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

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{
  "not_a_certificate": true,
  "is_new_bound": false,
  "E22_hylleraas_upper": {
    "exact": "-54353/18800",
    "float": -2.8911170212765955,
    "note": "variational upper on E(2,2); legal threshold only as an upper"
  },
  "E22_published_comparison": -2.9037243770341195,
  "three_electron_variational_uppers": {
    "hydrogenic_doublet": {
      "energy": "-17410872362191/6480000000000",
      "float": -2.6868630188566356,
      "above_hylleraas": 0.20425400241995995
    },
    "hydrogenic_4P": {
      "energy": "-131653344966733/65610000000000",
      "float": -2.006604861556668,
      "above_hylleraas": 0.8845121597199276
    }
  },
  "temple": {
    "applies_if_E1_is_published_He": false,
    "applies_if_E1_is_hylleraas_upper": false,
    "reason": "\u03bc > E(2,2) for every trial here. Temple needs \u03bc < E_1. Taking E_1 as the HVZ threshold E(2,2) makes the hypothesis false. No Temple number is claimed."
  },
  "intermediate_hamiltonian": {
    "repulsion_dropped": {
      "lower": -6.0,
      "below_he_upper_by": -3.1088829787234045
    },
    "triangle_minorant_product_scan": {
      "approx_float": -3.818689668783247,
      "zeta": 1.6,
      "below_he_upper_by": -0.9275726475066515,
      "note": "Product (not fermionic) expectation of the minorant. A number this low cannot prove E(3,2) \u2265 E(2,2)."
    }
  },
  "note": "No Temple or intermediate-Hamiltonian inequality certified Nc(2)<3 or Nc(2)<4. Variational uppers on E(3,2) are not used as non-binding evidence."
}