files / problems / union-closed / compute / q2 / certs / hunt_protocols.json

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{
  "ceiling": 0.3830513565868256,
  "claimed": 0.38304,
  "pi_at_bstar": {
    "ex4": 0.5,
    "half": 0.5,
    "target": 0.5
  },
  "half_target": {
    "b": 0.2964939298406104,
    "a": 0.1230372137750061,
    "mean": 0.38305135658682565,
    "Hmix": 1.0,
    "hb": 0.8769627862249939
  },
  "example4": {
    "b": 0.2964939233253704,
    "a": 0.12303722189664579,
    "mean": 0.38305135658682554,
    "Hmix": 1.0,
    "hb": 0.8769627781033542
  },
  "scaled_best": {
    "alpha": 0.9999999999999999,
    "b": 0.2964939233253704,
    "a": 0.12303722189664579,
    "mean": 0.38305135658682554,
    "Hmix": 1.0,
    "hb": 0.8769627781033542,
    "below_ceiling": true
  },
  "scaled_sample": [
    {
      "alpha": 0.0,
      "b": 0.381966010989124,
      "a": 4.2227610297373985e-10,
      "mean": 0.3819660112501051,
      "Hmix": 0.9594187284467,
      "hb": 0.9594187280415604,
      "below_ceiling": true
    },
    {
      "alpha": 0.19999999999999998,
      "b": 0.3239808888084211,
      "a": 0.08684736124286419,
      "mean": 0.3826913647651561,
      "Hmix": 0.9950780050285757,
      "hb": 0.9086581060610304,
      "below_ceiling": true
    },
    {
      "alpha": 0.39999999999999997,
      "b": 0.3040521752114047,
      "a": 0.11336947195726943,
      "mean": 0.382951412617498,
      "Hmix": 0.9995008747913592,
      "hb": 0.8861879883954339,
      "below_ceiling": true
    },
    {
      "alpha": 0.6,
      "b": 0.2988278117182823,
      "a": 0.1200740577381606,
      "mean": 0.38302040153841366,
      "Hmix": 0.9999174471597249,
      "hb": 0.8798533018760739,
      "below_ceiling": true
    },
    {
      "alpha": 0.7999999999999999,
      "b": 0.2970056835629259,
      "a": 0.12238915114396842,
      "mean": 0.38304456121069375,
      "Hmix": 0.9999874247775574,
      "hb": 0.8775998127043891,
      "below_ceiling": true
    },
    {
      "alpha": 0.9999999999999999,
      "b": 0.2964939233253704,
      "a": 0.12303722189664579,
      "mean": 0.38305135658682554,
      "Hmix": 1.0,
      "hb": 0.8769627781033542,
      "below_ceiling": true
    },
    {
      "alpha": 1.2,
      "b": 0.29731610475045167,
      "a": 0.12199559055534981,
      "mean": 0.38304044152515393,
      "Hmix": 0.999978281350642,
      "hb": 0.8779853403747467,
      "below_ceiling": true
    },
    {
      "alpha": 1.4,
      "b": 0.3239808888084211,
      "a": 0.08684736124286419,
      "mean": 0.3826913647651561,
      "Hmix": 0.9950780050285757,
      "hb": 0.9086581060610304,
      "below_ceiling": true
    }
  ],
  "anyone_beats_claimed_0_38304": true,
  "anyone_beats_ceiling": false,
  "note": "half-target coincides with Example 4 on the {b,1} diagonal at the optimizer.  Scaled a(t) peaks at \u03b1=1.  No new protocol in this list moves 0.38304."
}