{
  "parameters": {
    "a": "6",
    "b": "27",
    "u": "16",
    "v": "2",
    "e": "1/100000",
    "d": "1/10000",
    "g": "1",
    "eta": "0"
  },
  "flagship_theorem_scope": true,
  "exact_stationary_roots": [
    {
      "z_interval": [
        "18451601/18529536",
        "11114287/11161231"
      ],
      "multiplicity": 1,
      "state_intervals": [
        [
          "923355847600602502809592280435939/71189253568801385275356159197184",
          "230838961900153409291094235020009/17797313392200317593454006410832"
        ],
        [
          "223224620/11145583",
          "1111772160/55510673"
        ],
        [
          "18451601/18529536",
          "11114287/11161231"
        ],
        [
          "32581127323731875/3637297368225792",
          "126092697443700000/14076757750195793"
        ]
      ],
      "state": [
        12.970438673137998,
        20.028079284861114,
        0.9957940123271325,
        8.957509938106723
      ]
    },
    {
      "z_interval": [
        "15477893/7644008",
        "28112204/13883667"
      ],
      "multiplicity": 1,
      "state_intervals": [
        [
          "227794839317295607891546946506367/12592688907497333917559598072752",
          "227794839317299163064075588140978/12592688907497304436401831290289"
        ],
        [
          "416510010/27939769",
          "152880160/10255303"
        ],
        [
          "15477893/7644008",
          "28112204/13883667"
        ],
        [
          "247097973966791875/12173704134787334",
          "78253996910283200000/3855316943547146889"
        ]
      ],
      "state": [
        18.089451823246026,
        14.907424968331002,
        2.0248399792360283,
        20.297681891306222
      ]
    },
    {
      "z_interval": [
        "23733603/7974017",
        "42683282/14340731"
      ],
      "multiplicity": 1,
      "state_intervals": [
        [
          "252341096918877905477981667593607/12051393591710849322776853222562",
          "153970838797961265614644354937000/7353392700026945986897690320397"
        ],
        [
          "71703655/5947062",
          "478441020/39681637"
        ],
        [
          "23733603/7974017",
          "42683282/14340731"
        ],
        [
          "13848674278050780000/423920842424298763",
          "44791588567764400000/1371112322950944787"
        ]
      ],
      "state": [
        20.938748286542072,
        12.05698797153957,
        2.976367243761837,
        32.66806651650731
      ]
    }
  ],
  "equilibria": [
    {
      "state": [
        12.970438673137998,
        20.028079284861114,
        0.9957940123271325,
        8.957509938106723
      ],
      "eigenvalues_real": [
        -46.272197770197664,
        -2.6857276315030116,
        -1.0001244089494612,
        -0.03280440270211383
      ],
      "eigenvalues_imag": [
        0.0,
        0.0,
        0.0,
        0.0
      ],
      "numerical_sink": true,
      "activity": [
        6.970438673138001,
        -6.971920715138889,
        6.973402757139771,
        0.0008957509938127828
      ],
      "signature": [
        false,
        true
      ],
      "field_residual": 7.105427357601002e-15
    },
    {
      "state": [
        18.089451823246026,
        14.907424968331002,
        2.0248399792360283,
        20.297681891306222
      ],
      "eigenvalues_real": [
        -49.61370267369244,
        -3.5290634935972918,
        -1.0002388521686707,
        0.01118665993019811
      ],
      "eigenvalues_imag": [
        0.0,
        0.0,
        0.0,
        0.0
      ],
      "numerical_sink": false,
      "activity": [
        12.089451823246026,
        -12.092575031668998,
        12.095698240091977,
        0.0020297681891268127
      ],
      "signature": [
        false,
        true
      ],
      "field_residual": 7.105427357601002e-15
    },
    {
      "state": [
        20.938748286542072,
        12.05698797153957,
        2.976367243761837,
        32.66806651650731
      ],
      "eigenvalues_real": [
        -54.43392406296306,
        -4.395248853056448,
        -1.000310913441182,
        -0.015756885866895182
      ],
      "eigenvalues_imag": [
        0.0,
        0.0,
        0.0,
        0.0
      ],
      "numerical_sink": true,
      "activity": [
        14.938748286542069,
        -14.943012028460425,
        14.947275770378795,
        0.0032668066516450267
      ],
      "signature": [
        false,
        true
      ],
      "field_residual": 1.4210854715202004e-14
    }
  ],
  "trajectories": [
    {
      "initial": [
        18.08381868812832,
        14.913060174637609,
        2.023314305554043,
        20.279401175826685
      ],
      "endpoint": [
        12.970438675535712,
        20.028079282462734,
        0.995794012681952,
        8.957509941710871
      ],
      "first_sampled_numerical_selection": [
        0.0,
        "low_z_sink"
      ],
      "last_verdict": "low_z_sink",
      "independent_solver_max_difference": 1.6092896970576476e-07,
      "largest_sampled_energy_increase": 1.4210854715202004e-14,
      "maximum_dV_plus_D": -4.667126952889188e-22
    },
    {
      "initial": [
        18.09508495836373,
        14.901789762024395,
        2.0263656529180136,
        20.31596260678576
      ],
      "endpoint": [
        20.93865865700642,
        12.05707764012166,
        2.9763303517097692,
        32.66754771162589
      ],
      "first_sampled_numerical_selection": [
        0.0,
        "high_z_sink"
      ],
      "last_verdict": "high_z_sink",
      "independent_solver_max_difference": 1.119630148593842e-07,
      "largest_sampled_energy_increase": -2.2382096176443156e-12,
      "maximum_dV_plus_D": -3.9374348048924873e-13
    }
  ],
  "fixed_fold_certificate": {
    "scope": "fixed e=1/100000; local fold only; Lean proofs not rerun",
    "box": {
      "z": [
        "1617456100591/1000000000000",
        "1617456102591/1000000000000"
      ],
      "g": [
        "194037598439/200000000000",
        "194037598479/200000000000"
      ]
    },
    "contraction_norm": "135922546750022663541454816401934997908137445744647953881192972985456992317556880824048851786357494152586883997912432427962083936060258016819334569200045997846781382278808858227361349859492265911785763659392959964701261560185505926035558719266052040597537165938044836862062379136239307543598941742018140602456320131177452789129942792807461129513834183794160043496817531713313772233050430248251321323865236299545768378870659071244769082174000663207334764/1239293024058634661615725907194871109318646500568882621595855647121558474014435814377306903672561884959966446266423989948642756898609634218534634236300324930194216951200194688633312323104977029536051168583002808143833318463305400458934974854037276633855573892363836698973078838323548709217855151052155887692319624120431071939140786637750488994636680640912598986825844179206107732983184636513181143014966118747805372228444464451910408857231847724757433336325545",
    "newton_errors": [
      [
        "-9305963970913364507405150723786207710505331309587373379352869295927013122529062878320320832264390171093652749682083202117475489115631001210091961125262014268085007047471884653140178592622968150514653584429008899775397099089690475491553618715446320181069849450239831251493728975062909983482555581573164670501294250891943184609008809228897466432224281507204706555192168085097357593714137273651725419249186635491030260882764733032592932515154716976728301833691/309823256014658665403931476798717777329661625142220655398963911780389618503608953594326725918140471239991611566605997487160689224652408554633658559075081232548554237800048672158328080776244257384012792145750702035958329615826350114733743713509319158463893473090959174743269709580887177304463787763038971923079906030107767984785196659437622248659170160228149746706461044801526933245796159128295285753741529686951343057111116112977602214307961931189358334081386250000000",
        "-9305896009639989496073379996378006743006377240864501055375928699440520394032904099879908807838496992346576456240084245901261508073662971081083551457977414245086083656780745248711064911948038404381697691547179203295414748458910382738590600936086687155049550681656862229075297943873341863828783782102293661430993022731877595882614244257501062701659524590112809475170419676331500936828020748436601293588524702872880487998575297703057310130613629976396698166309/309823256014658665403931476798717777329661625142220655398963911780389618503608953594326725918140471239991611566605997487160689224652408554633658559075081232548554237800048672158328080776244257384012792145750702035958329615826350114733743713509319158463893473090959174743269709580887177304463787763038971923079906030107767984785196659437622248659170160228149746706461044801526933245796159128295285753741529686951343057111116112977602214307961931189358334081386250000000"
      ],
      [
        "40950414508227298716255500445199704287401078409131103629142148821784517837537346593499454312702324969300272973128383439565273741330784137049621024511925502883944079116918598780205533862596222187396644312532995171920829708538077339997228115387319766569760527735292740571294003641743609394724614054650318906966641278804122148612868477206533997399666691657080608029651034956348791886895661129346715090933340841602529045053302349693144346000288049654693311015949/5218075890773198575224109082925773091867985265553189985666760619459193574797624481588660647042365831410385036911258905046916871152040565130672144152843473390291439794527135531087630834126219071730741762454748665868771867213917475616568315174893796353076100599426680837781384582414941933548863793903814263967661575243920302901645417422107322082680760593316206260319343912446769402034461627423920602168278394727601567277660902955412247819923569367399719310844400000000000",
        "40950490880114449283104896229696521029417884702783251300843721954364410840390503976667802642617259974102903466499505441169502894437461463414409261896906205741376726986006605089561269696343162946990822563902331326783789769027056837646272538718031321230062792376232423268512088072760260963699279019295045138487588611155687451860406896579404569626680622907659126528185900626318460487520694370230242853882767742249097111661854566428104547526469978279976146127949/5218075890773198575224109082925773091867985265553189985666760619459193574797624481588660647042365831410385036911258905046916871152040565130672144152843473390291439794527135531087630834126219071730741762454748665868771867213917475616568315174893796353076100599426680837781384582414941933548863793903814263967661575243920302901645417422107322082680760593316206260319343912446769402034461627423920602168278394727601567277660902955412247819923569367399719310844400000000000"
      ]
    ],
    "Qg": [
      "54894177844405051223341743444458831914919319490592191119656684274306637776163175297594944147428217104147880416910207479448026705373/15769228473953563714286247444127270537450330894623963703079914907952145698218553219909413750194396138677400436051953125000000000000",
      "54894178953032281599974116990590987765343923275955468129635773812208734824623310924860290351261944911437692951810762477381449339653/15769228481498238860253899103233672177563840611903204131867884039781937216591692323470878367379538689665509594645703125000000000000"
    ],
    "Qzz": [
      "-96115839274615720117223174573761351789232006619972598994024749893767205815497587694733532534472643130747961906686022396765322338525763220866159853714354165754518599630544651234963561916760234655581593669421965210139798245358/164284696250362312443694526394362022545339034220563902105959632350396148309094416588969256805406606620415765743184253702534242866979654589520558835475282908233735127664744640621755624477074195443639377880433638463096536484375",
      "-32038611192020708989627910648499836899204061449297044345058129097513143520552432860665019671916508984968758722207200395940239592519538479109563842020510387929107643810971819425640228338418372767403222577608809751117829689706/54761565454276575327945883096868532293281629258675996179521804106124782306233112973486286431115170669815574264828282592171817229452278813716729385948603640914504606046694464726953860777314749074691521569693889126139994453125"
    ],
    "state": [
      [
        "19003571807584147148219707903021089200767442773670003/1163976074190140681346994769143577534196250000000000",
        "6334523962765707708217796303380450862987393416227241/387992024544414870678032567602082988898750000000000"
      ],
      [
        "12000000000000000000000000/719809699352960689559089",
        "12000000000000000000000000/719809698860187248577449"
      ],
      [
        "1617456100591/1000000000000",
        "1617456102591/1000000000000"
      ],
      [
        "5185271014022347703516427/333350000000000000000000",
        "5185271021512289172304427/333350000000000000000000"
      ]
    ],
    "cubic_coefficients": [
      [
        "9630930818067748576658634477341607518442964697978200994390472293/186236171870422509015519163062972405471400000000000000000000000",
        "3210310273194060090510368403255242408263952064789760756277730591/62078723927106379308485210816333278223800000000000000000000000"
      ],
      [
        "1218595311636141248608808991931325638664339281573312922356558559444345522313922530802882773364098175654824274328922654275899816467/6030862708238423673900165770938293926297119915581883612738481459390324015783726650263462500000000000000000000000000000000000000",
        "406198437572839635914104354479694675199209623479499378265019075990736477541981547310230700300818875923815769329756980155410121489/2010287568451000109835561297812066067587299001645897637602505458167465255181978530529487500000000000000000000000000000000000000"
      ],
      [
        "82136577876157326956251419775757336232994550194490816346730414622862876252825164739145632517381459262682774571757944480974611178346851294525228654468351477451435653/542634183735529132031760129206104132630043799905495304689144209236625451808455183331186270703001056661773269645312500000000000000000000000000000000000000000000000",
        "27378859378528872643069357430072539545483864626010752014055333049300562701790109217739320635531548090054314312761910181848412235255035091239446915805601048978782911/180878061282463596460278955642311153432932814094914739004841763901529519484511818029859331571574392184011017110937500000000000000000000000000000000000000000000000"
      ]
    ],
    "hurwitz_gap": [
      "538484173155051243544206889219111917057313405603862722674663320535337543636457335352673120752710856295754127272934831894903649006726876301616767194164920619377143640330518182747538312366403328927883352378541892155035898371055667/52290862863202727937172182238250900552537602136840872347396815989922615160049680239436976910331435789986400238683861433524045231282276360265953065531527241456432500000000000000000000000000000000000000000000000000000000000000",
      "179494724671622674187177672864643187648754565912134293948766957145545470394921873794964673901379441907303157612509531992643286242707302647640097451485814597762777372407610594674110207649269980421616923178462803630418289441007929/17430287612728178908615444542276547126974565832436260566246366964093844925770269555806394864002250363664564913276475524052148833529666335522573520678707042480477500000000000000000000000000000000000000000000000000000000000000"
    ]
  },
  "scope": "exact rational stationary isolation and local fold; numerical flows and selection only"
}
