files / problems / simon-ionization-excess / compute / q3 / certs / leading.json

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{
  "arxiv": "2504.18487v1",
  "beta3_lower": "0.8995260524666926617922278920310721986121",
  "source": "q2 compact R=12 n=22, lifted by mass-opt dichotomy",
  "b_interval": [
    "1.111696539814256967989266155857831490919",
    "1.111696539814256967989266155857831490919"
  ],
  "b_hi": "1.111696539814256967989266155857831490919",
  "printed_leading": "1.1118",
  "a1_at_left": [
    "3.875014342007594344805550128437768520409",
    "3.875014342007594344805550128437768520409"
  ],
  "a1_at_9/4": [
    "3.850571130048037457905277869340962771255",
    "3.850571130048037457905277869340962771255"
  ],
  "a1_max_hi_on_interval": "3.875014342007594344805550128437768520409",
  "a2": [
    "0.01323448261683639247606269233164085108237",
    "0.01323448261683639247606269233164085108237"
  ],
  "a3": [
    "0.1832456062507374527213583183871416713133",
    "0.1832456062507374527213583183871416713133"
  ],
  "a4": [
    "0.01955232689613809693955699252478325958937",
    "0.01955232689613809693955699252478325958937"
  ],
  "Z4_remainder_coeff": [
    "3.960960692381081622471407411296228191789",
    "3.960960692381081622471407411296228191789"
  ],
  "r_max": [
    "0.4705180144405142455387763635073145689990",
    "0.4705180144405142455387763635073145689990"
  ],
  "checks": {
    "leading_lt_1.1118": true,
    "a1_lt_3.880": true,
    "Z4_coeff_lt_3.966": true,
    "extras_ok": true,
    "r_max_lt_0.5": true,
    "beats_1.1185": true
  },
  "inequalities": [
    {
      "beats": "HPS Theorem 2.2 / Prop. 2.5 leading 1.1185",
      "range": "Z >= 4",
      "inequality": "N < 1.1118 Z + 3.880 Z^{1/3} + 0.0133 + 0.1833 Z^{-1/3} + 0.01956 Z^{-2/3}"
    },
    {
      "beats": "HPS simplified 1.1185 Z + 4 Z^{1/3}",
      "range": "Z >= 4",
      "inequality": "N_c < 1.1118 Z + 3.966 Z^{1/3}"
    }
  ],
  "LT_factor": "1.456",
  "note": "\u03b2_3 \u2265 compact \u03b3 on every radial probability, by the aspect-12 compact certificate plus the mass-stationary cut Q>12/13 off that class. Not the R=4 number 1.1087."
}