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

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{
  "source": "https://arxiv.org/abs/2211.12401",
  "x": 0.3,
  "closed_form": -0.04679700005769244,
  "direct": -0.046797000057692606,
  "means_unperturbed": [
    0.5,
    0.5
  ],
  "q_unperturbed": [
    0.09,
    0.16,
    0.16,
    0.59
  ],
  "matches_ellis_below_-0.04": true,
  "closed_minus_direct": 1.6653345369377348e-16,
  "perturbed": {
    "eps": 0.001,
    "functional": -0.04342167440191891,
    "means": [
      0.499,
      0.499
    ],
    "means_below_half": true,
    "still_negative": true
  },
  "note": "Gilmer Conjecture 1 fails.  The KL+entropy 2-sample strengthening does not give Frankl 1/2."
}