files / problems / simon-ionization-excess / compute / q2 / certs / alpha_n.json

4.7 KB · on GitHub

{
  "not_a_certificate": true,
  "is_new_bound": false,
  "note": "search_min is an upper bound on alpha_{N,s}. It cannot prove non-binding. A value below the threshold needed for Z=2 shows the Nam\u2013HPS pair geometry does not, by itself, exclude that N.",
  "thresholds": {
    "N4_Z2_kinetic_dropped": 0.6666666666666666,
    "N3_Z2_kinetic_dropped": 1.0,
    "Nam_sqrt5_over_4": 0.5590169943749475
  },
  "rows": [
    {
      "N": 3,
      "s": 1.0,
      "search_min": 0.5,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": null,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": 1.0
    },
    {
      "N": 3,
      "s": 1.25,
      "search_min": 0.5773502691896258,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": null,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": 1.0
    },
    {
      "N": 3,
      "s": 1.5,
      "search_min": 0.5773502691896258,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": null,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": 1.0
    },
    {
      "N": 3,
      "s": 2.0,
      "search_min": 0.5773502691896257,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": null,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": 1.0
    },
    {
      "N": 3,
      "s": 2.5,
      "search_min": 0.5773502691896258,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": null,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": 1.0
    },
    {
      "N": 3,
      "s": 3.0,
      "search_min": 0.5773502691896256,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": null,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": 1.0
    },
    {
      "N": 4,
      "s": 1.0,
      "search_min": 0.5000011170243487,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": 0.6666666666666666,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": null
    },
    {
      "N": 4,
      "s": 1.25,
      "search_min": 0.6105694746033381,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": 0.6666666666666666,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": null
    },
    {
      "N": 4,
      "s": 1.5,
      "search_min": 0.6123724356957945,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": 0.6666666666666666,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": null
    },
    {
      "N": 4,
      "s": 2.0,
      "search_min": 0.6123724356957944,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": 0.6666666666666666,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": null
    },
    {
      "N": 4,
      "s": 2.5,
      "search_min": 0.6123724356957944,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": 0.6666666666666666,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": null
    },
    {
      "N": 4,
      "s": 3.0,
      "search_min": 0.6123724356957945,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": 0.6666666666666666,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": null
    },
    {
      "N": 5,
      "s": 1.0,
      "search_min": 0.5045715567397302,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": null,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": null
    },
    {
      "N": 5,
      "s": 1.25,
      "search_min": 0.622443619550234,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": null,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": null
    },
    {
      "N": 5,
      "s": 1.5,
      "search_min": 0.6470095206535147,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": null,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": null
    },
    {
      "N": 5,
      "s": 2.0,
      "search_min": 0.6474226764154579,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": null,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": null
    },
    {
      "N": 5,
      "s": 2.5,
      "search_min": 0.6474168883387811,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": null,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": null
    },
    {
      "N": 5,
      "s": 3.0,
      "search_min": 0.647407251148609,
      "search_min_is_upper_on_inf": true,
      "need_for_Nc_lt_4_at_Z2_if_kinetic_dropped": null,
      "need_for_Nc_lt_3_at_Z2_if_kinetic_dropped": null
    }
  ]
}