{
  "date": "2026-10-08",
  "scope": "Massless additional bulk Dirac fields; flat Wilson background; alpha-dependent one-loop terms; large R5/R6 limit. No global minimum or physical validity certificate.",
  "source": "https://arxiv.org/pdf/2503.04090v1",
  "paper_sha256": "1b2f8e75c93e50a68ff2a33afeac659694629cb6e9ec553b0fcf3b993c109e02",
  "lab_input_sha256": "17b8d5d7c92310c3646a54486d41c8bffc3327551cd0cb5135a34c82fe6427f8",
  "python": "3.14.2",
  "sympy": "1.14.0",
  "mpmath": "1.3.0",
  "fundamental_simultaneous_weights_q_p6_B": [
    [
      0,
      1,
      1
    ],
    [
      0,
      1,
      1
    ],
    [
      0,
      1,
      1
    ],
    [
      0,
      -1,
      -1
    ],
    [
      0,
      -1,
      1
    ],
    [
      1,
      -1,
      -1
    ],
    [
      -1,
      -1,
      -1
    ]
  ],
  "representations": {
    "7": [
      {
        "q": -1,
        "p6": -1,
        "B": -1,
        "count": 1
      },
      {
        "q": 0,
        "p6": -1,
        "B": -1,
        "count": 1
      },
      {
        "q": 0,
        "p6": -1,
        "B": 1,
        "count": 1
      },
      {
        "q": 0,
        "p6": 1,
        "B": 1,
        "count": 3
      },
      {
        "q": 1,
        "p6": -1,
        "B": -1,
        "count": 1
      }
    ],
    "28": [
      {
        "q": -2,
        "p6": 1,
        "B": 1,
        "count": 1
      },
      {
        "q": -1,
        "p6": -1,
        "B": -1,
        "count": 3
      },
      {
        "q": -1,
        "p6": 1,
        "B": -1,
        "count": 1
      },
      {
        "q": -1,
        "p6": 1,
        "B": 1,
        "count": 1
      },
      {
        "q": 0,
        "p6": -1,
        "B": -1,
        "count": 3
      },
      {
        "q": 0,
        "p6": -1,
        "B": 1,
        "count": 3
      },
      {
        "q": 0,
        "p6": 1,
        "B": -1,
        "count": 1
      },
      {
        "q": 0,
        "p6": 1,
        "B": 1,
        "count": 9
      },
      {
        "q": 1,
        "p6": -1,
        "B": -1,
        "count": 3
      },
      {
        "q": 1,
        "p6": 1,
        "B": -1,
        "count": 1
      },
      {
        "q": 1,
        "p6": 1,
        "B": 1,
        "count": 1
      },
      {
        "q": 2,
        "p6": 1,
        "B": 1,
        "count": 1
      }
    ],
    "84": [
      {
        "q": -3,
        "p6": -1,
        "B": -1,
        "count": 1
      },
      {
        "q": -2,
        "p6": -1,
        "B": -1,
        "count": 1
      },
      {
        "q": -2,
        "p6": -1,
        "B": 1,
        "count": 1
      },
      {
        "q": -2,
        "p6": 1,
        "B": 1,
        "count": 3
      },
      {
        "q": -1,
        "p6": -1,
        "B": -1,
        "count": 9
      },
      {
        "q": -1,
        "p6": -1,
        "B": 1,
        "count": 1
      },
      {
        "q": -1,
        "p6": 1,
        "B": -1,
        "count": 3
      },
      {
        "q": -1,
        "p6": 1,
        "B": 1,
        "count": 3
      },
      {
        "q": 0,
        "p6": -1,
        "B": -1,
        "count": 9
      },
      {
        "q": 0,
        "p6": -1,
        "B": 1,
        "count": 9
      },
      {
        "q": 0,
        "p6": 1,
        "B": -1,
        "count": 3
      },
      {
        "q": 0,
        "p6": 1,
        "B": 1,
        "count": 19
      },
      {
        "q": 1,
        "p6": -1,
        "B": -1,
        "count": 9
      },
      {
        "q": 1,
        "p6": -1,
        "B": 1,
        "count": 1
      },
      {
        "q": 1,
        "p6": 1,
        "B": -1,
        "count": 3
      },
      {
        "q": 1,
        "p6": 1,
        "B": 1,
        "count": 3
      },
      {
        "q": 2,
        "p6": -1,
        "B": -1,
        "count": 1
      },
      {
        "q": 2,
        "p6": -1,
        "B": 1,
        "count": 1
      },
      {
        "q": 2,
        "p6": 1,
        "B": 1,
        "count": 3
      },
      {
        "q": 3,
        "p6": -1,
        "B": -1,
        "count": 1
      }
    ],
    "48": [
      {
        "q": -2,
        "p6": 1,
        "B": 1,
        "count": 1
      },
      {
        "q": -1,
        "p6": -1,
        "B": -1,
        "count": 6
      },
      {
        "q": -1,
        "p6": 1,
        "B": -1,
        "count": 2
      },
      {
        "q": -1,
        "p6": 1,
        "B": 1,
        "count": 2
      },
      {
        "q": 0,
        "p6": -1,
        "B": -1,
        "count": 6
      },
      {
        "q": 0,
        "p6": -1,
        "B": 1,
        "count": 6
      },
      {
        "q": 0,
        "p6": 1,
        "B": -1,
        "count": 2
      },
      {
        "q": 0,
        "p6": 1,
        "B": 1,
        "count": 12
      },
      {
        "q": 1,
        "p6": -1,
        "B": -1,
        "count": 6
      },
      {
        "q": 1,
        "p6": 1,
        "B": -1,
        "count": 2
      },
      {
        "q": 1,
        "p6": 1,
        "B": 1,
        "count": 2
      },
      {
        "q": 2,
        "p6": 1,
        "B": 1,
        "count": 1
      }
    ]
  },
  "coefficient_comparisons": [
    {
      "representation": "7",
      "eta_eta_prime": 1,
      "terms": [
        [
          "1",
          -1,
          1
        ]
      ],
      "matches_lab": true
    },
    {
      "representation": "7",
      "eta_eta_prime": -1,
      "terms": [
        [
          "1",
          1,
          1
        ]
      ],
      "matches_lab": true
    },
    {
      "representation": "28",
      "eta_eta_prime": 1,
      "terms": [
        [
          "4",
          -1,
          1
        ],
        [
          "1",
          1,
          1
        ],
        [
          "1",
          1,
          2
        ]
      ],
      "matches_lab": true
    },
    {
      "representation": "28",
      "eta_eta_prime": -1,
      "terms": [
        [
          "1",
          -1,
          1
        ],
        [
          "1",
          -1,
          2
        ],
        [
          "4",
          1,
          1
        ]
      ],
      "matches_lab": true
    },
    {
      "representation": "48",
      "eta_eta_prime": 1,
      "terms": [
        [
          "8",
          -1,
          1
        ],
        [
          "2",
          1,
          1
        ],
        [
          "1",
          1,
          2
        ]
      ],
      "matches_lab": true
    },
    {
      "representation": "48",
      "eta_eta_prime": -1,
      "terms": [
        [
          "2",
          -1,
          1
        ],
        [
          "1",
          -1,
          2
        ],
        [
          "8",
          1,
          1
        ]
      ],
      "matches_lab": true
    },
    {
      "representation": "84",
      "eta_eta_prime": 1,
      "terms": [
        [
          "12",
          -1,
          1
        ],
        [
          "1",
          -1,
          2
        ],
        [
          "1",
          -1,
          3
        ],
        [
          "4",
          1,
          1
        ],
        [
          "4",
          1,
          2
        ]
      ],
      "matches_lab": true
    },
    {
      "representation": "84",
      "eta_eta_prime": -1,
      "terms": [
        [
          "4",
          -1,
          1
        ],
        [
          "4",
          -1,
          2
        ],
        [
          "12",
          1,
          1
        ],
        [
          "1",
          1,
          2
        ],
        [
          "1",
          1,
          3
        ]
      ],
      "matches_lab": true
    }
  ],
  "printed_gauge": [
    [
      "-7/2",
      -1,
      1
    ],
    [
      "-2",
      1,
      1
    ],
    [
      "-1",
      1,
      2
    ]
  ],
  "candidate_gauge": [
    [
      "-3",
      -1,
      1
    ],
    [
      "-3/2",
      1,
      1
    ],
    [
      "-3/4",
      1,
      2
    ]
  ],
  "certificate_arithmetic": {
    "type": "integer fixed-point outward intervals",
    "decimal_places": 50,
    "pi_method": "Machin identity with rational alternating series bounds, 80 terms",
    "pi_interval": [
      "3.14159265358979323846264338327950288419716939937484",
      "3.14159265358979323846264338327950288419716939937544"
    ],
    "trig_method": "exact rational phase reduction, Taylor polynomial plus analytic remainder",
    "rounding_halfwidth": "1/2000",
    "exclusion_fourier_cutoff": 512
  },
  "rows": [
    {
      "row": "(1)",
      "published_alpha": "43/1000",
      "published_rounding_box": [
        "17/400",
        "87/2000"
      ],
      "terms": [
        [
          "91/2",
          -1,
          1
        ],
        [
          "5",
          -1,
          2
        ],
        [
          "4",
          -1,
          3
        ],
        [
          "18",
          1,
          1
        ],
        [
          "15",
          1,
          2
        ]
      ],
      "derivative_over_rounding_box": [
        "-0.30537842027146549836425350457651364934213403578475",
        "-0.28494480665671425939185115546714628743378808577835"
      ],
      "candidate_derivative_over_rounding_box": [
        "-0.85495373823769312190438788922173352337229607931112",
        "-0.84669020404771401478938076539636221305685566957081"
      ],
      "required_relative_fermion_factor_interval": [
        "0.83397592113325919560263870905867640317223779616420",
        "0.86272797016006763272344405427641899475247301924297"
      ],
      "finite_cutoffs": {
        "tested_cutoffs": [
          1,
          64
        ],
        "not_excluded_cutoffs": [],
        "derivative_intervals": [
          [
            "9.61913566946050549493284967021310955086849757670190",
            "9.83836628881385067136086501749132962471269477463650"
          ],
          [
            "0.63889620776071888374669989456770030789251287317207",
            "0.66738847703392241774147342634233463460098409497933"
          ],
          [
            "0.93183049797433806853741280640931385707777914601275",
            "0.96405901145734554065915180542504341649279857036145"
          ],
          [
            "-0.04225992266375286504683086006942918746478590923453",
            "-0.02395687535377489424463950733098203373789110706132"
          ],
          [
            "0.00034776153518007128569125145539745504050397395613",
            "0.01840590814760444495874874615743599151883730384952"
          ],
          [
            "-0.22671407129548224347613918006241726692488532617622",
            "-0.20922425636797936605557105320153279049647089190842"
          ],
          [
            "-0.21758200052128920809405968818700305598922497535264",
            "-0.20025469677047301776405476280776985534485220537629"
          ],
          [
            "-0.28559818778605265078838662112135609253318654432913",
            "-0.26729782997880251311606780250162760615836792254045"
          ],
          [
            "-0.28233459491006550971817685388779196405176423414629",
            "-0.26392050228575735852984101721606741305327717531082"
          ],
          [
            "-0.30457269392583633931488671628001563211373075175305",
            "-0.28536312379719286057163884892105029265361313900221"
          ],
          [
            "-0.30203083940888736188388898918137852379943233143189",
            "-0.28257884269592634194717498993334095606710695428938"
          ],
          [
            "-0.30945455755071805810006556456857599446588044976731",
            "-0.28956060775266475510934376589392678114031707694393"
          ],
          [
            "-0.30692063673610662378532644832299391217782645939808",
            "-0.28679660347863640468159446210375433589500825582756"
          ],
          [
            "-0.30942984885255406078128855511443564056209117433265",
            "-0.28910939922085751724883005128573763856286355462439"
          ],
          [
            "-0.30713735725512202034930939862121434581977922359317",
            "-0.28667750501409702023137476437626271084974609409190"
          ],
          [
            "-0.30804346265483712976627957532839182116945642936902",
            "-0.28751019282804425557992590859999518031047534096683"
          ],
          [
            "-0.30628172084752892695858234714484125263631076103265",
            "-0.28571611623259033549678901813009509433947646945397"
          ],
          [
            "-0.30665578418251414439718740199518881295213860514253",
            "-0.28606134324408450846802323664907019392815665390810"
          ],
          [
            "-0.30554501965190472687705039558102875050434938241790",
            "-0.28499936579433854742472720270508606374423965541651"
          ],
          [
            "-0.30570845597132905587231379822079749691806112074595",
            "-0.28514378408362905948308076016816148260717701577206"
          ],
          [
            "-0.30519352706231709450709687802253116453749077397666",
            "-0.28471518490381287505262524396057805789625208944447"
          ],
          [
            "-0.30524579554266351556819928011666797573265375661358",
            "-0.28475022547683066651674876802524002265801910293436"
          ],
          [
            "-0.30516382702599519312105569792761787666586615398448",
            "-0.28475196631819133430842381589779159873387420012219"
          ],
          [
            "-0.30515221305514767329060195926240306473426934544090",
            "-0.28472666875983492560382156253821853268941448631296"
          ],
          [
            "-0.30531119884794799160620717395827655219054732071823",
            "-0.28494234874924907323014153746156026641855080969379"
          ],
          [
            "-0.30526931571761956304705778431278161957280859603279",
            "-0.28489141094051680745949525208095488418854640300146"
          ],
          [
            "-0.30550730250836107443233925070949310857977575900966",
            "-0.28515306456551494025936851210184871325070986352742"
          ],
          [
            "-0.30545516488206812469216415582448152688335150015149",
            "-0.28509387235833851743735960152314194100854467994818"
          ],
          [
            "-0.30566915879916037940016370851011387132751325719220",
            "-0.28530610827189519032379261903646010931964549836320"
          ],
          [
            "-0.30561104847306675633557954044146098760965690537078",
            "-0.28523857590151116181612967636644851065301909146865"
          ],
          [
            "-0.30575811654332476663906509997453985797150260895837",
            "-0.28537167913440334709409743711963818985918469727913"
          ],
          [
            "-0.30568761431762219997720644060856128734629184824529",
            "-0.28528674644341124699267869388384799783005937277530"
          ],
          [
            "-0.30576822996902200741007943319866516073302700135576",
            "-0.28535283443604559892664308499997674131383019349772"
          ],
          [
            "-0.30567779510856565546540523274965720636386473920745",
            "-0.28524415045688585122548518699880691851645504414722"
          ],
          [
            "-0.30571340647144315410180330759826307422930063310906",
            "-0.28527084950796371628280580894789535258400018992756"
          ],
          [
            "-0.30560268105429483195201849746905894841752580302946",
            "-0.28514265385738452232132320515415300703667333516545"
          ],
          [
            "-0.30561698659539082347643896726391880432855543372565",
            "-0.28515419923131030101958245413682047724646025653843"
          ],
          [
            "-0.30549573371246226888658953997844538546347939553064",
            "-0.28502185959299664522578425331150479008919099116801"
          ],
          [
            "-0.30550438417287347792426758995535811172718448534615",
            "-0.28503110958202878195226882864452896430217204316801"
          ],
          [
            "-0.30538949601480360100405544755889659598670209546261",
            "-0.28491528672271950421423223888655331002683453608324"
          ],
          [
            "-0.30539819686654645848258888303282817105599515992947",
            "-0.28492473141673830826276886277850296961382697722723"
          ],
          [
            "-0.30530717896411906536903869153234965491286288480288",
            "-0.28484310070152232995497262209134339463385945151587"
          ],
          [
            "-0.30531509358481370081000677624210852619677457073881",
            "-0.28485021440317557449903342269951962405921031174573"
          ],
          [
            "-0.30525960313416624491508040871192763260237407390062",
            "-0.28481106783966440035897205674130265162260126505527"
          ],
          [
            "-0.30526414187180624134754329177884061142344086468945",
            "-0.28481347595233218180743273478907388922764249791945"
          ],
          [
            "-0.30524644947521222870196117488471593353888404763713",
            "-0.28481381343179473957064903968478504882058273362696"
          ],
          [
            "-0.30524655446521448871383236923449864759584480223688",
            "-0.28481172391335349945372522124323024357220780898978"
          ],
          [
            "-0.30525996872973665770680859849230274950295809249086",
            "-0.28483990675478710947566237834462836441256355411681"
          ],
          [
            "-0.30525686211962791854603940821105041909744839604798",
            "-0.28483563747516438194739277483815427438312718826900"
          ],
          [
            "-0.30528926433905815181351258796446156711842107008970",
            "-0.28487666441620042666410081805403339313997787355711"
          ],
          [
            "-0.30528527366328888758986837723873769960496542319619",
            "-0.28487269357579316414138345668575064829520428441549"
          ],
          [
            "-0.30532379161415196656823211600990179339572952916522",
            "-0.28491345590479266881052183636894811792018099672691"
          ],
          [
            "-0.30532065050798910737236618196541519107980088731463",
            "-0.28491074824762889267179483279033482496314079792885"
          ],
          [
            "-0.30535546459487461971162375752259822330970072675681",
            "-0.28494323842767532534211604314011987798607906862846"
          ],
          [
            "-0.30535332140175676905624719198570935554278628143144",
            "-0.28494089588065359596083930953840206743699385388904"
          ],
          [
            "-0.30537941168059314074426696846529230144013293272934",
            "-0.28496269521440966459902283909697939886885949777839"
          ],
          [
            "-0.30537702578136715753684073697076221987192699726173",
            "-0.28495890795185516938810740556283481634719582798739"
          ],
          [
            "-0.30539378663517177792484270671111452631388672209098",
            "-0.28497158255770443976147013239510634733365149418577"
          ],
          [
            "-0.30538958845790878754301446431373633471210196233093",
            "-0.28496507600822075654545701940354121026764570162329"
          ],
          [
            "-0.30539910539559523079132746570401902626089949414471",
            "-0.28497179415244083409796483098511804603740563888448"
          ],
          [
            "-0.30539236133588006468539426488429790381592112503792",
            "-0.28496282087147523897560068062017056326636545864758"
          ],
          [
            "-0.30539744810837216658367988263619124361136005525640",
            "-0.28496641990981293027461519555111079242422975564243"
          ],
          [
            "-0.30538884198725360441985969913398282307438524056499",
            "-0.28495676478068061519524558624935476501593434234205"
          ],
          [
            "-0.30539168747452142477737712305830859240295513130614",
            "-0.28495888718142904173959604070845806395081360105817"
          ]
        ],
        "all_N_at_least_64_interval": [
          "-0.30583981293032172639037964810929052335428610114530",
          "-0.28448341399785803136572501193436941342163602041780"
        ],
        "all_N_at_least_64_excluded": true
      },
      "finite_k_at_least_10_derivative_error_bound": [
        "0.00000000000000000002160459457264002141034985503234",
        "0.00000000000000000002160459457264002141034985503235"
      ],
      "printed_local_minimum": {
        "numerical_alpha": "0.05530397929425407273244049",
        "certified_alpha_interval": [
          "55302979294254073/1000000000000000000",
          "55304979294254073/1000000000000000000"
        ],
        "certified_halfwidth": "1/1000000",
        "left_derivative": [
          "-0.00003192668113857337144392127023394150945879516853",
          "-0.00003170139175436622885303936421207780144504514033"
        ],
        "right_derivative": [
          "0.00003170203267055551621397372163255814165318849536",
          "0.00003192732205476265880485562765442184966693853134"
        ],
        "curvature_interval": [
          "31.79660455534710815589110774967789431021253789760139",
          "31.83210925420324017386563372849263871661809632251814"
        ],
        "numeric_curvature": "31.81435643594018687552",
        "cutoff": 1024,
        "global_minimum_certified": false
      },
      "candidate_local_minimum": {
        "numerical_alpha": "0.07611854895855868098882581",
        "certified_alpha_interval": [
          "76117548958558681/1000000000000000000",
          "76119548958558681/1000000000000000000"
        ],
        "certified_halfwidth": "1/1000000",
        "left_derivative": [
          "-0.00004709504798891314473534142899571294805603165188",
          "-0.00004686683276854746782509742029824062045768743833"
        ],
        "right_derivative": [
          "0.00004686888315620999360562760251307010139314107409",
          "0.00004709709837657567051587161121054242899148528308"
        ],
        "curvature_interval": [
          "46.96405080218518394331274548120390630213045269698927",
          "46.99988034550256206076158147780841497725546618810126"
        ],
        "numeric_curvature": "46.98196587911669507272",
        "cutoff": 1024,
        "global_minimum_certified": false
      }
    },
    {
      "row": "(2)",
      "published_alpha": "81/1000",
      "published_rounding_box": [
        "161/2000",
        "163/2000"
      ],
      "terms": [
        [
          "97/2",
          -1,
          1
        ],
        [
          "4",
          -1,
          2
        ],
        [
          "4",
          -1,
          3
        ],
        [
          "15",
          1,
          1
        ],
        [
          "16",
          1,
          2
        ]
      ],
      "derivative_over_rounding_box": [
        "-0.14222191713352211274243552836608325425175384433078",
        "-0.08441762263749674791039727307526404468868850747521"
      ],
      "candidate_derivative_over_rounding_box": [
        "-1.12077862610064810022996514015604417411133437892580",
        "-1.07315201579920393878949033442318407472523015383063"
      ],
      "required_relative_fermion_factor_interval": [
        "0.95238976578168635851162108306780504890923084043832",
        "0.97154558267394897204774593550082733238816859367549"
      ],
      "finite_cutoffs": {
        "tested_cutoffs": [
          1,
          64
        ],
        "not_excluded_cutoffs": [],
        "derivative_intervals": [
          [
            "15.73634613261234573215765135900301453264854843204531",
            "15.90356019151353477850466657530564640036501857933032"
          ],
          [
            "0.68470360907289622870918469009713541446761233553904",
            "0.72972087632583265284580428272849266348369755736945"
          ],
          [
            "1.00346166768296588112325139836817396881018004527194",
            "1.04788328296720974709148733478024217900291003028301"
          ],
          [
            "-0.11434629940023685055200380581808336809686745093911",
            "-0.06400556186996891319823019412535732075642654137054"
          ],
          [
            "-0.05976980766871799723246574306649554142253763348686",
            "-0.00773507304721858539902513798790292916616220451512"
          ],
          [
            "-0.19509667387031792720869300680687829981460002575756",
            "-0.13933182141174447469796263436491083348679953584959"
          ],
          [
            "-0.15290722516478306988507400290242643527395092830346",
            "-0.09547169021179878482900377832498073081440424403856"
          ],
          [
            "-0.17063194478344036698518527466408555011021607412392",
            "-0.11240876110055517708842748862526607166447551745326"
          ],
          [
            "-0.14408573625218555877322309863479310376425539619591",
            "-0.08567024446469532078887736842230751540247601828750"
          ],
          [
            "-0.14736909527065344285433402765030598029586998214566",
            "-0.08880342269160140369844677297189263107242544512601"
          ],
          [
            "-0.13917008456783927641698638550449939629229173039253",
            "-0.08125211210090159153979212873999345073444053225386"
          ],
          [
            "-0.13948376661631277563282906633092016846030827343572",
            "-0.08145588584399988920683570684956850614786955237113"
          ],
          [
            "-0.14134260822809095671021479647038880229741756613549",
            "-0.08380888645009410312118894869169337804436779997044"
          ],
          [
            "-0.14075342816541273317553213796947372832937180626640",
            "-0.08316365309101638564080477373146775850557630049666"
          ],
          [
            "-0.14414507013812245055114664099056211313899140916374",
            "-0.08661605522630243525224234170507752279928431124432"
          ],
          [
            "-0.14337729289499564838872016311213568781797133544360",
            "-0.08578328199122469098625567882781816625990966260496"
          ],
          [
            "-0.14504914448416290581818251223991769552163506442069",
            "-0.08734518008133730788092596581354420261207000273039"
          ],
          [
            "-0.14386958313132679379215958256818282802123219616383",
            "-0.08604427295069540162898561526667183162541550914837"
          ],
          [
            "-0.14428792631929946356150991714040069434670934172437",
            "-0.08640833421857871069314905504182133148757532470272"
          ],
          [
            "-0.14273298949520746220480959865367727323433169961221",
            "-0.08477010366389659312626918894142417567550034988463"
          ],
          [
            "-0.14286206477119724318793575586575172226518016534685",
            "-0.08489897658506031819041874469642359796712893493734"
          ],
          [
            "-0.14163284245301110173998533175073946283410899752267",
            "-0.08371462750956400049068599171015987406004602709572"
          ],
          [
            "-0.14171860127428632231325565576183743427069355705336",
            "-0.08379301126605473087028095951380344222610742716926"
          ],
          [
            "-0.14136537146421985882539787092198244509268416660647",
            "-0.08356023845476438667536715506456050056735200834302"
          ],
          [
            "-0.14135852809273581735571032171084563382659335370997",
            "-0.08354013475183223925111575741594837488700665008877"
          ],
          [
            "-0.14170053006484707995806347982531700438931455612454",
            "-0.08396209699790169887422911117866975413919736334051"
          ],
          [
            "-0.14165266385895053207924230398242304000394411655640",
            "-0.08391296788923961557024293826583842707485641604252"
          ],
          [
            "-0.14213245755195183385676999260033539015848606927406",
            "-0.08439450379301153482265180780379718644999911706173"
          ],
          [
            "-0.14209611652378830264471085437134991480268440973786",
            "-0.08435506164570626696760991522395743583053029527936"
          ],
          [
            "-0.14238048166601183544905186539702231550050659580606",
            "-0.08460996465813960245510233252047277028903283120249"
          ],
          [
            "-0.14230991206730891057993410882310310710902773213569",
            "-0.08452268008087806715496978424983493957609340795474"
          ],
          [
            "-0.14241220835008594666421120779224365702245804030795",
            "-0.08460761147542319386959179265996118195983622480103"
          ],
          [
            "-0.14228369611856448383040472738128151910387057822342",
            "-0.08446785584013214186972807266146690542101366268003"
          ],
          [
            "-0.14231698135358108489085195848030492643274612576321",
            "-0.08449637671662620678696980492799708266576375009617"
          ],
          [
            "-0.14220763996565433254148358163191243844935485650377",
            "-0.08439948854971063826702480141923398960375075298872"
          ],
          [
            "-0.14221876073624656959116469907145326506696791918685",
            "-0.08440691091375440199992885044483804413814535701813"
          ],
          [
            "-0.14220545964236178532177460883984743567818107229091",
            "-0.08441649963213858487861101686572456581600690320588"
          ],
          [
            "-0.14220008498638547730280451854902897987923727787409",
            "-0.08440793731183376849513397465861345929183482951349"
          ],
          [
            "-0.14226071296646593563687231118471367666506251928300",
            "-0.08447821204881946267255070393399441170470728703875"
          ],
          [
            "-0.14224642508392451460981158303194916312236248531598",
            "-0.08446109914582244960290768420780707410703918651747"
          ],
          [
            "-0.14230631661013108479998849336279458532812147612198",
            "-0.08451546226901916607782063941176112948085465534360"
          ],
          [
            "-0.14227956919543842685872909395497691584994497140228",
            "-0.08448127757830106348248952935885678050030031373583"
          ],
          [
            "-0.14230498218438052694725506742755088475195074788556",
            "-0.08450027508616502475384609169694810097748905237966"
          ],
          [
            "-0.14225270446666201478119501214232578238700793320936",
            "-0.08443857097789717817939319315869514602584205235533"
          ],
          [
            "-0.14225984187956287856150419432965852334607362069746",
            "-0.08444474385241134790689886339459155705972353109950"
          ],
          [
            "-0.14219389718768923131098452804568766755939313831849",
            "-0.08437868326231831843207720492078421411196439956652"
          ],
          [
            "-0.14219929393146252442100373310490282832362896134173",
            "-0.08438390322820359142988901705779005722190495036863"
          ],
          [
            "-0.14215867178871489780931660628250789658722000064965",
            "-0.08435562729954826372214963938728008263282579481312"
          ],
          [
            "-0.14216066830999608591475062484349270693683447677127",
            "-0.08435588533866709843766600885115925503246428673677"
          ],
          [
            "-0.14216786700652829674568938417736350671310652999779",
            "-0.08437657609754278799543256930543993992987076606070"
          ],
          [
            "-0.14216492521798083846693534750075918573293479853000",
            "-0.08437289475539681787957199331916588216053650974230"
          ],
          [
            "-0.14220128204307969502828258423362171492625251568734",
            "-0.08441303717366735346071896212968029536068008147443"
          ],
          [
            "-0.14219809137970494289356571123665065830213939837801",
            "-0.08440986884175620707391300616835150145412315554381"
          ],
          [
            "-0.14223063652924259060916981161567807395790287699868",
            "-0.08443833265442194008624478284901165094945838802731"
          ],
          [
            "-0.14222637146144482994112719800291271657174206824958",
            "-0.08443193202839132926323680758522877600085790711894"
          ],
          [
            "-0.14224210161660191598385952238970098670158061384479",
            "-0.08444355132681414370883582408130965825464774918567"
          ],
          [
            "-0.14223110245729446608769532419886695529627462665519",
            "-0.08442958408856724924700254231782240351512836171034"
          ],
          [
            "-0.14223659554423080071725387891319526320912017803776",
            "-0.08443364894288228403275957860408502190121528815188"
          ],
          [
            "-0.14222180315381974210708827155387044103509812333816",
            "-0.08441966403867428989597221425401820874670156144459"
          ],
          [
            "-0.14222405567665379329143608942814775059021523588510",
            "-0.08442121219002190341599003786249206172586406739990"
          ],
          [
            "-0.14221689155632577282668075452369821649659620659751",
            "-0.08441875464966547230754222379122864387104660996374"
          ],
          [
            "-0.14221700625871439850926282172954161771917270057063",
            "-0.08441806843053226273883353506082172763550475591989"
          ],
          [
            "-0.14222220765941836254579055171493213278047409536957",
            "-0.08442683737740294447925197370861844656965577297890"
          ],
          [
            "-0.14222063303479697003691711250489784534891336076375",
            "-0.08442469441102860111454985096291730861447587861097"
          ]
        ],
        "all_N_at_least_64_interval": [
          "-0.14268330979237834076856167189886012826390590969133",
          "-0.08395622997864051988427112954248717067653644211466"
        ],
        "all_N_at_least_64_excluded": true
      },
      "finite_k_at_least_10_derivative_error_bound": [
        "0.00000000000000000002160459457264002141034985503234",
        "0.00000000000000000002160459457264002141034985503235"
      ],
      "printed_local_minimum": {
        "numerical_alpha": "0.08306176126444370481697011",
        "certified_alpha_interval": [
          "16612152252888741/200000000000000000",
          "16612552252888741/200000000000000000"
        ],
        "certified_halfwidth": "1/1000000",
        "left_derivative": [
          "-0.00005645927809915503592951937892615783676339992022",
          "-0.00005623398871494789333863747290429412874964986141"
        ],
        "right_derivative": [
          "0.00005623536062286568390902715124917007059363535180",
          "0.00005646065000707282649990905727103377860738541298"
        ],
        "curvature_interval": [
          "56.32956701295771217766510970104199262316926350393593",
          "56.36507171181384419563963567985673702957482192898584"
        ],
        "numeric_curvature": "56.34731959371757416063",
        "cutoff": 1024,
        "global_minimum_certified": false
      },
      "candidate_local_minimum": {
        "numerical_alpha": "0.1004043348609135921884494",
        "certified_alpha_interval": [
          "10040333486091359/100000000000000000",
          "10040533486091359/100000000000000000"
        ],
        "certified_halfwidth": "1/1000000",
        "left_derivative": [
          "-0.00006921258962843384266345378382902148562302794831",
          "-0.00006898437440806816575320977513154915802468371594"
        ],
        "right_derivative": [
          "0.00006898546365409335327192921303846795151476077760",
          "0.00006921367887445903018217322173594027911310501404"
        ],
        "curvature_interval": [
          "69.08111187154724335968622308118575962852074741739135",
          "69.11694141486462147713505907779026830364576090866438"
        ],
        "numeric_curvature": "69.09902589729915659753",
        "cutoff": 1024,
        "global_minimum_certified": false
      }
    },
    {
      "row": "(3)",
      "published_alpha": "21/1000",
      "published_rounding_box": [
        "41/2000",
        "43/2000"
      ],
      "terms": [
        [
          "97/2",
          -1,
          1
        ],
        [
          "2",
          -1,
          2
        ],
        [
          "2",
          -1,
          3
        ],
        [
          "13",
          1,
          1
        ],
        [
          "11",
          1,
          2
        ]
      ],
      "derivative_over_rounding_box": [
        "-0.19716099469647015459260214431033375930487744354960",
        "-0.19190943666818692252002117909155792464357606756778"
      ],
      "candidate_derivative_over_rounding_box": [
        "-0.48135531157716238578585563448982640326019429824894",
        "-0.46305938785169256584334299970109570376169236857499"
      ],
      "required_relative_fermion_factor_interval": [
        "0.77459664429065727115693938228722898916824883909317",
        "0.84742583829319619965933341202912300403012158405327"
      ],
      "finite_cutoffs": {
        "tested_cutoffs": [
          1,
          64
        ],
        "not_excluded_cutoffs": [],
        "derivative_intervals": [
          [
            "3.53187837299795501217018094331739041635126009558297",
            "3.70625327987944678523742882203745904173634275994811"
          ],
          [
            "0.23611612264625276116899553885524933431513739851782",
            "0.25285694791899993753741402437080531796838359402037"
          ],
          [
            "0.36484269859728672993718903199384217261448857021748",
            "0.38761856722687719187074316279949013783198800102811"
          ],
          [
            "-0.03608339651414336832967901875118577403404583628383",
            "-0.03134156019009274633612811854482004531132552800286"
          ],
          [
            "-0.00912302105258036484264275741094457645347483773311",
            "-0.00319502720633972620686715268479498040782818489984"
          ],
          [
            "-0.12409594423333003782030831821504374389638617418576",
            "-0.11985645271459166150784444169737234166055668504206"
          ],
          [
            "-0.11427990039611030428043542578186718617010989334156",
            "-0.11042578548141896733771580147636750958353847042227"
          ],
          [
            "-0.16074719212547190876392511966939304097736445956305",
            "-0.15537934739277582218313376086169760499303070994301"
          ],
          [
            "-0.15633830163163014308387926314032456742263769159011",
            "-0.15113563434327755480899880177289516599429538603519"
          ],
          [
            "-0.17808994692293378229447777350001459702460698873374",
            "-0.17235059279963260158286952612173671457822561751847"
          ],
          [
            "-0.17576690953984716585558514338440404763347300785070",
            "-0.17011661320833765327818592625512276231695515831288"
          ],
          [
            "-0.18705051533960783823423753649356516870193555616899",
            "-0.18123119074310901991098485471889443030762752358791"
          ],
          [
            "-0.18567139753048530226811795868388459668875151471919",
            "-0.17991155749860225688853637075379361777802260481233"
          ],
          [
            "-0.19191803468180768434046181194642756584808076166232",
            "-0.18613622044279555516702514902774795795980797314228"
          ],
          [
            "-0.19101440680463125057567061542579305440829421420732",
            "-0.18527954458757346152051691484950349646740497679704"
          ],
          [
            "-0.19462397075196905718516753602037331594913757569271",
            "-0.18892390862427068580835738603293393792138746055489"
          ],
          [
            "-0.19398043204055406725612022688132102047931660934226",
            "-0.18832111694829446908135257717527633296177555023818"
          ],
          [
            "-0.19612760858698660579611386160681964069068435332773",
            "-0.19052056250453396574350569189378730261714206309704"
          ],
          [
            "-0.19563742826460171071461409135061178347986405005262",
            "-0.19006693932898853495691629255975405147724615094026"
          ],
          [
            "-0.19694082548311857426422123167413630888308442815792",
            "-0.19142288647546360284405646825541213535844054743724"
          ],
          [
            "-0.19654854552208586426742717248625656952323445607767",
            "-0.19106321296953545213082547164794413255509608393544"
          ],
          [
            "-0.19735160605511487335174748164360913548237688034636",
            "-0.19191216419003288810445784804421217261423220169860"
          ],
          [
            "-0.19702755576814902559501437823772047315685194256242",
            "-0.19161635768159733759376518460116009840884013503763"
          ],
          [
            "-0.19752830326597289519757481386093460040917274812202",
            "-0.19215428609106092028787137315136138479625406922878"
          ],
          [
            "-0.19725627361580561260461315297097035611999972085326",
            "-0.19190561092457942400907496423570720552886266724621"
          ],
          [
            "-0.19757192746162377827767611472321776543776465523971",
            "-0.19224998087914312733784577081961861689036914818357"
          ],
          [
            "-0.19734280651975294223053568918505963385320572165221",
            "-0.19203894418551930948120164199009044450215978535182"
          ],
          [
            "-0.19754396787757133162714112055631455415486251970886",
            "-0.19226157976536877038603510829976650150588010348504"
          ],
          [
            "-0.19735229902879513485352750437942234239301196492688",
            "-0.19208260483245192082028553420534543491519336121263"
          ],
          [
            "-0.19748194191441665908810657087872959095684474745061",
            "-0.19222799711770805973587267258253723528013023698949"
          ],
          [
            "-0.19732401703823449176110791233292277270823428465954",
            "-0.19207754792336361709579245481256737605438309970999"
          ],
          [
            "-0.19740845426182668419173085666091930393437050701259",
            "-0.19217347198657173655492345836180494425083897471133"
          ],
          [
            "-0.19728126232857965310609933664076630040536068432861",
            "-0.19204898190196397960924787405136581455363508005074"
          ],
          [
            "-0.19733666578957145062828238092940617607049206341238",
            "-0.19211285405726689112954514654153942892084374250420"
          ],
          [
            "-0.19723734144510194899048328772873279262727584793032",
            "-0.19201212328643629420360253848234849752210948911891"
          ],
          [
            "-0.19727369778731352023989122297409900053771788614900",
            "-0.19205490005464123097622481204880967204380901873502"
          ],
          [
            "-0.19719927135472845401828454458598636954180369160656",
            "-0.19197577727079898108322109890727815469601924447099"
          ],
          [
            "-0.19722280773301658141145593726458639965077971620504",
            "-0.19200438520124609832287480243922767313367581505136"
          ],
          [
            "-0.19717013805492163548029491325012646028697970199378",
            "-0.19194462555749571029217690003557598278430802257855"
          ],
          [
            "-0.19718481145988454374140852948683292159082114092447",
            "-0.19196348739075955389767876325655636630013859052833"
          ],
          [
            "-0.19715062617400003629105118158333261673821770910016",
            "-0.19192071998171653902142065294839197104184375437001"
          ],
          [
            "-0.19715902986212553976011900197197270863231810676721",
            "-0.19193271265000923032084510081063076069874685344273"
          ],
          [
            "-0.19714002265173230068597042040741109741627836362202",
            "-0.19190447348432605964172227703483500398302160034775"
          ],
          [
            "-0.19714392752911005516444587454740117275047719241784",
            "-0.19191152387881174706692541800263005332796031068490"
          ],
          [
            "-0.19713687757688304850464956360117332855049566729109",
            "-0.19189532419883341562860552385951494058340744020712"
          ],
          [
            "-0.19713754651570110259543343427561790656983073810016",
            "-0.19189877297281211096140277352513598677445859340360"
          ],
          [
            "-0.19713943621595582427463610483304708226372563275878",
            "-0.19189218169052127521690221472075562032734185425347"
          ],
          [
            "-0.19713780032940091184059574380375238031928711304741",
            "-0.19189299956119012001491709115451481056181250190643"
          ],
          [
            "-0.19714591543735226327205087328188771839526049750320",
            "-0.19189372489032685559548240812761193353259081877837"
          ],
          [
            "-0.19714267009640515182351894201210566370775615479629",
            "-0.19189263712476939644384434003903489132960596714273"
          ],
          [
            "-0.19715467293832164823687162199127314381788659554123",
            "-0.19189859730317670757135559991542484433632091069454"
          ],
          [
            "-0.19715033062238300514515315000151393983613502125196",
            "-0.19189615331372428051769269026702262693345906271678"
          ],
          [
            "-0.19716430220803445318524000198270210831625765811851",
            "-0.19190553017998778781258726707773174066949152239146"
          ],
          [
            "-0.19715922517924251758113946357763245190650738790639",
            "-0.19190214249612404722656027057360905916193583638143"
          ],
          [
            "-0.19717367621912936552001312034705282402597273414353",
            "-0.19191341486201484178722628767963131842077151463316"
          ],
          [
            "-0.19716810226031390193754544922791822821896533632098",
            "-0.19190938296773343486480605182562845110333360393554"
          ],
          [
            "-0.19718195624811972727364817099827876477780223935967",
            "-0.19192133931186399362788352470020157903912069444504"
          ],
          [
            "-0.19717602400385704991167485480118166079274747212300",
            "-0.19191686765391319829529189343857166671789059042750"
          ],
          [
            "-0.19718857770354107835122829129991820101376755300136",
            "-0.19192859968245095122407957957002979727296931957133"
          ],
          [
            "-0.19718235371349849537884824187392028802494626967544",
            "-0.19192381480481565638363110978039339933823741540364"
          ],
          [
            "-0.19719322163252567292590996189116141040881642355889",
            "-0.19193469489097403906792859902702406885351385588788"
          ],
          [
            "-0.19718672841287157965019960171648532580421685703514",
            "-0.19192966366363187484554010630926914850915046150798"
          ],
          [
            "-0.19719577822932455265002180387630564986920772879956",
            "-0.19193931010338365204610366996877572866886577482899"
          ],
          [
            "-0.19718902134465255395943947443034253712450294022369",
            "-0.19193405907679507453192962568995496994112692670429"
          ]
        ],
        "all_N_at_least_64_interval": [
          "-0.19753450303935376775660902240829599064804816312719",
          "-0.19153592832530330935601430099359569330040534799019"
        ],
        "all_N_at_least_64_excluded": true
      },
      "finite_k_at_least_10_derivative_error_bound": [
        "0.00000000000000000001796244069832522852891156529509",
        "0.00000000000000000001796244069832522852891156529510"
      ],
      "printed_local_minimum": {
        "numerical_alpha": "0.04359266363085941236546867",
        "certified_alpha_interval": [
          "10897915907714853/250000000000000000",
          "10898415907714853/250000000000000000"
        ],
        "certified_halfwidth": "1/1000000",
        "left_derivative": [
          "-0.00002098079082759603901382747222157700231997185704",
          "-0.00002079841370704739977358973877530638154693612976"
        ],
        "right_derivative": [
          "0.00002079897740434721027128997656595312460908613241",
          "0.00002098135452489584951152771001222374538212186028"
        ],
        "curvature_interval": [
          "20.87807002985407543744267174230417118304929882348765",
          "20.90169819917649731532358741003066066543486498512878"
        ],
        "numeric_curvature": "20.8898835991906204081",
        "cutoff": 1024,
        "global_minimum_certified": false
      },
      "candidate_local_minimum": {
        "numerical_alpha": "0.0672676272671844632054567",
        "certified_alpha_interval": [
          "67266627267184463/1000000000000000000",
          "67268627267184463/1000000000000000000"
        ],
        "certified_halfwidth": "1/1000000",
        "left_derivative": [
          "-0.00003941982702341618827491474083946484819971151663",
          "-0.00003923452406670901471531490471758560784208161663"
        ],
        "right_derivative": [
          "0.00003923573307790473146367661570824648687762119119",
          "0.00003942103603461190502327645183012572723525109303"
        ],
        "curvature_interval": [
          "39.31580354347735120114661000376980829324041694347321",
          "39.33975655726101917850183568928606204434543817126823"
        ],
        "numeric_curvature": "39.32777946187992485741",
        "cutoff": 1024,
        "global_minimum_certified": false
      }
    },
    {
      "row": "(4)",
      "published_alpha": "13/500",
      "published_rounding_box": [
        "51/2000",
        "53/2000"
      ],
      "terms": [
        [
          "97/2",
          -1,
          1
        ],
        [
          "3",
          -1,
          2
        ],
        [
          "3",
          -1,
          3
        ],
        [
          "15",
          1,
          1
        ],
        [
          "13",
          1,
          2
        ]
      ],
      "derivative_over_rounding_box": [
        "-0.25834825284963417351873600428950443962761429491430",
        "-0.25425953330872222374313339987649699020583434877897"
      ],
      "candidate_derivative_over_rounding_box": [
        "-0.60652215385521266933766408665624831985979459628154",
        "-0.59075817875949837659861297773178872043002762060154"
      ],
      "required_relative_fermion_factor_interval": [
        "0.77220341308030871753837775374150728133248180340325",
        "0.82788212399659705229515270607269978071464289222106"
      ],
      "finite_cutoffs": {
        "tested_cutoffs": [
          1,
          64
        ],
        "not_excluded_cutoffs": [],
        "derivative_intervals": [
          [
            "5.12640945485343456637188526315746755573985386287980",
            "5.32840412786717377754195494551475369863321587424522"
          ],
          [
            "0.34099969173064303983005630179575117281006181388432",
            "0.36152847231827943437902852750326072545583958425943"
          ],
          [
            "0.52204655589430769897055865477699011249857492788470",
            "0.54887529497528795534627501119979788204156796710542"
          ],
          [
            "-0.04880809984126523633038921015005301729141320240420",
            "-0.04140887518236245898301588335380244056669413822611"
          ],
          [
            "-0.01314592293903049596279412212455295043352483805674",
            "-0.00475904147469246982621108371909375351109394139422"
          ],
          [
            "-0.16958041741035782508658420447340042876087398281683",
            "-0.16550578994028184639106202973367166401131569282849"
          ],
          [
            "-0.15813555992174515163436009426572098279266243173083",
            "-0.15383913023829054359668835834126888889449183575118"
          ],
          [
            "-0.21755007294608341363208609923553231971339608312109",
            "-0.21380127427149384162941427716696548416612732416733"
          ],
          [
            "-0.21281687697446567665163660466022067005256593699410",
            "-0.20913342546031986881897076726472687897543181841141"
          ],
          [
            "-0.23928670337975685075688421162615893816457383604017",
            "-0.23541922035560154199422539830397031664857270988455"
          ],
          [
            "-0.23699133274184861038213339183644588165387749388581",
            "-0.23316445972275087270000872716942253816391385899963"
          ],
          [
            "-0.24969533140686969826235478057782293418202517103529",
            "-0.24595641864897146888322227356673024690950222295901"
          ],
          [
            "-0.24836986307486185835992991811413278186424884715433",
            "-0.24467747256464423942589253934902899409878017295008"
          ],
          [
            "-0.25478520332379651658565238048173735200617291659473",
            "-0.25124239892355864465869950016386737208100746776601"
          ],
          [
            "-0.25387697191043179967327698329741715830317986558417",
            "-0.25038951980563977898761890927142895877385133677814"
          ],
          [
            "-0.25734194017901375689298134150546271185551318072031",
            "-0.25374058681413489665870189547270822424164763015003"
          ],
          [
            "-0.25668957967250045811668298533344421049071675592014",
            "-0.25302914833314618157800972506808092722865881054929"
          ],
          [
            "-0.25856886127344133654620892495700372971911740730402",
            "-0.25479951587584219994375982284407236844617696105827"
          ],
          [
            "-0.25802433301852747821538697306242809368570020033369",
            "-0.25419875864541077590425478322184474853145425007342"
          ],
          [
            "-0.25905486440537008715483615431916482156739954584963",
            "-0.25515227844255367245444121552593589098280554715738"
          ],
          [
            "-0.25858310972254763579932011871048940886105474999102",
            "-0.25463271695088020875590562476455464569938223878105"
          ],
          [
            "-0.25915688677211862495969937432705768818521388800543",
            "-0.25515564861016672823896733895626435429716355778791"
          ],
          [
            "-0.25874758846016876115014875208051823655721299257770",
            "-0.25471062411620429183568534299793212450246317963543"
          ],
          [
            "-0.25907355428565525972082254187977170377370416462655",
            "-0.25500459940387225560796335424985517975283503069395"
          ],
          [
            "-0.25872573429955613442936041319509916856249175253081",
            "-0.25463469025550203012993765134982986801846188735316"
          ],
          [
            "-0.25891589942752049553725687232497860424811840388522",
            "-0.25480511757436378264878100694466335081869431064082"
          ],
          [
            "-0.25863053371305476823784276837197895076219983116029",
            "-0.25451095798731111126946022267412048175046342849564"
          ],
          [
            "-0.25874474104009960432976171394353203862496856852776",
            "-0.25461262215991465318951524393267046989177387573106"
          ],
          [
            "-0.25852139211771066269871634274980454092412632769054",
            "-0.25439195636439687609738357043809373496516930103673"
          ],
          [
            "-0.25859142855119101618765095891643576136125188459261",
            "-0.25445324619450285351490085463720347697293857646201"
          ],
          [
            "-0.25842702830206922180436384722005000253907178733554",
            "-0.25430023430568240621115462595939389851100646212761"
          ],
          [
            "-0.25846983849992937333968839713873002603086861619686",
            "-0.25433612141217080668199523007031972168755565258206"
          ],
          [
            "-0.25835865310897251793780777653999207628179958701814",
            "-0.25424183979063740919380643654560884224978273087693"
          ],
          [
            "-0.25838356015006050021233876660181256042658402704177",
            "-0.25426072062997366538007669905698138116743168586633"
          ],
          [
            "-0.25831778000157107903596525092536614777878194462926",
            "-0.25421423043644943946960184948831334586162382752631"
          ],
          [
            "-0.25833032774756095986538503190009077706800375675454",
            "-0.25422137094025466815244389242877728994720488123146"
          ],
          [
            "-0.25830093245130960680119246594572404121369264671822",
            "-0.25421095644513089186008278835253961713742401446429"
          ],
          [
            "-0.25830481697283586414369652049671128763089678846505",
            "-0.25421008095507859453754581169401872362419072667623"
          ],
          [
            "-0.25830248551560229203228732148279358234100815497603",
            "-0.25422440070189991102468657826464872993688401206570"
          ],
          [
            "-0.25830043253569048803787270212359947704260433324039",
            "-0.25421832062632658896684969132390994824010467657027"
          ],
          [
            "-0.25831634921032600471463870252297498294583320024528",
            "-0.25424731660674661527389414337994943626958262161913"
          ],
          [
            "-0.25831044881642885435535296733995441817850264008107",
            "-0.25423812116932766920396625020059116170521066995749"
          ],
          [
            "-0.25833691689835263423197829959442565497345601176614",
            "-0.25427361130869064401416988299624922543097051087157"
          ],
          [
            "-0.25832871853261433929861375151057384240918103340024",
            "-0.25426271411754063456747679235283334272990557728990"
          ],
          [
            "-0.25835954296108803980183512914289418402407124995769",
            "-0.25429865686755160255228632241962257603432816958446"
          ],
          [
            "-0.25835008166026347899011814788191739157328191274406",
            "-0.25428684645676241945302306839571030658731066125982"
          ],
          [
            "-0.25838072119213078115206735778843665329557180116120",
            "-0.25431931378429006258963650976828397739422628904231"
          ],
          [
            "-0.25837055996439455574143914094334253770552594464897",
            "-0.25430686349499875646825093754278236738499953559169"
          ],
          [
            "-0.25839807840670826488879146971657195664595539259039",
            "-0.25433378968067805218937746272853710679488732629498"
          ],
          [
            "-0.25838739600005110712322669475925143333043093981575",
            "-0.25432062621929247577621262774957981650506539530643"
          ],
          [
            "-0.25841026093164880068948238946236361495828113882033",
            "-0.25434141495213242128470992048058736935675427788700"
          ],
          [
            "-0.25839898048300096597494788864691143403390074441310",
            "-0.25432731592898187829696042087360671600343124214976"
          ],
          [
            "-0.25841676659995323641252208237836117597427319740104",
            "-0.25434238881788860314014207530779358424559828961243"
          ],
          [
            "-0.25840470326723851371564417027558514161783067484901",
            "-0.25432717034825875253972123361675553481903624729681"
          ],
          [
            "-0.25841775718609362291758159295541063652448293028958",
            "-0.25433752907026674816505310655893265119561096397257"
          ],
          [
            "-0.25840475765205067677247406439222048135448733867412",
            "-0.25432118895811883376256616378123187082248941769470"
          ],
          [
            "-0.25841387348910074200835875886456167092387756424385",
            "-0.25432804463510855358172754054210237580787602798844"
          ],
          [
            "-0.25839992349900148555107042785399421542492198119287",
            "-0.25431083917953389766294014910149324836936781839341"
          ],
          [
            "-0.25840606615474770054454899820892224615229981913704",
            "-0.25431534037422531846128422699914587350535253159287"
          ],
          [
            "-0.25839135062705850761613580192856524205126963912292",
            "-0.25429778850933861468569259547569016965903309758056"
          ],
          [
            "-0.25839544899155626611464029718493575944227329936578",
            "-0.25430085736408443694870911719549677631388215337255"
          ],
          [
            "-0.25838035969886532593787721817526898225210157086353",
            "-0.25428368064656505313113901859309153285758792038061"
          ],
          [
            "-0.25838317737275074355467824274588390563362935685493",
            "-0.25428594830903753755666827286523248285774507837450"
          ],
          [
            "-0.25836827322726912899815171279543171695662530095588",
            "-0.25426996635410139605477835696204179990395711455934"
          ]
        ],
        "all_N_at_least_64_interval": [
          "-0.25876570335050409411380251510487399230527568738337",
          "-0.25384208280785230314806688906112743752817295630990"
        ],
        "all_N_at_least_64_excluded": true
      },
      "finite_k_at_least_10_derivative_error_bound": [
        "0.00000000000000000001978351763548262496963071016372",
        "0.00000000000000000001978351763548262496963071016373"
      ],
      "printed_local_minimum": {
        "numerical_alpha": "0.04687894514701185695028246",
        "certified_alpha_interval": [
          "46877945147011857/1000000000000000000",
          "46879945147011857/1000000000000000000"
        ],
        "certified_halfwidth": "1/1000000",
        "left_derivative": [
          "-0.00002482266334298951238194171081974902109642604889",
          "-0.00002461883009061162146638189108568185670303317191"
        ],
        "right_derivative": [
          "0.00002462113436092908001449521184702592710873137233",
          "0.00002482496761330697093005503158109309150212424974"
        ],
        "curvature_interval": [
          "24.70727335005279146641120288936428693286893278115876",
          "24.73652435206905272387513733308500002510152739096880"
        ],
        "numeric_curvature": "24.72189957668685852304",
        "cutoff": 1024,
        "global_minimum_certified": false
      },
      "candidate_local_minimum": {
        "numerical_alpha": "0.06897794214445045872967926",
        "certified_alpha_interval": [
          "68976942144450459/1000000000000000000",
          "68978942144450459/1000000000000000000"
        ],
        "certified_halfwidth": "1/1000000",
        "left_derivative": [
          "-0.00004209733559836121902444641179550941812501649550",
          "-0.00004189057650982479378952448938583363414702944385"
        ],
        "right_derivative": [
          "0.00004189142596436654333952634360175363164178120706",
          "0.00004209818505290296857444826601142941561976825770"
        ],
        "curvature_interval": [
          "41.97959285843010421754956615380039490081635024557554",
          "42.00916870490761157448781061531087226176839992161824"
        ],
        "numeric_curvature": "41.99438036315316971629",
        "cutoff": 1024,
        "global_minimum_certified": false
      }
    },
    {
      "row": "(5)",
      "published_alpha": "43/1000",
      "published_rounding_box": [
        "17/400",
        "87/2000"
      ],
      "terms": [
        [
          "91/2",
          -1,
          1
        ],
        [
          "4",
          -1,
          2
        ],
        [
          "4",
          -1,
          3
        ],
        [
          "15",
          1,
          1
        ],
        [
          "15",
          1,
          2
        ]
      ],
      "derivative_over_rounding_box": [
        "-0.30588839517965186911943858018147432750902279902999",
        "-0.28554480711813664589115107793381895682387647826773"
      ],
      "candidate_derivative_over_rounding_box": [
        "-0.85546371314587949265957296482669420153918484255637",
        "-0.84729020450913640128868068786303488244694406206018"
      ],
      "required_relative_fermion_factor_interval": [
        "0.83378014998371818994849624040168186451888653829293",
        "0.86243781573927468917921146857122409725178476242683"
      ],
      "finite_cutoffs": {
        "tested_cutoffs": [
          1,
          64
        ],
        "not_excluded_cutoffs": [],
        "derivative_intervals": [
          [
            "9.21587490149905940750630261449710441062716434367201",
            "9.42625803569271111441841231221331687602411745485835"
          ],
          [
            "0.59097433960616787651870673800356991155451410005701",
            "0.61841768744594501117771280355767455318880425503015"
          ],
          [
            "0.87357160227378784789577203303298286613671910273089",
            "0.90475139101406834067432348138020176817174558583357"
          ],
          [
            "-0.06026830404884301266239646176120644769218712588181",
            "-0.04232690346624675452311760434286216627384026507910"
          ],
          [
            "-0.01810115076590557049868204617198398802475381094077",
            "-0.00028868553552202819913658116772509952192418113767"
          ],
          [
            "-0.23509378344647942293648165034412219634849018038611",
            "-0.21776437084614243929918847492770567690431106745023"
          ],
          [
            "-0.22530588074140037000179281950807520851419530847871",
            "-0.20805220540076005493796999569047798478948170505934"
          ],
          [
            "-0.29000996420018857069549798928994605121077093995482",
            "-0.27179895273932500668973023235471389336074377403682"
          ],
          [
            "-0.28605128216398513182830628337427299711628213535879",
            "-0.26767134978764703175648817586260484127621747358433"
          ],
          [
            "-0.30708744519304763540837348933714726335529551605292",
            "-0.28794129749012511549075161811158346738872799654721"
          ],
          [
            "-0.30399219472807395453219540266386416547281461925000",
            "-0.28457250084148121985803630818780889380150696503659"
          ],
          [
            "-0.31098058863170420481275727534141373455449922947694",
            "-0.29114253353870887357528660899106911281573751551143"
          ],
          [
            "-0.30804976731486742044141422659395778386012085087578",
            "-0.28796736387728780766988387256641267674880767471633"
          ],
          [
            "-0.31041645888160537224983530327843633385841013055749",
            "-0.29015257018247750340630316657796402158617908083823"
          ],
          [
            "-0.30786036981377378085628656326080227236818768201751",
            "-0.28745376872045354316152585925060394479073829728318"
          ],
          [
            "-0.30873187434615263434033606005528184457261730870387",
            "-0.28825954158108709785227016169240784830076666796146"
          ],
          [
            "-0.30680950774988567088545131979782455903628129033908",
            "-0.28630788285284793144530543862190405810678244296431"
          ],
          [
            "-0.30718280693152555245282821164784429260650326881204",
            "-0.28665517896335412219953500269376854671145931551781"
          ],
          [
            "-0.30598572662183300018077328706705548743891587306154",
            "-0.28551286061900108506808826035258045512145867481833"
          ],
          [
            "-0.30615423880722925220159392909436783538124680005757",
            "-0.28566255806985344460078513020146044527204355701395"
          ],
          [
            "-0.30560300319155482801550994280296393414441487546999",
            "-0.28520419737803992995753548269082146699512011281259"
          ],
          [
            "-0.30565778359571747413966857512761523854904435070453",
            "-0.28524099442714006614646988036124082905677067164828"
          ],
          [
            "-0.30557026633889592584384519404691750012227326647568",
            "-0.28524285557563493275459034889245833119415721458554"
          ],
          [
            "-0.30555805484972480296265348280029995053784302414280",
            "-0.28521629326746319907303619841207688749089892502963"
          ],
          [
            "-0.30572792857614567802395671847609804410872645674572",
            "-0.28544695503030511284313144554269169538201621192111"
          ],
          [
            "-0.30568427481020898328883630394473422944126440674100",
            "-0.28539416019933651876504296619972172799963711121788"
          ],
          [
            "-0.30593968602375265450652477649573776318718833456880",
            "-0.28567561823000255178077520585642826347848210107563"
          ],
          [
            "-0.30588663376058705893646157264913512198693116426619",
            "-0.28561607996000850649413923230768672054974717061385"
          ],
          [
            "-0.30611839440815731644791733652446947027760562135752",
            "-0.28584697961044499664336426687324292699322522169045"
          ],
          [
            "-0.30606144675867383427742948224551464329639182948171",
            "-0.28578164566977044425396882057114077527100982105739"
          ],
          [
            "-0.30622332779641244023323343495032396108027280865397",
            "-0.28592939952886799848575119908391061022698347484274"
          ],
          [
            "-0.30615632975689209014974227238203482653588593050941",
            "-0.28584917143637815520170722787473857619649710521325"
          ],
          [
            "-0.30624759418771798517627527818540554181433341498226",
            "-0.28592515629404765231833994970950748001236606097637"
          ],
          [
            "-0.30616251702870425524308688762307211752700098542599",
            "-0.28582289567908434149980746884769885566985739499735"
          ],
          [
            "-0.30620474225303721098283683736062157316718468430882",
            "-0.28585527741931649460157090469745205724542826580157"
          ],
          [
            "-0.30610031929833175181176583997348089943180659693337",
            "-0.28573409686277838196628408599571806388388265773207"
          ],
          [
            "-0.30611804553897581109530769905378472753481091707139",
            "-0.28574824266812536507459277002154198637353835199100"
          ],
          [
            "-0.30600303643385031258788297372940906546076128328943",
            "-0.28562240547288143088360851197677590434456503863445"
          ],
          [
            "-0.30601299088006916407058704946461127030218963978597",
            "-0.28563240130828011891728436115368289397669634070700"
          ],
          [
            "-0.30590343995873807940594904527308240809545454247828",
            "-0.28552173637555251965187251485499460588266707528596"
          ],
          [
            "-0.30591231944017112289660418307665164424473163932997",
            "-0.28553109050854219726251133947831969332360622094416"
          ],
          [
            "-0.30582518650708228710942740913086087022001015185939",
            "-0.28545283342795353946780227308654833785535277462357"
          ],
          [
            "-0.30583288775684651050419203746286016940733988291039",
            "-0.28545969180529033827916921961514350403324484768858"
          ],
          [
            "-0.30577963071319742485677181941061825756898778340192",
            "-0.28542209010057059160783546228548071511581021021986"
          ],
          [
            "-0.30578398728817961392626774349802071186685898202838",
            "-0.28542439547856505956367740012211234928438424726233"
          ],
          [
            "-0.30576698621199105570504649795758984306131265573371",
            "-0.28542471909256006738246156026030551555830074682837"
          ],
          [
            "-0.30576708708779102178216787077527186561359492121795",
            "-0.28542271783690598748128549410484128085160876605442"
          ],
          [
            "-0.30577997895616357189295668418279290125728603981948",
            "-0.28544978744702671669648461283894612139905339715100"
          ],
          [
            "-0.30577699938382089558113335139323623914994572710476",
            "-0.28544567015990719380547154448938529343913436384633"
          ],
          [
            "-0.30580810203502490045940757397278900426366263388992",
            "-0.28548500084089789596186213681624906691060242070132"
          ],
          [
            "-0.30580422685194943964914650685921251424032026190403",
            "-0.28548106639543442818414488519879165769442111646098"
          ],
          [
            "-0.30584110825340264998556324365086193996308902929818",
            "-0.28552001220578795182212775856957301162924980401206"
          ],
          [
            "-0.30583791997343540101379894937921171373948904549077",
            "-0.28551708207128976611373769049406953031785674153790"
          ],
          [
            "-0.30587112497710876024392426871744793219827918140158",
            "-0.28554797300422765609873815368783504440800965341182"
          ],
          [
            "-0.30586867320870505295727405128623580238491371759016",
            "-0.28554509172716268246755842062115348385468829708935"
          ],
          [
            "-0.30589342570088182476799059497488937219040715429459",
            "-0.28556569349610464557922206882415019125420361039691"
          ],
          [
            "-0.30589045173011574600289862379946352666424684913856",
            "-0.28556109049649922707585043921235556917326400446435"
          ],
          [
            "-0.30590625930347016898373170367435833705282278965093",
            "-0.28557301115503607648180929218003614237704572079851"
          ],
          [
            "-0.30590125428585846823204275546538653789765265542133",
            "-0.28556552743407027358319231485324279864639134060676"
          ],
          [
            "-0.30591020328434523958608689388910703325899001802971",
            "-0.28557187189193085917514608739101664063777586206961"
          ],
          [
            "-0.30590254957681688608303292709208918189563217159872",
            "-0.28556191360294084351198632592389656600370422879841"
          ],
          [
            "-0.30590737800526930550333933553615314260941917139163",
            "-0.28556539961342828063136671118703091431931104520087"
          ],
          [
            "-0.30589789627117035913553413516876457322696074974808",
            "-0.28555490092895527619380184745068373198842777867563"
          ],
          [
            "-0.30590068227758015775336905235244803443179460370579",
            "-0.28555704232342295075316310781688870183866052136807"
          ]
        ],
        "all_N_at_least_64_interval": [
          "-0.30632981413033250285871943611542969182367910398533",
          "-0.28510338816745601215187022199986359250922017331239"
        ],
        "all_N_at_least_64_excluded": true
      },
      "finite_k_at_least_10_derivative_error_bound": [
        "0.00000000000000000002077683232847756848275024372842",
        "0.00000000000000000002077683232847756848275024372843"
      ],
      "printed_local_minimum": {
        "numerical_alpha": "0.05527691758873501914881606",
        "certified_alpha_interval": [
          "55275917588735019/1000000000000000000",
          "55277917588735019/1000000000000000000"
        ],
        "certified_halfwidth": "1/1000000",
        "left_derivative": [
          "-0.00003208043911020031382909991427844515557834245280",
          "-0.00003186490251318828563609168384194351284657293934"
        ],
        "right_derivative": [
          "0.00003186557149276360397757638348012032478133385783",
          "0.00003208110808977563217058461391662196751310337011"
        ],
        "curvature_interval": [
          "31.95584693161871513478451637885715214703390982864856",
          "31.99016367157968825769008017185604770698696213864571"
        ],
        "numeric_curvature": "31.97300490017901144267",
        "cutoff": 1024,
        "global_minimum_certified": false
      },
      "candidate_local_minimum": {
        "numerical_alpha": "0.07592984924781069385590431",
        "certified_alpha_interval": [
          "37964424623905347/500000000000000000",
          "37965424623905347/500000000000000000"
        ],
        "certified_halfwidth": "1/1000000",
        "left_derivative": [
          "-0.00004747980379777453303536592835821033079504586853",
          "-0.00004726134136460397052299559524610006847868217977"
        ],
        "right_derivative": [
          "0.00004726311450955246021137115287950596952436403695",
          "0.00004748157694272302272374148599161623184072772377"
        ],
        "curvature_interval": [
          "47.35413836263561962426062759422722459167965771764529",
          "47.38877994705783884664050140501588442035216509385245"
        ],
        "numeric_curvature": "47.37145775111863382239",
        "cutoff": 1024,
        "global_minimum_certified": false
      }
    }
  ],
  "common_relative_fermion_factor_excluded": true,
  "common_integer_fourier_cutoff_excluded": true,
  "checks": [
    {
      "name": "Machin pi enclosed between 3 and 22/7",
      "passed": true
    },
    {
      "name": "Signed integer interval arithmetic encloses exact rationals",
      "passed": true
    },
    {
      "name": "Trig special value 0",
      "passed": true
    },
    {
      "name": "Trig special value 1/2",
      "passed": true
    },
    {
      "name": "Trig special value 1",
      "passed": true
    },
    {
      "name": "Trig special value -1/2",
      "passed": true
    },
    {
      "name": "Trig special value 5/2",
      "passed": true
    },
    {
      "name": "Q, P6 and B simultaneously diagonalized exactly",
      "passed": true
    },
    {
      "name": "P5 and P5p reverse Q; P6 preserves Q",
      "passed": true
    },
    {
      "name": "Sym2 occupation weights equal Newton character identity",
      "passed": true
    },
    {
      "name": "Sym3 occupation weights equal Newton character identity",
      "passed": true
    },
    {
      "name": "7: dimension and charge reflection",
      "passed": true
    },
    {
      "name": "28: dimension and charge reflection",
      "passed": true
    },
    {
      "name": "84: dimension and charge reflection",
      "passed": true
    },
    {
      "name": "48: dimension and charge reflection",
      "passed": true
    },
    {
      "name": "Published gauge reconstructed from adjoint weights matches lab",
      "passed": true
    },
    {
      "name": "Gauge + ghost 3+1 reconstruction matches existing candidate",
      "passed": true
    },
    {
      "name": "Independent 7 (+,+) coefficients match lab",
      "passed": true
    },
    {
      "name": "Independent 7 (+,-) coefficients match lab",
      "passed": true
    },
    {
      "name": "Independent 28 (+,+) coefficients match lab",
      "passed": true
    },
    {
      "name": "Independent 28 (+,-) coefficients match lab",
      "passed": true
    },
    {
      "name": "Independent 48 (+,+) coefficients match lab",
      "passed": true
    },
    {
      "name": "Independent 48 (+,-) coefficients match lab",
      "passed": true
    },
    {
      "name": "Independent 84 (+,+) coefficients match lab",
      "passed": true
    },
    {
      "name": "Independent 84 (+,-) coefficients match lab",
      "passed": true
    },
    {
      "name": "Sym3 quartet lower weight contributes c=1 antiperiodic",
      "passed": true
    },
    {
      "name": "Row (1): full printed rounding box nonstationary",
      "passed": true
    },
    {
      "name": "Exact Taylor lower bound exp(6)>400",
      "passed": true
    },
    {
      "name": "Row (1): finite k>=10 correction cannot close gap",
      "passed": true
    },
    {
      "name": "Local stationary point bracket with strictly positive curvature",
      "passed": true
    },
    {
      "name": "Local stationary point bracket with strictly positive curvature",
      "passed": true
    },
    {
      "name": "Row (2): full printed rounding box nonstationary",
      "passed": true
    },
    {
      "name": "Exact Taylor lower bound exp(6)>400",
      "passed": true
    },
    {
      "name": "Row (2): finite k>=10 correction cannot close gap",
      "passed": true
    },
    {
      "name": "Local stationary point bracket with strictly positive curvature",
      "passed": true
    },
    {
      "name": "Local stationary point bracket with strictly positive curvature",
      "passed": true
    },
    {
      "name": "Row (3): full printed rounding box nonstationary",
      "passed": true
    },
    {
      "name": "Exact Taylor lower bound exp(6)>400",
      "passed": true
    },
    {
      "name": "Row (3): finite k>=10 correction cannot close gap",
      "passed": true
    },
    {
      "name": "Local stationary point bracket with strictly positive curvature",
      "passed": true
    },
    {
      "name": "Local stationary point bracket with strictly positive curvature",
      "passed": true
    },
    {
      "name": "Row (4): full printed rounding box nonstationary",
      "passed": true
    },
    {
      "name": "Exact Taylor lower bound exp(6)>400",
      "passed": true
    },
    {
      "name": "Row (4): finite k>=10 correction cannot close gap",
      "passed": true
    },
    {
      "name": "Local stationary point bracket with strictly positive curvature",
      "passed": true
    },
    {
      "name": "Local stationary point bracket with strictly positive curvature",
      "passed": true
    },
    {
      "name": "Row (5): full printed rounding box nonstationary",
      "passed": true
    },
    {
      "name": "Exact Taylor lower bound exp(6)>400",
      "passed": true
    },
    {
      "name": "Row (5): finite k>=10 correction cannot close gap",
      "passed": true
    },
    {
      "name": "Local stationary point bracket with strictly positive curvature",
      "passed": true
    },
    {
      "name": "Local stationary point bracket with strictly positive curvature",
      "passed": true
    },
    {
      "name": "One common matter normalization cannot repair all five rounding boxes",
      "passed": true
    },
    {
      "name": "No common positive integer Fourier cutoff repairs all five rows",
      "passed": true
    }
  ],
  "passed": 53,
  "elapsed_seconds": 46.874667899974156,
  "script_sha256": "3e80629f1bc70d9a7f3469818cec82c900420d7094b9e4dd89d896c5c6144698"
}