files / problems / simon-ionization-excess / compute / q4 / work / moment_region.json

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{
  "not_a_lower_bound": true,
  "method": "Endpoint identities M_{-1}=Q+(Q-1)D, M_3=(Q-1)R^3+QDR; support [1,R] linear ineqs; 2/3-atom moment reconstruction.",
  "regions": [
    {
      "R": 4,
      "gamma": 0.901924285641075,
      "cut": 0.8,
      "cut_beats_gamma": false,
      "positivity_only_nonempty_below_gamma": true,
      "support_only_nonempty_below_gamma": true,
      "full_moment_nonempty_below_gamma": false,
      "positivity_below_gamma_count": 95840,
      "support_below_gamma_count": 1466,
      "measure_below_gamma_count": 0,
      "best_positivity_only": {
        "Q": 0.8000010000000001,
        "D": 3.999975156281541
      },
      "best_with_support": {
        "Q": 0.8942672775378222,
        "D": 2.691982118274256,
        "M_minus1": 0.6096366793531849,
        "M_3": 2.862511842779096
      },
      "best_with_measure": null
    },
    {
      "R": 8,
      "gamma": 0.9005000199382865,
      "cut": 0.8888888888888888,
      "cut_beats_gamma": false,
      "positivity_only_nonempty_below_gamma": true,
      "support_only_nonempty_below_gamma": false,
      "full_moment_nonempty_below_gamma": false,
      "positivity_below_gamma_count": 95840,
      "support_below_gamma_count": 0,
      "measure_below_gamma_count": 0,
      "best_positivity_only": {
        "Q": 0.8888898888888889,
        "D": 7.99991950634312
      },
      "best_with_support": null,
      "best_with_measure": null
    },
    {
      "R": 9,
      "gamma": 0.900256528070388,
      "cut": 0.9,
      "cut_beats_gamma": false,
      "positivity_only_nonempty_below_gamma": true,
      "support_only_nonempty_below_gamma": false,
      "full_moment_nonempty_below_gamma": false,
      "positivity_below_gamma_count": 95840,
      "support_below_gamma_count": 0,
      "measure_below_gamma_count": 0,
      "best_positivity_only": {
        "Q": 0.900001,
        "D": 8.999900625113884
      },
      "best_with_support": null,
      "best_with_measure": null
    }
  ],
  "interior_stationarity_scan": [
    {
      "R": 4,
      "gamma": 0.901924285641075,
      "moment_feasible_below_gamma_with_3_stationarity": false,
      "count": 0,
      "sample": []
    },
    {
      "R": 8,
      "gamma": 0.9005000199382865,
      "moment_feasible_below_gamma_with_3_stationarity": false,
      "count": 0,
      "sample": []
    },
    {
      "R": 9,
      "gamma": 0.900256528070388,
      "moment_feasible_below_gamma_with_3_stationarity": false,
      "count": 0,
      "sample": []
    }
  ],
  "positivity_only_witnesses": [
    {
      "R": 4.0,
      "Q": 0.801,
      "D": 4.0,
      "M_minus1": 0.0050000000000002265,
      "M_3": 0.08000000000000362,
      "positivity_interval": [
        3.975031210986266,
        4.025125628140705
      ],
      "D_in_positivity_interval": true,
      "support_ok": false,
      "three_atom_ok": false
    },
    {
      "R": 4.0,
      "Q": 0.8942672775378222,
      "D": 2.691982118274256,
      "M_minus1": 0.6096366793531849,
      "M_3": 2.862511842779096,
      "positivity_interval": [
        1.8917426611567982,
        8.457810001607735
      ],
      "D_in_positivity_interval": true,
      "support_ok": true,
      "three_atom_ok": false
    }
  ],
  "summary": {
    "4": {
      "gamma": 0.901924285641075,
      "cut": 0.8,
      "cut_beats_gamma": false,
      "positivity_only_below_gamma": true,
      "support_only_below_gamma": true,
      "full_moment_below_gamma": false,
      "rigorous_R_lift_from_moments_alone": false
    },
    "8": {
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      "cut_beats_gamma": false,
      "positivity_only_below_gamma": true,
      "support_only_below_gamma": false,
      "full_moment_below_gamma": false,
      "rigorous_R_lift_from_moments_alone": false
    },
    "9": {
      "gamma": 0.900256528070388,
      "cut": 0.9,
      "cut_beats_gamma": false,
      "positivity_only_below_gamma": true,
      "support_only_below_gamma": false,
      "full_moment_below_gamma": false,
      "rigorous_R_lift_from_moments_alone": false
    }
  }
}