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

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{
  "claimed_c": 0.38304,
  "P0": {
    "atoms": [
      0.29649392356933757,
      1.0
    ],
    "weights": [
      0.781798506688816,
      0.21820149331118394
    ],
    "mean": 0.44999999999999996,
    "ratio_ex4": 0.891484252169206
  },
  "P1": {
    "atoms": [
      0.01
    ],
    "weights": [
      1.0
    ],
    "mean": 0.01,
    "ratio_ex4": 1.7436964335940552
  },
  "q": 0.1521818181818181,
  "mixture_mean": 0.38304,
  "ciid_example4_ratio": 0.9091371378730101,
  "ciid_example5_ratio": 0.9052721511245316,
  "product_iid_ratio": 1.0465836965509054,
  "liu_beta_0_10_ex5_ratio": 1.032452542008268,
  "repo_beta_0_20_ex4_ratio": 1.0190943848153267,
  "product_ex4_ratio": 1.0466387936290182,
  "fails_pure_ex4": true,
  "mean_matches_claimed": true,
  "iid_weight_saves": true,
  "note": "pure Example 4 on this 2-mixture is below 1.  The {b,1} ray claim is a single 2-atomic law and is untouched.  Liu's positive iid weight saves the witness and lowers the ray."
}