{
  "classification": "Fresh certified computation of a fixed existing claim; not original-evidence recovery",
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        "lower_dyadic": {
          "numerator": "1222564097902771013997358979793633883114762723779280989386088619540732730640385084224802087546993",
          "denominator": "1067993517960455041197510853084776057301352261178326384973520803911109862890320275011481043468288"
        },
        "upper_dyadic": {
          "numerator": "1222564097902771013997358979793633883114762723779280989386088619540732730640385084224802087546997",
          "denominator": "1067993517960455041197510853084776057301352261178326384973520803911109862890320275011481043468288"
        }
      },
      "archimedean": {
        "display_only": "[-1.225146193103467200296542873009019111006373805713532063861068605578349 +/- 3.14e-70]",
        "lower_dyadic": {
          "numerator": "-327112048197107729377253110685647394548802741861720156111352523086854816192590530946275873337849",
          "denominator": "266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072"
        },
        "upper_dyadic": {
          "numerator": "-654224096394215458754506221371294789097605483723440312222705046173709632385181061892551746675695",
          "denominator": "533996758980227520598755426542388028650676130589163192486760401955554931445160137505740521734144"
        }
      },
      "prime_sum_with_factor_two": {
        "display_only": "[-2.061323540407239864287356030540814203734152907992384256473656043532640 +/- 7.93e-71]",
        "lower_dyadic": {
          "numerator": "-1100740089787114150423045278594477670566728931009787224322632466242348597346605841961226104446719",
          "denominator": "533996758980227520598755426542388028650676130589163192486760401955554931445160137505740521734144"
        },
        "upper_dyadic": {
          "numerator": "-1100740089787114150423045278594477670566728931009787224322632466242348597346605841961226104446685",
          "denominator": "533996758980227520598755426542388028650676130589163192486760401955554931445160137505740521734144"
        }
      },
      "continuum_with_factor_two": {
        "display_only": "[-1.476204465464669810412474552276563640047148849028242254577826653463808 +/- 9.27e-71]",
        "lower_dyadic": {
          "numerator": "-1576576800300545770759960847871505801597181182960733248924774184864595153377377231251525621501377",
          "denominator": "1067993517960455041197510853084776057301352261178326384973520803911109862890320275011481043468288"
        },
        "upper_dyadic": {
          "numerator": "-1576576800300545770759960847871505801597181182960733248924774184864595153377377231251525621501335",
          "denominator": "1067993517960455041197510853084776057301352261178326384973520803911109862890320275011481043468288"
        }
      },
      "continuum_complex_expression": {
        "display_only": "[-1.476204465464669810412474552276563640047148849028242254577826653463808 +/- 9.27e-71]",
        "lower_dyadic": {
          "numerator": "-1576576800300545770759960847871505801597181182960733248924774184864595153377377231251525621501389",
          "denominator": "1067993517960455041197510853084776057301352261178326384973520803911109862890320275011481043468288"
        },
        "upper_dyadic": {
          "numerator": "-1576576800300545770759960847871505801597181182960733248924774184864595153377377231251525621501323",
          "denominator": "1067993517960455041197510853084776057301352261178326384973520803911109862890320275011481043468288"
        }
      },
      "continuum_expressions_overlap": true,
      "beta": {
        "display_only": "[-0.6400271181608971464216613947447685473193697467493900619652392155095173 +/- 2.01e-73]",
        "lower_dyadic": {
          "numerator": "-1367089627029496774845765466850280077317868576776078849449838689454634446909055342228353811918801",
          "denominator": "2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962086936576"
        },
        "upper_dyadic": {
          "numerator": "-1367089627029496774845765466850280077317868576776078849449838689454634446909055342228353811918579",
          "denominator": "2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962086936576"
        }
      },
      "outward_rational_enclosure": {
        "lower": {
          "numerator": "-640027118160897146421661394744768547319369747",
          "denominator": "1000000000000000000000000000000000000000000000"
        },
        "upper": {
          "numerator": "-320013559080448573210830697372384273659684873",
          "denominator": "500000000000000000000000000000000000000000000"
        },
        "lower_decimal_exact": "-0.640027118160897146421661394744768547319369747",
        "upper_decimal_exact": "-0.640027118160897146421661394744768547319369746",
        "strict": true
      },
      "historical_reported_interval_verified": true,
      "beta_strictly_below_minus_three_fifths": true
    }
  ],
  "same_outward_rational_interval_at_both_precisions": true,
  "all_gates_pass": true,
  "scope": [
    "One point: a=log4, xi=1. No parameter scan.",
    "This validates the numerical premise of the full-line negative-index implication.",
    "It gives no compact physical-window negative test and does not contradict certified W4 positivity.",
    "Both historical original-evidence groups remain recovery OPEN.",
    "RH, G2 and cofinal signed-arithmetic lower bounds remain open."
  ]
}