files / problems / simon-ionization-excess / compute / q2 / certs / beta3_lift.json

5.6 KB · on GitHub

{
  "status": "residue",
  "is_new_bound": false,
  "beats_1.1185_in_HPS_theorem": false,
  "R": 12,
  "gamma_R_compact": "0.899526050000000000000000",
  "fmin": "0.894107456974982284669208",
  "p12_max_grid": "0.995000000000000000000000",
  "p12_at": {
    "eta": "0.00500000000000000000000000",
    "Win": "0.00102777777777777777777778",
    "Wout": "0.0"
  },
  "gamma_aspect_le_R2": "0.894134549940107373245862",
  "inv_aspect_le_R2": "1.11839990979767408424087",
  "beats_1.1185_on_aspect_le_R2": true,
  "aspect_limit": 144,
  "corners": [
    {
      "eta": "0.0100000000000000000000000",
      "Win": "0.0000694444444444444444444444",
      "Wout": "0.0",
      "p12": "0.990000000000000000000000"
    },
    {
      "eta": "0.0100000000000000000000000",
      "Win": "0.0000694444444444444444444444",
      "Wout": "0.00687500000000000000000000",
      "p12": "0.0198000000000000000000000"
    },
    {
      "eta": "0.0100000000000000000000000",
      "Win": "0.0100000000000000000000000",
      "Wout": "0.0",
      "p12": "0.990000000000000000000000"
    },
    {
      "eta": "0.0100000000000000000000000",
      "Win": "0.0100000000000000000000000",
      "Wout": "0.00687500000000000000000000",
      "p12": "0.590740740740740740740741"
    },
    {
      "eta": "0.100000000000000000000000",
      "Win": "0.000694444444444444444444444",
      "Wout": "0.0",
      "p12": "0.900000000000000000000000"
    },
    {
      "eta": "0.100000000000000000000000",
      "Win": "0.000694444444444444444444444",
      "Wout": "0.00625000000000000000000000",
      "p12": "0.180000000000000000000000"
    },
    {
      "eta": "0.100000000000000000000000",
      "Win": "0.100000000000000000000000",
      "Wout": "0.0",
      "p12": "0.900000000000000000000000"
    },
    {
      "eta": "0.100000000000000000000000",
      "Win": "0.100000000000000000000000",
      "Wout": "0.00625000000000000000000000",
      "p12": "0.852941176470588235294118"
    },
    {
      "eta": "0.300000000000000000000000",
      "Win": "0.00208333333333333333333333",
      "Wout": "0.0",
      "p12": "0.700000000000000000000000"
    },
    {
      "eta": "0.300000000000000000000000",
      "Win": "0.00208333333333333333333333",
      "Wout": "0.00486111111111111111111111",
      "p12": "0.420000000000000000000000"
    },
    {
      "eta": "0.300000000000000000000000",
      "Win": "0.300000000000000000000000",
      "Wout": "0.0",
      "p12": "0.700000000000000000000000"
    },
    {
      "eta": "0.300000000000000000000000",
      "Win": "0.300000000000000000000000",
      "Wout": "0.00486111111111111111111111",
      "p12": "0.693621867881548974943052"
    },
    {
      "eta": "0.500000000000000000000000",
      "Win": "0.00347222222222222222222222",
      "Wout": "0.0",
      "p12": "0.500000000000000000000000"
    },
    {
      "eta": "0.500000000000000000000000",
      "Win": "0.00347222222222222222222222",
      "Wout": "0.00347222222222222222222222",
      "p12": "0.500000000000000000000000"
    },
    {
      "eta": "0.500000000000000000000000",
      "Win": "0.500000000000000000000000",
      "Wout": "0.0",
      "p12": "0.500000000000000000000000"
    },
    {
      "eta": "0.500000000000000000000000",
      "Win": "0.500000000000000000000000",
      "Wout": "0.00347222222222222222222222",
      "p12": "0.500000000000000000000000"
    },
    {
      "eta": "0.700000000000000000000000",
      "Win": "0.00486111111111111111111111",
      "Wout": "0.0",
      "p12": "0.300000000000000000000000"
    },
    {
      "eta": "0.700000000000000000000000",
      "Win": "0.00486111111111111111111111",
      "Wout": "0.00208333333333333333333333",
      "p12": "0.420000000000000000000000"
    },
    {
      "eta": "0.700000000000000000000000",
      "Win": "0.700000000000000000000000",
      "Wout": "0.0",
      "p12": "0.300000000000000000000000"
    },
    {
      "eta": "0.700000000000000000000000",
      "Win": "0.700000000000000000000000",
      "Wout": "0.00208333333333333333333333",
      "p12": "0.301186943620178041543027"
    },
    {
      "eta": "0.900000000000000000000000",
      "Win": "0.00625000000000000000000000",
      "Wout": "0.0",
      "p12": "0.100000000000000000000000"
    },
    {
      "eta": "0.900000000000000000000000",
      "Win": "0.00625000000000000000000000",
      "Wout": "0.000694444444444444444444444",
      "p12": "0.180000000000000000000000"
    },
    {
      "eta": "0.900000000000000000000000",
      "Win": "0.900000000000000000000000",
      "Wout": "0.0",
      "p12": "0.100000000000000000000000"
    },
    {
      "eta": "0.900000000000000000000000",
      "Win": "0.900000000000000000000000",
      "Wout": "0.000694444444444444444444444",
      "p12": "0.100616808018504240555127"
    },
    {
      "eta": "0.990000000000000000000000",
      "Win": "0.00687500000000000000000000",
      "Wout": "0.0",
      "p12": "0.0100000000000000000000000"
    },
    {
      "eta": "0.990000000000000000000000",
      "Win": "0.00687500000000000000000000",
      "Wout": "0.0000694444444444444444444444",
      "p12": "0.0198000000000000000000000"
    },
    {
      "eta": "0.990000000000000000000000",
      "Win": "0.990000000000000000000000",
      "Wout": "0.0",
      "p12": "0.0100000000000000000000000"
    },
    {
      "eta": "0.990000000000000000000000",
      "Win": "0.990000000000000000000000",
      "Wout": "0.0000694444444444444444444444",
      "p12": "0.0100687381637090552009539"
    }
  ],
  "note": "Valid for z-support aspect \u2264 R\u00b2 = 144 after inf=1, assuming the out-piece, rescaled, has aspect \u2264 R so Q2\u2265\u03b3_R. Not a bound for arbitrarily spread measures (k\u2192\u221e windows)."
}