files / problems / simon-ionization-excess / compute / q4 / certs / large_aspect.json

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{
  "not_a_lower_bound": true,
  "gamma4": 0.901924285641075,
  "cut4": 0.8,
  "best_power": {
    "alpha": -2.0,
    "aspect": 3.5,
    "Q": 0.920665391536305,
    "inv": 1.0861709467880727,
    "below_gamma4": false
  },
  "power_rows": [
    {
      "alpha": -2.2,
      "aspect": 3.5,
      "Q": 0.9207230223264543,
      "inv": 1.0861029601206573,
      "below_gamma4": false
    },
    {
      "alpha": -2.2,
      "aspect": 4.0,
      "Q": 0.9211646720536268,
      "inv": 1.0855822312102126,
      "below_gamma4": false
    },
    {
      "alpha": -2.2,
      "aspect": 6.0,
      "Q": 0.9266622113416348,
      "inv": 1.0791418790588057,
      "below_gamma4": false
    },
    {
      "alpha": -2.2,
      "aspect": 8.0,
      "Q": 0.9328557119826303,
      "inv": 1.0719771419683604,
      "below_gamma4": false
    },
    {
      "alpha": -2.2,
      "aspect": 12.0,
      "Q": 0.9428436585862097,
      "inv": 1.060621229080011,
      "below_gamma4": false
    },
    {
      "alpha": -2.2,
      "aspect": 20.0,
      "Q": 0.9553852689935203,
      "inv": 1.0466981567064357,
      "below_gamma4": false
    },
    {
      "alpha": -2.0,
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      "inv": 1.0861709467880727,
      "below_gamma4": false
    },
    {
      "alpha": -2.0,
      "aspect": 4.0,
      "Q": 0.9211120366571997,
      "inv": 1.0856442649789835,
      "below_gamma4": false
    },
    {
      "alpha": -2.0,
      "aspect": 6.0,
      "Q": 0.9266668515748365,
      "inv": 1.079136475315305,
      "below_gamma4": false
    },
    {
      "alpha": -2.0,
      "aspect": 8.0,
      "Q": 0.9329395908160076,
      "inv": 1.0718807625318345,
      "below_gamma4": false
    },
    {
      "alpha": -2.0,
      "aspect": 12.0,
      "Q": 0.943080370133174,
      "inv": 1.0603550149801,
      "below_gamma4": false
    },
    {
      "alpha": -2.0,
      "aspect": 20.0,
      "Q": 0.9558416122492062,
      "inv": 1.0461984362104555,
      "below_gamma4": false
    },
    {
      "alpha": -1.8,
      "aspect": 3.5,
      "Q": 0.9207230223264543,
      "inv": 1.0861029601206573,
      "below_gamma4": false
    },
    {
      "alpha": -1.8,
      "aspect": 4.0,
      "Q": 0.9211646720536268,
      "inv": 1.0855822312102126,
      "below_gamma4": false
    },
    {
      "alpha": -1.8,
      "aspect": 6.0,
      "Q": 0.9266622113416348,
      "inv": 1.0791418790588057,
      "below_gamma4": false
    },
    {
      "alpha": -1.8,
      "aspect": 8.0,
      "Q": 0.9328557119826301,
      "inv": 1.0719771419683606,
      "below_gamma4": false
    },
    {
      "alpha": -1.8,
      "aspect": 12.0,
      "Q": 0.9428436585862094,
      "inv": 1.0606212290800112,
      "below_gamma4": false
    },
    {
      "alpha": -1.8,
      "aspect": 20.0,
      "Q": 0.9553852689935206,
      "inv": 1.0466981567064355,
      "below_gamma4": false
    },
    {
      "alpha": -1.5,
      "aspect": 3.5,
      "Q": 0.9210238411758317,
      "inv": 1.0857482241972616,
      "below_gamma4": false
    },
    {
      "alpha": -1.5,
      "aspect": 4.0,
      "Q": 0.9214401146197488,
      "inv": 1.0852577222695265,
      "below_gamma4": false
    },
    {
      "alpha": -1.5,
      "aspect": 6.0,
      "Q": 0.9266473779136692,
      "inv": 1.079159153562257,
      "below_gamma4": false
    },
    {
      "alpha": -1.5,
      "aspect": 8.0,
      "Q": 0.9324418902918554,
      "inv": 1.072452889999396,
      "below_gamma4": false
    },
    {
      "alpha": -1.5,
      "aspect": 12.0,
      "Q": 0.9416637020148458,
      "inv": 1.0619502459958199,
      "below_gamma4": false
    },
    {
      "alpha": -1.5,
      "aspect": 20.0,
      "Q": 0.9531007722373684,
      "inv": 1.0492069979678407,
      "below_gamma4": false
    }
  ],
  "forced_endpoint": [
    {
      "R": 4.0,
      "k": 8,
      "Q": 0.9226411079180559,
      "below_gamma4": false,
      "cut": 0.8
    },
    {
      "R": 6.0,
      "k": 8,
      "Q": 0.9239575316806363,
      "below_gamma4": false,
      "cut": 0.8571428571428571
    },
    {
      "R": 8.0,
      "k": 8,
      "Q": 0.9250612323012103,
      "below_gamma4": false,
      "cut": 0.8888888888888888
    },
    {
      "R": 12.0,
      "k": 8,
      "Q": 0.9270440647777736,
      "below_gamma4": false,
      "cut": 0.9230769230769231
    }
  ],
  "any_power_below_gamma4": false,
  "note": "Numerical only. A trial below \u03b34 with aspect>4 would kill an R=4 lift; none is expected near the known minimizer (aspect~3.5)."
}