files / problems / simon-ionization-excess / compute / q2 / certs / nam_smallz.json
{
"not_a_certificate": true,
"is_new_bound": false,
"beta_used": "0.821800000000000000000000",
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{
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{
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"rhs": "4.84050279392921887465594",
"contradiction": false
},
{
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},
{
"Z": 2,
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{
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{
"Z": 3,
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{
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{
"Z": 3,
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{
"Z": 3,
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"rhs": "6.38849616560066924076612",
"contradiction": false
},
{
"Z": 4,
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"rhs": "7.44470921391666915962322",
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{
"Z": 4,
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"rhs": "7.45888546563100764352860",
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{
"Z": 4,
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{
"Z": 4,
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},
{
"Z": 5,
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"rhs": "8.74681242391039430210686",
"contradiction": false
},
{
"Z": 5,
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"rhs": "8.70826617089521178101209",
"contradiction": false
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{
"Z": 5,
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"rhs": "8.72597141800126387432830",
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},
{
"Z": 5,
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"rhs": "8.76912235911257476131520",
"contradiction": false
}
],
"note": "No (N,Z) in this table yields a contradiction from published lower bounds on alpha_N. At Z=2, N=4 the Prop. 1 remainder is larger than \u03b2, so that lower bound is useless. The search upper on alpha_4*(3) is still below the Lemma-1 RHS once the kinetic 0.68 N^{-2/3} is kept. HPS (7.10) likewise does not exclude N=4 at Z=2: the N^{1/3} remainder is ~2.5."
}