "7.0281007e-231",
      "generator_ball_radius": "4.4456331e-124"
    },
    {
      "region": "unit-disk",
      "n": 7,
      "passed": true,
      "absolute_discrepancy_ulps": "[0.10047237407969013494675896851653574680844261127833142856356923175949171427165070342984326188331562091429090820231123474487163976 +/- 2.30e-129]",
      "independent_ball_radius": "1.0338046e-230",
      "generator_ball_radius": "7.7903443e-124"
    },
    {
      "region": "unit-disk",
      "n": 8,
      "passed": true,
      "absolute_discrepancy_ulps": "[0.4647728077157199712713153649166041517942067809611959571142801664895015932121911760993997540412755923393013855354259929597490053 +/- 5.31e-128]",
      "independent_ball_radius": "2.6768285e-230",
      "generator_ball_radius": "1.9469747e-123"
    }
  ],
  "catalan_checks": [
    {
      "n": 3,
      "catalan": 2,
      "source": "T264 formula-small: C_2(q)=q+1",
      "passed": true
    },
    {
      "n": 4,
      "catalan": 5,
      "source": "T264 row 3",
      "passed": true
    },
    {
      "n": 5,
      "catalan": 14,
      "source": "T264 row 4",
      "passed": true
    },
    {
      "n": 6,
      "catalan": 42,
      "source": "T264 row 5",
      "passed": true
    },
    {
      "n": 7,
      "catalan": 132,
      "source": "T264 row 6",
      "passed": true
    },
    {
      "n": 8,
      "catalan": 429,
      "source": "T264 row 7",
      "passed": true
    }
  ],
  "scope": "All stored values, the unchanged attached generator, and the linked Catalan identity. Closed forms check transcription and precision; they do not re-prove the disk formulas."
}