erdos_699_off_diagonal_gcd_sharp.json

{
  "scope": "Sample uniform analytic gcd bounds; no finite bootstrap is claimed here.",
  "records": [
    {
      "A": 17,
      "B": 11,
      "C": 26,
      "directions": [
        17,
        11,
        26
      ],
      "terms": 10000,
      "m0": 1000000000000,
      "rounding_denominator": 1000000000000,
      "root_scale": 1000000,
      "eligible_terms": 4816,
      "positive_terms": 4009,
      "largest_positive_t": 9999,
      "floor_stability_bound": 9956,
      "ell_lower": "1064826114977/250000000000",
      "theta_mode": "broadbent_johnston_yang",
      "source": "BFT Lemma 5.2 and retained small-x theta lower bound; Broadbent et al. Corollary 2.1 and final global theta table; Johnston--Yang Lemma 2.2",
      "finite_RH_range_patched": true,
      "conclusion": "For every integer m>=m0, both coefficient gcds are at least exp(ell_lower*m).",
      "requested_log_rate": "85141791/20000000",
      "strict_margin": "553727477/250000000000",
      "old_log_helper_margin_at_same_m0": "-678149637/200000000000",
      "trials": [
        [
          8,
          -0.042891642523
        ],
        [
          10,
          -0.005768615418
        ],
        [
          12,
          0.002214909908
        ]
      ]
    },
    {
      "A": 152,
      "B": 71,
      "C": 152,
      "directions": [
        152,
        71,
        152
      ],
      "terms": 100000,
      "m0": 100000000000000,
      "rounding_denominator": 1000000000000,
      "root_scale": 1000000,
      "eligible_terms": 49867,
      "positive_terms": 43550,
      "largest_positive_t": 99996,
      "floor_stability_bound": 99788,
      "ell_lower": "3382222836947/50000000000",
      "theta_mode": "broadbent_johnston_yang",
      "source": "BFT Lemma 5.2 and retained small-x theta lower bound; Broadbent et al. Corollary 2.1 and final global theta table; Johnston--Yang Lemma 2.2",
      "finite_RH_range_patched": true,
      "conclusion": "For every integer m>=m0, both coefficient gcds are at least exp(ell_lower*m).",
      "requested_log_rate": "33820369970999/500000000000",
      "strict_margin": "1858398471/500000000000",
      "old_log_helper_margin_at_same_m0": "-7909951837/250000000000",
      "trials": [
        [
          10,
          -0.037739276923
        ],
        [
          12,
          -0.003521129807
        ],
        [
          14,
          0.003716796942
        ]
      ]
    },
    {
      "A": 65,
      "B": 42,
      "C": 65,
      "directions": [
        65,
        42,
        65
      ],
      "terms": 100000,
      "m0": 100000000000000,
      "rounding_denominator": 1000000000000,
      "root_scale": 1000000,
      "eligible_terms": 49419,
      "positive_terms": 40474,
      "largest_positive_t": 100000,
      "floor_stability_bound": 99888,
      "ell_lower": "31453143071373/1000000000000",
      "theta_mode": "broadbent_johnston_yang",
      "source": "BFT Lemma 5.2 and retained small-x theta lower bound; Broadbent et al. Corollary 2.1 and final global theta table; Johnston--Yang Lemma 2.2",
      "finite_RH_range_patched": true,
      "conclusion": "For every integer m>=m0, both coefficient gcds are at least exp(ell_lower*m).",
      "requested_log_rate": "1258063123473/40000000000",
      "strict_margin": "391246137/250000000000",
      "old_log_helper_margin_at_same_m0": "-15605042937/1000000000000",
      "trials": [
        [
          10,
          -0.023133933503
        ],
        [
          12,
          -0.002799965996
        ],
        [
          14,
          0.001564984548
        ]
      ]
    },
    {
      "A": 159,
      "B": 79,
      "C": 159,
      "directions": [
        159,
        79,
        159
      ],
      "terms": 100000,
      "m0": 100000000000000,
      "rounding_denominator": 1000000000000,
      "root_scale": 1000000,
      "eligible_terms": 49870,
      "positive_terms": 43715,
      "largest_positive_t": 99998,
      "floor_stability_bound": 99643,
      "ell_lower": "77159654306033/1000000000000",
      "theta_mode": "broadbent_johnston_yang",
      "source": "BFT Lemma 5.2 and retained small-x theta lower bound; Broadbent et al. Corollary 2.1 and final global theta table; Johnston--Yang Lemma 2.2",
      "finite_RH_range_patched": true,
      "conclusion": "For every integer m>=m0, both coefficient gcds are at least exp(ell_lower*m).",
      "requested_log_rate": "77155925155351/1000000000000",
      "strict_margin": "1864575341/500000000000",
      "old_log_helper_margin_at_same_m0": "-6362174247/200000000000",
      "trials": [
        [
          10,
          -0.038668429392
        ],
        [
          12,
          -0.003719702562
        ],
        [
          14,
          0.003729150682
        ]
      ]
    }
  ]
}