{
  "results": {
    "base_case_charpoly": [
      "1",
      "10",
      "27",
      "10"
    ],
    "feedback_table": [
      {
        "n": 2,
        "v": "8/9",
        "v_float": 0.8888888888888888,
        "gap": "220/279",
        "gap_float": 0.7885304659498208,
        "asymptotic_ratio": 0.8870967741935484
      },
      {
        "n": 3,
        "v": "28/81",
        "v_float": 0.345679012345679,
        "gap": "14/39",
        "gap_float": 0.358974358974359,
        "asymptotic_ratio": 0.8076923076923077
      },
      {
        "n": 4,
        "v": "80/729",
        "v_float": 0.10973936899862825,
        "gap": "6200/43047",
        "gap_float": 0.14402861988059562,
        "asymptotic_ratio": 0.8202879991637048
      },
      {
        "n": 5,
        "v": "208/6561",
        "v_float": 0.0317024843773815,
        "gap": "4264/81171",
        "gap_float": 0.052531076369639405,
        "asymptotic_ratio": 0.8616409801530103
      },
      {
        "n": 6,
        "v": "512/59049",
        "v_float": 0.008670764957916306,
        "gap": "4352/246777",
        "gap_float": 0.01763535499661638,
        "asymptotic_ratio": 0.9039497197875005
      },
      {
        "n": 7,
        "v": "1216/531441",
        "v_float": 0.0022881185305612477,
        "gap": "185440/33437007",
        "gap_float": 0.0055459509279643365,
        "asymptotic_ratio": 0.9398423810932062
      },
      {
        "n": 8,
        "v": "2816/4782969",
        "v_float": 0.0005887556452906134,
        "gap": "499840/301225671",
        "gap_float": 0.0016593539267109807,
        "asymptotic_ratio": 0.9688279286483024
      },
      {
        "n": 9,
        "v": "6400/43046721",
        "v_float": 0.00014867566800268016,
        "gap": "144000/301301447",
        "gap_float": 0.0004779266791904919,
        "asymptotic_ratio": 0.9921477824831024
      },
      {
        "n": 10,
        "v": "14336/387420489",
        "v_float": 3.7003721814000394e-05,
        "gap": "465920/3486710673",
        "gap_float": 0.0001336273765437262,
        "asymptotic_ratio": 1.0111324914913582
      }
    ],
    "prefix_convergence": [
      {
        "n": 2,
        "err_r1e3": 0.0008503303160905598,
        "err_r1e6": 8.520014466890311e-07,
        "first_power_of_two_hurwitz": "2",
        "first_power_of_two_diagonal": "2"
      },
      {
        "n": 3,
        "err_r1e3": 0.007350362418231869,
        "err_r1e6": 7.39976818600869e-06,
        "first_power_of_two_hurwitz": "4",
        "first_power_of_two_diagonal": "4"
      },
      {
        "n": 4,
        "err_r1e3": 0.030046114634454536,
        "err_r1e6": 3.0715335937718974e-05,
        "first_power_of_two_hurwitz": "4",
        "first_power_of_two_diagonal": "4"
      },
      {
        "n": 5,
        "err_r1e3": 0.17683153312733207,
        "err_r1e6": 0.0001878830392354411,
        "first_power_of_two_hurwitz": "8",
        "first_power_of_two_diagonal": "16"
      },
      {
        "n": 6,
        "err_r1e3": 0.7299019829269039,
        "err_r1e6": 0.000840966487152702,
        "first_power_of_two_hurwitz": "8",
        "first_power_of_two_diagonal": "32"
      }
    ],
    "ordered_design": [
      {
        "n": 2,
        "r": "2",
        "last_current": "1",
        "epsilon": "1",
        "delta": "1/2",
        "unstable_counts": [
          0,
          1,
          0
        ]
      },
      {
        "n": 3,
        "r": "4",
        "last_current": "1",
        "epsilon": "1",
        "delta": "1/2",
        "unstable_counts": [
          0,
          1,
          0,
          1,
          0
        ]
      },
      {
        "n": 4,
        "r": "4",
        "last_current": "1",
        "epsilon": "1",
        "delta": "1/2",
        "unstable_counts": [
          0,
          1,
          0,
          1,
          0,
          1,
          0
        ]
      },
      {
        "n": 5,
        "r": "8",
        "last_current": "1",
        "epsilon": "1",
        "delta": "1/4",
        "unstable_counts": [
          0,
          1,
          0,
          1,
          0,
          1,
          0,
          1,
          0
        ]
      },
      {
        "n": 6,
        "r": "8",
        "last_current": "1",
        "epsilon": "1",
        "delta": "1/4",
        "unstable_counts": [
          0,
          1,
          0,
          1,
          0,
          1,
          0,
          1,
          0,
          1,
          0
        ]
      },
      {
        "n": 7,
        "r": "8",
        "last_current": "1",
        "epsilon": "1",
        "delta": "1/4",
        "unstable_counts": [
          0,
          1,
          0,
          1,
          0,
          1,
          0,
          1,
          0,
          1,
          0,
          1,
          0
        ]
      }
    ],
    "benchmark": {
      "unstable_counts": [
        0,
        1,
        0,
        1,
        0
      ],
      "E": [
        "1/2",
        "5/4",
        "2",
        "11/4",
        "7/2"
      ],
      "F": [
        "4/3",
        "8/9",
        "2/3",
        "8/15",
        "4/9"
      ],
      "u": [
        "3/8",
        "45/32",
        "3",
        "165/32",
        "63/8"
      ],
      "readout_micromolar": [
        0.0033797089609090463,
        0.026742835496517278,
        0.07295005284246274,
        0.1380190885606943,
        0.21615668846376326
      ],
      "S3_micromolar": [
        0.0014484466975324484,
        0.014157971733450325,
        0.04377003170547764,
        0.09001244906132237,
        0.14964693816722072
      ],
      "slopes": [
        -0.2923502653749346,
        0.0205035687751477,
        -0.007722774773992059,
        0.010015899084939123,
        -0.08439153213966638
      ],
      "unimolecular_spread": 33445.66681015928,
      "rates_physical": [
        [
          2.0,
          5.9618359158601435e-06,
          0.0019733258203581943,
          0.17189038363723524,
          0.04272722386813793,
          0.19939757761869914
        ],
        [
          1.8687518643314975,
          0.0007831833237902356,
          0.016299892270144715,
          1.9962620549011472,
          0.026810151901967574,
          0.19193363014912332
        ],
        [
          0.21784288343500138,
          0.012676902732563564,
          0.03832034158143834,
          1.9999995459333244,
          0.012703775412552928,
          0.1872961791807795
        ]
      ],
      "D": [
        "1",
        "505005048/38591245",
        "48362752/38591245"
      ],
      "B": [
        "111414528/1102607",
        "5946508756/38591245",
        "236379904/38591245"
      ],
      "N": [
        "10165/4",
        "1926",
        "64"
      ],
      "J": [
        "385/2",
        "3562",
        "768"
      ]
    },
    "sharpened_certificate": [
      {
        "index": 0,
        "M": 5846.111404,
        "c": 0.9851578900613179,
        "tenfold_seconds": 356051.23582593206,
        "margin_per_second": 8.425753650428707e-06,
        "old_tenfold_seconds": 12000000.0,
        "initial_radius": "1/16384000000",
        "M_exact": "1461527851/250000",
        "c_exact": "145328706557919795738200856652951977017906713348296860215415578415070659372549966905706916126497068518796501570986655871171030380578575525468020010699522030388281656686731039503788471774227646587932242542009158882939856627805511725142898028807245900895900601403855446869234183163639600499077498724723533291287783039058223737167908907669692425427927980479981305315509520136641719800106586798633287/147518187717985264629029662871450618248297804654867439360424533064196965264232620940555528919100246603253139536304228791805554875655870391721042474498140050757606931496157285101009613438702403145840099756586334344176951797052448987570758761747296683351880455610313709240839881864807535774833312099179458870266117962264125303783964746002232474758026570409199588515600429133437337600000000000000000"
      },
      {
        "index": 2,
        "M": 535109.885606,
        "c": 0.9753715791079702,
        "tenfold_seconds": 32917294.11033609,
        "margin_per_second": 9.113750328153475e-08,
        "old_tenfold_seconds": 1200000000.0,
        "initial_radius": "1/327680000000",
        "M_exact": "267554942803/500000",
        "c_exact": "2313420339089540192561208978756556878652132333783377953977603237309733852100519015643643880949575727617939337589710945882233864690643091334453384923329461471309539060259439463862583634237265311178207991671970124297000712496016409172492231098762644568365016468017855760446206638257993793024276551843986844268013585858308908996828547066676913655720639507834006074512307335229863958871689631417751859416013479/2371834886972293759807356663340487578848094772830564478699949075620927899269630752084563379314149251945105737883692422216313142888340473333639154054712602729861383804113812612901146974517873148383968023918225436596139463664037998797598263048494918468334179369652401438989145016876614416422302191863415327731624349350418221107831806668042560930943823284832902024714881512569532020809741107200000000000000000"
      },
      {
        "index": 4,
        "M": 383168.493033,
        "c": 0.9811170028297717,
        "tenfold_seconds": 23432587.05706978,
        "margin_per_second": 1.2802683684449937e-07,
        "old_tenfold_seconds": 1200000000.0,
        "initial_radius": "1/40960000000",
        "M_exact": "383168493033/1000000",
        "c_exact": "390391618960160560848407330506436102114539076028171632905800972471658874124172427557686801503784664104351904762226836122673373930778307533649171765975183222533224810177025240176172054706813283787235201336323362346879785134133858998951511585538531590850128524479152036179478524190177139141100505093626053667549304744618008693609886598680472583430200524459893820003559169405399541797046566680347643819/397905262913780449054944299661547063862403588391038724741018604082590549329007434883146588782394115748134894419481894824607627478457439971670653869033010226804262120084226044390136808097138614088760037713211328967275899787021273788293864738683900976805929970791949664238890281526317678471063484088179828894023803261912877092341144466099570260741641883465218500370410610597023029657600000000000000000"
      }
    ],
    "readout_intervals_micromolar": [
      [
        0.002379708857768514,
        0.004379709064049579
      ],
      [
        0.07195005172933326,
        0.0739500539555922
      ],
      [
        0.21515666207744877,
        0.2171567148500778
      ]
    ],
    "refinement_gaps": [
      {
        "xs": [
          "2",
          "3",
          "4",
          "5",
          "6"
        ],
        "r": "5",
        "gap": 7.950517931443828e-05
      },
      {
        "xs": [
          "3/2",
          "5/2",
          "7/2",
          "9/2",
          "11/2"
        ],
        "r": "4",
        "gap": 9.76711399446246e-05
      },
      {
        "xs": [
          "2",
          "7/2",
          "5",
          "13/2",
          "8"
        ],
        "r": "9",
        "gap": 0.0001257838012306314
      }
    ]
  },
  "checks": 2365,
  "full": true,
  "scope": "Fresh exact arithmetic and rational-interval replay, not a Lean compilation or a new proof of the universal upper bound."
}
