{
  "schema": "ghu-mathematical-video-certificates-v1",
  "passed": true,
  "checkCount": 113,
  "checks": [
    {
      "name": "Machin alternating-series enclosure of pi has width below 1e-80",
      "passed": true
    },
    {
      "name": "Uncoupled first root is exactly zero",
      "passed": true
    },
    {
      "name": "a=1/50: rational bracket stays inside first monotone branch",
      "passed": true
    },
    {
      "name": "a=1/50: exact Taylor bounds certify opposite residual signs",
      "passed": true
    },
    {
      "name": "a=1/50: laboratory root lies inside certified bracket",
      "passed": true
    },
    {
      "name": "a=1/10: rational bracket stays inside first monotone branch",
      "passed": true
    },
    {
      "name": "a=1/10: exact Taylor bounds certify opposite residual signs",
      "passed": true
    },
    {
      "name": "a=1/10: laboratory root lies inside certified bracket",
      "passed": true
    },
    {
      "name": "a=1/2: rational bracket stays inside first monotone branch",
      "passed": true
    },
    {
      "name": "a=1/2: exact Taylor bounds certify opposite residual signs",
      "passed": true
    },
    {
      "name": "a=1/2: laboratory root lies inside certified bracket",
      "passed": true
    },
    {
      "name": "a=1: rational bracket stays inside first monotone branch",
      "passed": true
    },
    {
      "name": "a=1: exact Taylor bounds certify opposite residual signs",
      "passed": true
    },
    {
      "name": "a=1: laboratory root lies inside certified bracket",
      "passed": true
    },
    {
      "name": "a=2: rational bracket stays inside first monotone branch",
      "passed": true
    },
    {
      "name": "a=2: exact Taylor bounds certify opposite residual signs",
      "passed": true
    },
    {
      "name": "a=2: laboratory root lies inside certified bracket",
      "passed": true
    },
    {
      "name": "a=4: rational bracket stays inside first monotone branch",
      "passed": true
    },
    {
      "name": "a=4: exact Taylor bounds certify opposite residual signs",
      "passed": true
    },
    {
      "name": "a=4: laboratory root lies inside certified bracket",
      "passed": true
    },
    {
      "name": "a=8: rational bracket stays inside first monotone branch",
      "passed": true
    },
    {
      "name": "a=8: exact Taylor bounds certify opposite residual signs",
      "passed": true
    },
    {
      "name": "a=8: laboratory root lies inside certified bracket",
      "passed": true
    },
    {
      "name": "a=16: rational bracket stays inside first monotone branch",
      "passed": true
    },
    {
      "name": "a=16: exact Taylor bounds certify opposite residual signs",
      "passed": true
    },
    {
      "name": "a=16: laboratory root lies inside certified bracket",
      "passed": true
    },
    {
      "name": "a=32: rational bracket stays inside first monotone branch",
      "passed": true
    },
    {
      "name": "a=32: exact Taylor bounds certify opposite residual signs",
      "passed": true
    },
    {
      "name": "a=32: laboratory root lies inside certified bracket",
      "passed": true
    },
    {
      "name": "a=100: rational bracket stays inside first monotone branch",
      "passed": true
    },
    {
      "name": "a=100: exact Taylor bounds certify opposite residual signs",
      "passed": true
    },
    {
      "name": "a=100: laboratory root lies inside certified bracket",
      "passed": true
    },
    {
      "name": "M=1 Gram leading principal minor 1 is rigorously positive",
      "passed": true
    },
    {
      "name": "M=1 Gram leading principal minor 2 is rigorously positive",
      "passed": true
    },
    {
      "name": "M=1 Gram leading principal minor 3 is rigorously positive",
      "passed": true
    },
    {
      "name": "A rigorous positive lower bound on the smallest Gram eigenvalue exceeds 0.1",
      "passed": true
    },
    {
      "name": "M=0: independent quadrature/eigensolver agrees with laboratory",
      "passed": true
    },
    {
      "name": "M=0.25: independent quadrature/eigensolver agrees with laboratory",
      "passed": true
    },
    {
      "name": "M=0.5: independent quadrature/eigensolver agrees with laboratory",
      "passed": true
    },
    {
      "name": "M=0.75: independent quadrature/eigensolver agrees with laboratory",
      "passed": true
    },
    {
      "name": "M=1: independent quadrature/eigensolver agrees with laboratory",
      "passed": true
    },
    {
      "name": "Reported smallest eigenvalue respects certified lower bound",
      "passed": true
    },
    {
      "name": "Positive half-spin representation has 512 weights",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (1,1)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (1,2)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (1,3)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (1,4)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (1,5)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (1,6)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (1,7)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (1,8)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (1,9)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (1,10)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (2,2)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (2,3)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (2,4)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (2,5)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (2,6)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (2,7)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (2,8)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (2,9)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (2,10)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (3,3)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (3,4)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (3,5)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (3,6)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (3,7)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (3,8)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (3,9)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (3,10)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (4,4)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (4,5)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (4,6)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (4,7)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (4,8)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (4,9)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (4,10)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (5,5)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (5,6)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (5,7)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (5,8)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (5,9)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (5,10)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (6,6)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (6,7)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (6,8)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (6,9)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (6,10)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (7,7)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (7,8)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (7,9)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (7,10)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (8,8)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (8,9)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (8,10)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (9,9)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (9,10)",
      "passed": true
    },
    {
      "name": "Exact degree-two polynomial coefficient (10,10)",
      "passed": true
    },
    {
      "name": "Exact polynomial agrees with source probe -2,-1",
      "passed": true
    },
    {
      "name": "Exact polynomial agrees with source probe -1,0",
      "passed": true
    },
    {
      "name": "Exact polynomial agrees with source probe 0,2",
      "passed": true
    },
    {
      "name": "Exact polynomial agrees with source probe 1,2",
      "passed": true
    },
    {
      "name": "Exact polynomial agrees with source probe 2,-2",
      "passed": true
    },
    {
      "name": "s=-1, residue class n=0: mod-six condition iff n=0 mod3",
      "passed": true
    },
    {
      "name": "s=-1, residue class n=1: mod-six condition iff n=0 mod3",
      "passed": true
    },
    {
      "name": "s=-1, residue class n=2: mod-six condition iff n=0 mod3",
      "passed": true
    },
    {
      "name": "s=-1: adding three families preserves the residue",
      "passed": true
    },
    {
      "name": "s=1, residue class n=0: mod-six condition iff n=0 mod3",
      "passed": true
    },
    {
      "name": "s=1, residue class n=1: mod-six condition iff n=0 mod3",
      "passed": true
    },
    {
      "name": "s=1, residue class n=2: mod-six condition iff n=0 mod3",
      "passed": true
    },
    {
      "name": "s=1: adding three families preserves the residue",
      "passed": true
    },
    {
      "name": "Mixed assignments give a two-family counterexample to identical-assignment inference",
      "passed": true
    },
    {
      "name": "Four-profile restriction has exact nonzero Vandermonde determinant 72",
      "passed": true
    }
  ],
  "proofAssistantFormalization": false,
  "method": "Exact Fraction arithmetic; alternating arctangent series; Taylor derivative/remainder bounds; Sylvester criterion. Analytic implications are stated in proof notes, not mechanically formalized.",
  "pi": {
    "lower": "33306675330447832566394056715540429478318954333089023506157464730379965223951114567353051370191873904532166852911044633640542766313572230194002803287327921187827029845107902993467017019173143516452856491843246908540172372452076613826334697747397630708110629803320021427719855341371288773389976564502387548692704651711719318391772561131736601131614287105879776088388953092527916733714575546973019989824803434088465056812/10601844033595318138829381918629017485509239618738530610553503803936273680330620218356400232349489895501010083851267114096456350063153044335221903777601741379754288447174687300404734507050923842434178882389182883852336649195004435042646889468367101812410643345519388707626482780217248047731974710041093370431194328471231439277064744792126939321335694728338671793824507773727392444251815817324313684366643428802490234375",
    "upper": "14577246253762991091890047756315728662978131656084900258292687772614259739829097252916363534544420142054920293743211198476879513069630677306271307519226981472126236728104777237421109937731675151892914157595006424258750205262790330719359115486292385605301378276135829731196952405489946347727172708326779806551250586701660432076792107096185288192862406936833797465727484176545528458935079517029292236236275885534863392/4640081595908386643629042698232268992800038347866165950593259836109431592728865136445615549600624067987697205866173173656123120246123599173343386748131922313927578494413038681222639006254671592949256351599754417750186730447210498346775655830765874990113374829537030473742792834604282158808483180459504109885678790843661455190326125589593555488058548838578925348744116775672428898413812703438452444970607757568359375",
    "display": [
      3.141592653589793,
      3.141592653589793
    ]
  },
  "rootCertificates": [
    {
      "a": "1/50",
      "x": {
        "lower": "140951676371/1000000000000",
        "upper": "17618959547/125000000000",
        "display": [
          0.140951676371,
          0.140951676376
        ]
      },
      "kR": {
        "lower": "2678895736592433610578082756107368009163444774194468214737308614136664480149840181093937808134932324067882589269155036812983701043045709487910175453084798168296790056452940020934238403822262334162004486946016349445332410182917432371971492954109504539349414844708949242246590253944178723631687877515365639650306534337144289233607746617551636064583923838956644783297122545888510787570613302932542865164577960968017578125/59708400655413211512381635609869224603558427263323751457966849116628007894339982347945425037493944901856953523172193068961298485533207254246487275598753716109829065638317167564476866304948941422153376389509146313763840840756389194626494937031853611439314445419052358578982717052886820240290499413306490087633922403130001129786540470665974940437964418813271234419619775187130484567798085701751980999623786027150800453632",
        "upper": "765106016876622722075157339993448057968815929496714747894019665103519028591271965542980495451369731010222301040699610103631453748485998114456257453776451854527065182005412913103690358812693354286389656530848497422250471192954115094536129598867621080999909407362870695296367044569250960280184371259969858770030996767663952207450892957255120764893336532687831911838121684510678863384847137041333553497679531574249267578125/17053017769189290273993757038356699892899304618541580035152621941954542194662970658484762301538239439120469428690454852423957896352548981859329435283111895648167439280695246332655112713816649480423862523823742417172568254695463226279083365246667586922552642459299850970992565934782099851975668001025222424930664781676400291016587551299449139779386514998210445357255143983374293367661862680050186234790299358253294109087744",
        "display": [
          0.04486631206306751,
          0.044866312064659054
        ]
      },
      "leftResidual": {
        "lower": "-228705694772946852834105368524929902129798106864300190761650307614708198044129191587789932239139324299980859041820643483198729224867586121766704703730710793610304019737082093955243933279478534718417273557884206775481735980116469290260927523500001094981050784403082413095900632378805141425160275960629579769813168692692823877068432302103652965768295573319044552894462720340871635006202767766999527446126092186792621134588973641457501226309759070038382527040473833438244672045471906371178725841069585149267983386201358601225227169393071308415339456924937830082961163985000267088582022766310930700922653001208769634065560568716433236421537397119100336091362525855355411673699/354326080054975108893644529295064602122563616768000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "-2973174032048309086843369790824088727687375389235902479901453998991206574573679490641269119108809461123928752347825959091650677793520055882778799377829605989419068178913391279570596371637389270504814169433942048044652228271270620863472221747563343866668545437369339965643350159565559856362381452563413830836155506381851948860979465152067640261881395057008295678860906120545774247079814157699643977542961181359360862074289721937623045305145928976537967626955122652250482234208132021133759273855291249268187059155362680560001642327728137385236914870355540159441421428892369287267501268540216531616511459503405411454401267474675601133679909881595999930812287163880379648241913/4606239040714676415617378880835839827593327017984000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          -6.454667258403961e-13,
          -6.454667258403961e-13
        ]
      },
      "rightResidual": {
        "lower": "2264552321033320993523701007466673706779336346430931613995210921596684985016763285480366815687765021996561287516625280347940444290619486126524695929356269028106464493064191717270362790504276437485471167438736218527732618810780901696628758680275294326953152472054649873798460228652981545241889252641349662462419652941274644241583691461407331454105014354587449869478630365832928156951869408451211483213216367515111046322846308599885052639577310391941938371664578355913264691452986707438813054418327981896947137777093424984969765445759299885491369284423634448748409111266412598545390122895913287091068995780257108570167840159759/2945651776085583859969651346134994937072096800023778160533600056421991622450427903562308884488629701081663370132446289062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "52664007465891185895900023429457528064635728986765851488260719106899650814343332220473646876459677771190486421057602812926055722849686161812699164110666835462108200683140141144413637207516521539622577989619166898415870996482728866819201421721837756189853373760354365695248049633177920439722330940816668036332666270267445138740916810659022862872463721222654678556154984988793096524486280761665464540175220379611390360936488998964399137455203233467596354813146724403570101903008135187038717914007991652104147244961710711558256174549441225683595183562578853374293951571477954116242836247919593201496851079238206777437957205587/68503529676408926976038403398488254350513879070320422337990698986557944708149486129356020569503016304224729537963867187500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          7.687780135514314e-13,
          7.687780135514314e-13
        ]
      }
    },
    {
      "a": "1/10",
      "x": {
        "lower": "155526424099/500000000000",
        "upper": "311052848203/1000000000000",
        "display": [
          0.311052848198,
          0.311052848203
        ]
      },
      "kR": {
        "lower": "2955900101178214335643310780901995089843266935167781344563530997439114002696513634016527586985146895863485256310537255502720937113836716629220103713369873800380506059957019263021563174611943291965415184488746445534266797571993828955774029897500899924742922919242662024332937143252434738676971207241945849402628415615962355654287957076241054645752147135739207009371910073075345910809108573857884039171040058135986328125/29854200327706605756190817804934612301779213631661875728983424558314003947169991173972712518746972450928476761586096534480649242766603627123243637799376858054914532819158583782238433152474470711076688194754573156881920420378194597313247468515926805719657222709526179289491358526443410120145249706653245043816961201565000564893270235332987470218982209406635617209809887593565242283899042850875990499811893013575400226816",
        "upper": "13507517574569188251110556524755454663848502326400736282016841435281706233746819308065816885766225143847968859116996572242947762407052793295507897884897389497488074595521759613242514403672993985132921380547586840740358764990084614878135159771685320664411398250722977775069973285509976343976231026326925951159844610498381717233377411568551508566943431440545694514623006021068472620912104265045172724057920277118682861328125/136424142153514322191950056306853599143194436948332640281220975535636337557303765267878098412305915512963755429523638819391663170820391854874635482264895165185339514245561970661240901710533195843390900190589939337380546037563705810232666921973340695380421139674398807767940527478256798815805344008201779399445318253411202328132700410395593118235092119985683562858041151866994346941294901440401489878322394866026352872701952",
        "display": [
          0.0990111967070493,
          0.09901119670864085
        ]
      },
      "leftResidual": {
        "lower": "-500778115507110412252686574150210275780624389432437734773146065275444349401775708436463224233231142848981295483362149607270832128564717456592334929128491320972707322110589092153523199551463934417283254832452044974917317458781489204264544234365646732670442903110808618287210930129572534199344467378125793145367929365308892175059923018739588814759581267658002447155154468549737107182786055277202611731607173819718138793281828190033950052551154351696577836213636263659707313738654708327848160873712206600982813744439363722701697750599326310092902998760539995208699453564025005856575221707147988880433666016151925039271619810525066673379269709135964451550209660006801/344417550765503905957186207335963426215577003479003906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "-500778115507110412252686574150210275780624389432437734773146065275444349401775607299132257508276639818629447358456151771168527712631195946045049638440110594230779451620613646853157308625109476232035672779996247951128411837931858258475158847547850693785072782118969865493498255290966225736359506262861790279871013217518701854981367376913851584217663304555720844502808698759584611058027477295912635684025116739541671977369174964666734860136293654892701088430072679352686476133906041554595840257111669901552079661116128528962323119290216564590778936647307496754664117455194756972271288676691895501592838677385019063254784281497710323538354015864035548449790339993199/344417550765503905957186207335963426215577003479003906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          -1.4539854731388654e-12,
          -1.4539854731388654e-12
        ]
      },
      "rightResidual": {
        "lower": "21546398516911635187923432805376109078776796089733730192171554897543230134495978959687716237765687275008838980407307374602326786256225453908460135069479545037892192943020028507579064981354907196530882316918867122251635413771795367223503115091791754504160725811826204300995160054351592790681671083309353020019152271780328496540454992181767818724890915063237497827697720708296492608391849235360787888221449431314775699414900566726044724736391865549491075793918184903803664183241406284393099241475633309193876141538721571700012661156312373014776782256936869510241062898567749852067910106570297877699463087811640427786306281093997129274528922251069847299162736367590665362164059/12600374922115842115208186907249357934243098918912000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "7347321894266867599081890586633253195862887466599201995530500220062241475863130086976631517805458801279284903829032017329851352197639736890077492314730153578883569051805965660807859272470648011275543517007022060062290089461131647440781933379973480366901185233949404597236139032574348844204621842386001831598535629883093848376592230249420585168761392427648531439089421941795270612896902263626776385022048886234708495232423596741478721212249040792281874605235281168567795033980352439566527405690248228003765919600188551298713835681937063240253878666536210172295174975384317516746187583132239102644006358496827967461118350216636695811542455262014574816885506898651583111502055881/4296727848441502161285991735372031055576896731348992000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          1.7099807466120687e-12,
          1.7099807466120687e-12
        ]
      }
    },
    {
      "a": "1/2",
      "x": {
        "lower": "163317796773/250000000000",
        "upper": "653271187097/1000000000000",
        "display": [
          0.653271187092,
          0.653271187097
        ]
      },
      "kR": {
        "lower": "3103981171059521118988351777138431073143955714553500339903210982184154873240938499460915019352323779991909446991509970167378547259076836191565439122943797763521938112473309049902313014846435864982089025667269121781079819575209392430083109022895364720963008653883401259371042213213563926478166294096584609688238280811157400592331277167139697044968427141301567947681504519572069471233799475839987280778586864471435546875/14927100163853302878095408902467306150889606815830937864491712279157001973584995586986356259373486225464238380793048267240324621383301813561621818899688429027457266409579291891119216576237235355538344097377286578440960210189097298656623734257963402859828611354763089644745679263221705060072624853326622521908480600782500282446635117666493735109491104703317808604904943796782621141949521425437995249905946506787700113408",
        "upper": "28368401355751670699845414813391117154342465377464908093889575429038713440207918569406279393339792938665375076516187247466206750174411899665038886050652972117387143971071429625713341071279211049687108077915464704352460125294181567375318054109162388812492641016073972109561565442487707974436343141632112360461939006340690360524619601166664147558245403995426853066358811144333714761821274574771223342395387589931488037109375/136424142153514322191950056306853599143194436948332640281220975535636337557303765267878098412305915512963755429523638819391663170820391854874635482264895165185339514245561970661240901710533195843390900190589939337380546037563705810232666921973340695380421139674398807767940527478256798815805344008201779399445318253411202328132700410395593118235092119985683562858041151866994346941294901440401489878322394866026352872701952",
        "display": [
          0.20794267721040435,
          0.20794267721199589
        ]
      },
      "leftResidual": {
        "lower": "-5180726117936790614101877981062785361063546439546641235871571959003297255412408240714987957134828361310765302258558055730230925012608737204605901254594735553790597724478053609935971252325784990243681354883139389672089246587431590250281185476276477232171900984683835799537327156393741069237655178741641834744473191456688950253370975546231071996716358912360361618577344213915089578346459298485925219108117034570069261877905024927558263319288157455949985805572265626320787234647893280716540463383466157110426713676705953413168322620852296281287993254571485608318991452550124908323754222605425866168692002798105286220295524414520749179657/1507120148055835420492408235424637596468200317900709706009365618228912353515625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "-3972135672216116843529035891597213811683145847675163052823296259553927128201685210271342309567646618810591111933606613533699759434964187458312920670181524556099999648325639872486669333274902543231167218844400036324006250769041353641357978097734417781314115646413047875065722784685888397771573113425102629916763313125493898561645035185119477733901069955069637964464559230861220288708972035139376249565487228518909073789525622719649266420485998206975833288652801931522720472118908639041328311390303844801963131424582300309761284191242088178821771023360609519618177485074279169488790908320829937055707534436253483102433445719165456887859/1155530241539253615427322957174793263863954440040515692089684307575225830078125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          -3.437500404078505e-12,
          -3.437500404078505e-12
        ]
      },
      "rightResidual": {
        "lower": "155728850384844659910668507265466019459149929906732894843538614627778374169950769114861217385076446314144691568993602973941166616588703981619201830931261331163459966715475329872184889120075129658778879371142719355108338010408556467251287200691108643178753976720501583354127729963634233631459878797604015823521821344546532017132306780805766500420602577857139782566953950648874843191327895889176172140476307651747468028086705438681200265813304817278807363921494058789348420759840690896864652590866033325341557712377197135513849725258489897891643775511510263578083871289490631824707802136613771063821820123053674469765065069212056079660141129367923552299228869453234168565927822707/41922128467226548114168730174846032731439451892350976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "185869918201266206990152734478136861935114432469326358361642863571057345564098126307686538886906214084602873155716652058706270409272309598606902851564411810081387943438346046816817900418453229496446445201842318657235686392667669089688546773427656615976061229458347315936495416809328513118245293097240549751065487149364906787095282016196907312033835674247760091807072362525483451922755540674646965721503710193183714201800521970238102625184309444205872071378047008316617690739865469163347828281178956382144184815578051935456196292877421932611422492152418631659831486075323524341224183292519638218687438971758318791781518798141807562968999054863085283764465542910655992356795824511/50036088815722009039491710208687200356879345806999552000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          3.714717169157782e-12,
          3.714717169157782e-12
        ]
      }
    },
    {
      "a": "1",
      "x": {
        "lower": "860333589017/1000000000000",
        "upper": "430166794511/500000000000",
        "display": [
          0.860333589017,
          0.860333589022
        ]
      },
      "kR": {
        "lower": "16351305944021366306584497611350448799985748885647072034231176131254945776174166768892403041983233578577289847291525008125204888860181186390360269768221545859189723019322797471404529999393832643316573097709567867776283772221756856314931794045365321720187286154566795296684592088400744213072458117081514205536288701217849905517355820839711984760156767878034980189404956095193164299084198631817343994043767452239990234375/59708400655413211512381635609869224603558427263323751457966849116628007894339982347945425037493944901856953523172193068961298485533207254246487275598753716109829065638317167564476866304948941422153376389509146313763840840756389194626494937031853611439314445419052358578982717052886820240290499413306490087633922403130001129786540470665974940437964418813271234419619775187130484567798085701751980999623786027150800453632",
        "upper": "18680058936677452178872277818900592588926480380992542647042262789320343032569199042604644634258455243217526243872714343041033544379995903980722066562604330715138165203463434200981031959863646769729920898431890515260647339792227395079061225568142954987732438571259283270696530233996873387567662222125038879719587734158511518984683046781900908616369674617875199581998197941439337718162738699589908719644881784915924072265625/68212071076757161095975028153426799571597218474166320140610487767818168778651882633939049206152957756481877714761819409695831585410195927437317741132447582592669757122780985330620450855266597921695450095294969668690273018781852905116333460986670347690210569837199403883970263739128399407902672004100889699722659126705601164066350205197796559117546059992841781429020575933497173470647450720200744939161197433013176436350976",
        "display": [
          0.2738526868000934,
          0.27385268680168495
        ]
      },
      "leftResidual": {
        "lower": "-1330075034259580477075925629287017609739749195891410396760440178112741091621005710550383363720972496361460443615439302012155583217077832190508119110800782036559255722718282676990186842024619780340624420461326982950523018520088726616239894485995716686922479809307817442178730053395337075176054352231723940545602529210172273893442040327143733975972198191722266551177720574375801547941362864241581183463554033971810209408582037588314059461582831058236144829691612106745883566384337842016522054351156629007002000802953358709047896832885610091241665971643768753559425137641573546228881931206041448756054263360486232029640530799773031894858353525746492176933247997191392310816161/269067180859735189510313194934101491285347008512000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "-1330075034259580477075925629287017609739749195891410396750725744065856690518211320979360282586847318902980604405126570598778502389718826745490002331895683929839344286066281652051874461011408736860270656579872948297716570078775472068143658205839579815807928807466840027333156849093315654077178034198848704914924845081329908099010945237598249404302009373311010646239426862605609318182150127367800326379224127874098234606870745324451912785957870578957991600389318108579994767373566015913068638938149160130950534234039639660646975540269747112622680639700715306053706719938165531818208568509896705172002450683098024819120548145637766848622451996538057923066752002808607689183839/269067180859735189510313194934101491285347008512000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          -4.943282305964134e-12,
          -4.943282305964134e-12
        ]
      },
      "rightResidual": {
        "lower": "5192787278751064438777126591649443692210793331890200419125900177040188539582922595715034232832927784256077028738243396127583331497647025404026001137763083143940932312021505365305938945272980682966088370666729536881343371001691677534333741891521605863789570638174832005429866048181644028595661000395349433734169983233598903411978592316160446132063301611391710240339481623028092684280052319677064110814534307928841535104266499600123935310071904598512458443736555298028738391485622191425594471580498554112213635410518373850160140154024700680474984252048340972612171089229850805717288527897194261272155508672490170277249291464211356919525838761373995090845996660839/954065237577573146695806668520674310846473693847656250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "1874596207629134262398542699585449172888096392812362351316884856832238991447433154141305759913632252882412130290869016953035991430922704696530114083307175321631526711560631157183451562410706833504254889316483670329452510250004818978180054223950568613923588717428450190257496583530996147554101580837720211222412686425909623355327250197966669297815996543406441741034683324717811772995888944121049531639535930587059452307423005610241286667149826913298438981145779828531627512784845393966942393896471785081668103918360718008448544363152647925026533922456353398675797318526008976664495431963556621052632606502291283013583703426063239272484873482143987772204595205437121/344417550765503905957186207335963426215577003479003906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          5.442801051986604e-12,
          5.442801051986604e-12
        ]
      }
    },
    {
      "a": "2",
      "x": {
        "lower": "1076873986309/1000000000000",
        "upper": "538436993157/500000000000",
        "display": [
          1.076873986309,
          1.076873986314
        ]
      },
      "kR": {
        "lower": "20466823843778112835132048132878142905772252018256709923813327106777856494854455209549181813898035007520929079502302923546570786676500338468932771753015327708013767735746844466356369705379195217317595976926679978426682784750808398413523987379792555561319448234150483407625470259032371392174077871010630881927002905666145322828014686852763586664538904719303677980751483121785931455771656573006112012080848217010498046875/59708400655413211512381635609869224603558427263323751457966849116628007894339982347945425037493944901856953523172193068961298485533207254246487275598753716109829065638317167564476866304948941422153376389509146313763840840756389194626494937031853611439314445419052358578982717052886820240290499413306490087633922403130001129786540470665974940437964418813271234419619775187130484567798085701751980999623786027150800453632",
        "upper": "23381708895717554548015570485704260889259097289748445164858703706777226695803934162979761838869362691671318575534951249176710373363315229698324864280072442974871730368400593968953912676775444681520169456107103732709876179685666457803334919077259315472518643174217280242397608273689856909516934661408740353161867455604333169628725948492531319663973915388077385312788297347159446773305624400762781078810803592205047607421875/68212071076757161095975028153426799571597218474166320140610487767818168778651882633939049206152957756481877714761819409695831585410195927437317741132447582592669757122780985330620450855266597921695450095294969668690273018781852905116333460986670347690210569837199403883970263739128399407902672004100889699722659126705601164066350205197796559117546059992841781429020575933497173470647450720200744939161197433013176436350976",
        "display": [
          0.34277963601630274,
          0.3427796360178943
        ]
      },
      "leftResidual": {
        "lower": "-72017476151164941298674292091136392278190082029664135290521485591043771098227772153193455409507291127381255807140343198059834400715024172603796747833909572411696113745740209233406248830137715322918792774881508967607560746655385874000902002823427360120761930065916569050273915623947041740555746226433575352379751121803568894681700356576175654690304836875257129973882192160208115676213651846143210962035691840970269196072328120530110832800257622751390952638987683912457380191442249232923677715887241522299537293675653224296201230107372522341321571254316817977375929016192194083288240782674843000274222164720102126737879617391039554045973303077029506903350629624105142773215557/8149499841264427504553824173786485848818963185664000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "-936227189965144236882765797184773099616471066385633187017204809236790570968730351027774192033633127557162809593218578698735526601400029927535406190360664972630816345135381624588683959255093812435931176963912828746347492597208400021882161477981235107877431562276260612546193513960864717795266648203428032278244518996768677096671231138057764521969462020439786533668813889402893574935938647877074796257055428160251887818002197672342507419039373861534302640273663373520414011375820192510818386062113673975693516621472810811428177952579848755028989158544886710742425056387781049218623421576380252293005095035269550372359953897899148673990255317464100809156441814886633143948197759/105943497936437557559199714259224316034646521413632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          -8.837042463208532e-12,
          -8.837042463208532e-12
        ]
      },
      "rightResidual": {
        "lower": "337948405004239983911455381222424320757858220072457468649314019600598206923334464682369239277932384807580110954498872239182944867530551323926149513381850694104150108582711919504820219209297306926109999254831365340943566717999534329425588565040617115123736176372494384745568740298649961747205597378993789090890096190085857794340363325007115766365429612054502258156104548309576051508009515510561180265580503688244657610291628307032890001163513700985660294480724528822976207703360099274443894904852509012983102536694848198729022891694039695562371265227832033228332277646786125847416901772078960918602686582568565411199231939034859830850973608672449/48816736556690533035390159606933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "141720298872745799704803869544887618382327640675546790882819536825259771469555409819289610340240005832205515299569861099204020682350120223728981198140398431487650632445436119501654747760881797937016394186042364139070332304195782793726219750045964045588830962866656936341507989710732091162890307923724700936207222708874523886147079325268812095401149792451770759063204319053664365565972042052228290068417400545968535101211570253037495812887211014622490213837962189517764168831493465054269489737386948612061755091608588014583548221725017491599940799781683980407018497938834925840989557521793496763534696390374985863984333974759574909643140099588973/20471534685063771918066841125488281250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          6.922797975480866e-12,
          6.922797975480866e-12
        ]
      }
    },
    {
      "a": "4",
      "x": {
        "lower": "252918314257/200000000000",
        "upper": "126459157129/100000000000",
        "display": [
          1.264591571285,
          1.26459157129
        ]
      },
      "kR": {
        "lower": "24034541880362586491191944971951723059182734729774408607126716965174917853418355686902238772504502453670505175511482585512803962443622146903809394830064001750782892146462552799964451986775761275286954053393612237057347305711184588183539390138018160225097140289447536213538104629888894142042569312521332779549678976334990173805462052417250760209013945671087861896212640705524222865807626448031442123465240001678466796875/59708400655413211512381635609869224603558427263323751457966849116628007894339982347945425037493944901856953523172193068961298485533207254246487275598753716109829065638317167564476866304948941422153376389509146313763840840756389194626494937031853611439314445419052358578982717052886820240290499413306490087633922403130001129786540470665974940437964418813271234419619775187130484567798085701751980999623786027150800453632",
        "upper": "27457541335072388942171517832598700328118300949040494494649586548807197533054505346317441169520563231501517299137758278600174478023190526090496616015754389174812033477690433483434458036688509677465523509824456483614719941721219424520395915496311410752511554132029739308928320031643765629421696654019396415043965052257834904282381367860712756464653091672214672701489432993973745645958917105389218704658560454845428466796875/68212071076757161095975028153426799571597218474166320140610487767818168778651882633939049206152957756481877714761819409695831585410195927437317741132447582592669757122780985330620450855266597921695450095294969668690273018781852905116333460986670347690210569837199403883970263739128399407902672004100889699722659126705601164066350205197796559117546059992841781429020575933497173470647450720200744939161197433013176436350976",
        "display": [
          0.4025319991247094,
          0.4025319991263009
        ]
      },
      "leftResidual": {
        "lower": "-158901108390685708310771551044243977803757862406866221070318989636601541852719091012230983462664074069673773447963554856110046983178314943846682013135609056282339439233441615575334282450167891001249506420512207510273461303764218638619014752046456959052687497547330740082396692383524060095715214906353244550339485438078174109441585122980245876575537396320563778878769748679050176023425818203211811378766125866958042416778057209500915468613905213202741079954747469025911187810636826594088105796232475016462362372901177041032375605333931640282643051472454887624840325790302100315433196331990662809888776163009225130986350257899138431219491/11016098685977575027611175146647370574573976401958772275360563200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "-1747912192297542791418487061486683755841336486471507367681879130541413321910894204892640567837082124034666529052417660856002766080603542763949011356186287078674924677855146086819582901824077621709821586620872170050972215681194445521013154440620397651455602424759932664891281363696923393537048028078689345174633472621350529316174022125832598472442732847306801225741347011494422826064605512615335217296559745691474870343968582497546055286524947171424279351927685863281574444091610581688175642398417416965575903843670511506178533296612246816719313027716761668257480854575385250494808797264086983821121504270959209563150147163109477256585599/121177085545753325303722926613121076320313740421546495028966195200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          -1.442444488927386e-11,
          -1.442444488927386e-11
        ]
      },
      "rightResidual": {
        "lower": "3318829067042551691435558179380183281146282524858826797519445898630524582083940893464286261419860423211756482189481421118684492274237509339032807087920020104624469521654055304660348423759484105225396333059217270647992712613238737635179399009901706658695557709528501606021878504241394125872088942686015722995604745006628234451587021348073978340707550809139761185914086550092768792418845877714311995670250385725724022627488982775261255809094350819923083680760048211374600235597753962739889215187307712550639402544780231625648011431699777443145315666662425756561281433013864044757074879473113446200199181424778698191829897612271/293217155630885119135017583453554482242582177696972800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "474118438148935955919365454197169040163754646409793818707286197377138821446872141444188127402673612880874607183407606215558063097713128252941664225396054162965540639302470590967685245497729398762047612922113467256101747348368591280178157025644372381028601615168563440224095020892921587114617782019823497289572788255141172870344540334896597910422217895209895933738585333485711527441434360698702473375774184341722102389451041990626284479964422826220724461411793319551714492045806302038017857499544388816875684562787572670016322350658503904290458543436049975584154505372937235480080059118864581565840691082174471686881443198247/41888165090126445590716797636222068891797453956710400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          1.1318672878814917e-11,
          1.1318672878814917e-11
        ]
      }
    },
    {
      "a": "8",
      "x": {
        "lower": "55912624319/40000000000",
        "upper": "69890780399/50000000000",
        "display": [
          1.397815607975,
          1.39781560798
        ]
      },
      "kR": {
        "lower": "26566567841948834810534707116428384419571820547382719701650478324729667503808394076293158625231298969737792326197385589640269794952352933541815064824977740532728409879705586913117861309898029467166009304823976285422261847203205064250986273734702511141634761324660188116708901846535611532711220914100483593121223912524576768663301867845811900816107349185308388029959768037338943037772853728029076592065393924713134765625/59708400655413211512381635609869224603558427263323751457966849116628007894339982347945425037493944901856953523172193068961298485533207254246487275598753716109829065638317167564476866304948941422153376389509146313763840840756389194626494937031853611439314445419052358578982717052886820240290499413306490087633922403130001129786540470665974940437964418813271234419619775187130484567798085701751980999623786027150800453632",
        "upper": "15175089217053875373577538080845863899727000184396290627627711000594867314326546501562707913836355053693553742912173794287736997198907375680743526765671871317041115923250970257491587957804925652615996905081766489873882806106266728394684292127417773463291231577538688548074351093942654255434688808347724943742184709129771210989937364901304787358504368857465243083602413100192759132407716027302058137138374149799346923828125/34106035538378580547987514076713399785798609237083160070305243883909084389325941316969524603076478878240938857380909704847915792705097963718658870566223791296334878561390492665310225427633298960847725047647484834345136509390926452558166730493335173845105284918599701941985131869564199703951336002050444849861329563352800582033175102598898279558773029996420890714510287966748586735323725360100372469580598716506588218175488",
        "display": [
          0.4449385270804484,
          0.44493852708203996
        ]
      },
      "leftResidual": {
        "lower": "-21759217737944292212742001516369960887964530445505421568358950339032280476556915233582252354119655319057377807377016271614133109159905875718088876320208950602640116959028629622205212338975363301382567225611326141634006365156067060742606564647902684814045941055242753485277243621206671318872499807262980347035120455226823501285214557358239219929433222221786348327202516000598019614561807633481089574833597959276601096035323918422787680394543369882738986562179255020007059043958797002473477989516249341395301644730518575239160252338967882763507417994448131605008842271533803244241748475680668124855662653401/871479941775075024783920881871859475810364716289061432607087963748123755345052958720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "-21759217737944292212742001516369960887964530436878186584896269950374964002697846451645684235975393256959901135362072204641745082901874490340086101520150748461476936143234056723118847735377117468700344486440836391711491748339432126330822930574823960899479165335299373562178004339776664568652515962835508830902347362247488746170788181455404198175724995980955359428484947016028932838299649819797426385786839404774097788266385521450509379183818833635303182480188173039968016116186732660758773472152606682444786942344267414770344732370903213035349977659962371568240176606594838842785564964319331875144337346599/871479941775075024783920881871859475810364716289061432607087963748123755345052958720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          -2.496812226523998e-11,
          -2.496812226523998e-11
        ]
      },
      "rightResidual": {
        "lower": "48373382569664156149550760764097943578310150635893410863723796958989054153631272545704572381416991997619598750052728369321002041493781293519442794790550020401319388256635678246811228731411113607280646080157787468502489839532303613057257783248024146521941106004420366537758805613456608816885554459159094205016840129146587191992996379347399928783799553058616986899070543866280735145044155073491174793948825895205858439785303992385289458673820235284451696814117158073164711741792879643041717766753269792127191145600555070830202050381735028136660260130348384537175196426986718489651378486948030697383941933657839/2352418214367214711817404598975230013083648681640625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "48373382569664156149550760764097943578310150659181227077848545714694506959847980027176334625936618963731110368419027978287139598018708224449419892397260517080932700806323664908965138225914310446418704569610964675720920948475982407198003203873650123396857181746170556297657176636508977825147257273482724041361729121553867236661120493373914032522113847101266485758426051899575253860173103974214384368177507424431676052694940650960102129499482462963096489405389723976073090008580973270371359315807197309370624846049372438761845358123662602971102518667730936089543874205565264266339136265801969302616058066342161/2352418214367214711817404598975230013083648681640625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          2.0563257959076924e-11,
          2.0563257959076924e-11
        ]
      }
    },
    {
      "a": "16",
      "x": {
        "lower": "739321449143/500000000000",
        "upper": "1478642898291/1000000000000",
        "display": [
          1.478642898286,
          1.478642898291
        ]
      },
      "kR": {
        "lower": "14051376536079370456412036121308790604439180839200298403479277578652727886914892409089158808942132350328127709742985835606984035596660499124744640704448082547798978987795783217134121341431649251380430549520087295811519509762378899864376867267854517294051332410735239043598227085441739172264133620445438603869570480983063701943927070907068099476706209623932152519119327517432859776802533957607010961510241031646728515625/29854200327706605756190817804934612301779213631661875728983424558314003947169991173972712518746972450928476761586096534480649242766603627123243637799376858054914532819158583782238433152474470711076688194754573156881920420378194597313247468515926805719657222709526179289491358526443410120145249706653245043816961201565000564893270235332987470218982209406635617209809887593565242283899042850875990499811893013575400226816",
        "upper": "64210294329608303353064985338305579990987158175380048835802950272521933328181860428939718328118622435405956185718188199773796758282042975689656464082287658446391321964408002479071589207425667913752528793824004497435314938832243465707759373646242838884592650935806777128466183428533597028050815362694662721392340427765117397346215477259005238790057591711591233751605584568200116584064940372655883038532920181751251220703125/136424142153514322191950056306853599143194436948332640281220975535636337557303765267878098412305915512963755429523638819391663170820391854874635482264895165185339514245561970661240901710533195843390900190589939337380546037563705810232666921973340695380421139674398807767940527478256798815805344008201779399445318253411202328132700410395593118235092119985683562858041151866994346941294901440401489878322394866026352872701952",
        "display": [
          0.47066665265988705,
          0.47066665266147856
        ]
      },
      "leftResidual": {
        "lower": "-13497740212664277714540653512007914385868807293685086270124099305246587533663902406767066536401038247087569599281850871936737223505562834483482758882803769851516200008537955997911323337909753209466999911008699006497358665855492627815880452961803512071853345998688260920397427735114131725003427625821578530296028580729833047023565101925419988717267031442976265819351992111022322210270829159703180339931727199439766550309975825970285681604256208294280282870266742015665267096498152734871032967644508248459646629309441962275519935762446882383151454771731477706802654911389010225616825406133279808144025546829180512665066658578114019540462105905040956627637504802016801/344417550765503905957186207335963426215577003479003906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "-1928248601809182530648664787429702055124115311511226831890981036223252038034960149155473770021365083348334065377774450545851672648358580161348885455007851642513502559790524541770190884848476970368395661440714659082531311173584468752197375556526680346299095597461554984030321985082601542883107273226957308085210407738174878546561593671475443611136902858473171559524621692288279514179919257827056161009020473592869843008852860588969050468328437138795650340110719449067670434261265386285086171574084517597656336663002392002434476630312626890796800107080961096519444222641684679017599719538399429027123631706330930112674118165058207979038721659994149053194642171140457/49202507252214843708169458190851918030796714782714843750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          -3.919004761129084e-11,
          -3.919004761129084e-11
        ]
      },
      "rightResidual": {
        "lower": "31449478492644116574122062452002624692639695444685930741926217193938022094281769312939859334621443875944410532563425049528004148530797047009973398185140309541083800934922510505283639592382344037062590153714454438333242353253822735052822707799061670886093023859459076998674061188862110168068234166285064044999040442439874419772643709924115416257110416764022900200124498947011772578171438994838096850171240162329139937871817155148980785672532964371270998363346426477083096173303098495165212964108953101396323271340942374524458418488374593287374366569596381102039531176610124287727638641496568446753402613102755526531018256553616128107636309710037696653491292267135691/681763031440348467542868436361955770368000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "1594213195479655678872546944571561620364224204397885296242260797382332500405842928952929227840750126668960978866335378361223143604211590244588557236969437446527652508928358831094084792052530965446615049465548998390734734162451225222260153649994327400191665463126911193511550447882305384700061450295601884366869955869790362004931602253036923280728608405100519608309457833764215125248866899816320889231288225781894438716211559955904730537449441753871697629512422462333593432961633574752563241309041118454644010441681251131789755685932398058144725182960129341468307830179322481971271799316323080914916102384388867311668096627853211137670163852947397865491224815951647/34559416340294161949177662672725868544000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          4.612963308702933e-11,
          4.612963308702933e-11
        ]
      }
    },
    {
      "a": "32",
      "x": {
        "lower": "1523231253591/1000000000000",
        "upper": "380807813399/250000000000",
        "display": [
          1.523231253591,
          1.523231253596
        ]
      },
      "kR": {
        "lower": "28950189285785844463883827948763562875253233114370263043346478490878610199555477513661768645074129053601079409282494309540296119113897092821568136425744486415108222274895156429350231433488621159743949329606709166233015235761922275106057892921092801768711744195835317709515992838781718680283224382900507118433808876645382270508923853938502432809984987865878010109792697768729013464705790426023668260313570499420166015625/59708400655413211512381635609869224603558427263323751457966849116628007894339982347945425037493944901856953523172193068961298485533207254246487275598753716109829065638317167564476866304948941422153376389509146313763840840756389194626494937031853611439314445419052358578982717052886820240290499413306490087633922403130001129786540470665974940437964418813271234419619775187130484567798085701751980999623786027150800453632",
        "upper": "16536637621988013657667089391484041185396779856785245259837883255500804871564238031822031643270778025897101957641218746181831033823223014902931278794745844232515288561507204260858680096101107533333442026637911338721793249184891586407209751722875771372383874963382634322781689539623553119199292909760986381635986366485216521699175099577310546138727214848193416911823780892060081260976078798563548843958415091037750244140625/34106035538378580547987514076713399785798609237083160070305243883909084389325941316969524603076478878240938857380909704847915792705097963718658870566223791296334878561390492665310225427633298960847725047647484834345136509390926452558166730493335173845105284918599701941985131869564199703951336002050444849861329563352800582033175102598898279558773029996420890714510287966748586735323725360100372469580598716506588218175488",
        "display": [
          0.484859566962144,
          0.48485956696373556
        ]
      },
      "leftResidual": {
        "lower": "-90579042656539591495778485761777432447488354788796095966927917232441659891119536819224148615810633022947884176184119882331134892099658858033952522623522121343196551816957288250332767744482281429835546530953439418640067832849073434194226151939198861477352768046612461720410932157216085992110397889176693541087619363642457211472261398573611572072308596871435803362665419189870626664573022587162984289915133132601902792226659101959788033903907389338497062894027990860674194361809175715770432795239616397765925298259648477285020343497062134934108837888370499713864050737549139794685873752595837388819065188896275088533773145499994316546011581292880200859670310475968390031/1267397475447607801162192423196875777114112000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "-168218222076430669920731473557586660259621223502238675333050651160369326547717995369470153290746038370948484305927140827920391532339709468993183590026704172745305995590795212736859028224129286933589822188981294116929327618984830059121254490521855192254499869517179691637106453882079924370868668499936939155902767549184866320483641888699511761147899774502534453329975434047523743974633226928140611560582434499410279252887176435756191312599435970351121076423127496225175731128626395294502267464302060335117657727703283961711762124591693361469992865048135244929108377028462941716478167682828111060606695587974631801469605519107391918707022140743036769832040851973201561371/2353738168688414487872643071651340728926208000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          -7.146853643885453e-11,
          -7.146853643885453e-11
        ]
      },
      "rightResidual": {
        "lower": "3261875324235313756291203107594060265655395554040442024449150336554414154554073599745174062214299041314516878447924962406676910586274984864938369791827668716029784064413267436960587031773783091371301542091688870393321513997085468432698211376381959723016230520967557689284521255741430361370365566404338778257178859849838264572906116615183994482092580494394972114778675895226626952605057409948234543144081983202861107515378702669764021796388279720557635686466913900497328983722566538244512448473042560643165976880352914886324238080039109685355374082839305125711285166652345813880815022040603068946534451023022539241521354538457834245103425778456867/34809312238950036035807177095571180942421292523088205417280960318748839199542999267578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "3261875324235313756291203107594060265655395654898277983601136943470342115452712004255562873887946863353079255761364919404711586513967023138394471872209529018850172940547273631008973132758672309592597392272076501814665966591897152045205540867961601966176666675755819568677427377086175095020124224152462417547292878842775294926051522867612266487578048309802305010982888329731993604641715033054224016957099413341608912126767191628666069835701647069425086669912908594648579025367577108141442164255693403555618113668606822511145375379806335422192258774321652034520286242990733359466811242018328823180527252129393123681366921605292165754896574221543133/34809312238950036035807177095571180942421292523088205417280960318748839199542999267578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          9.37069742097755e-11,
          9.37069742097755e-11
        ]
      }
    },
    {
      "a": "100",
      "x": {
        "lower": "777622564627/500000000000",
        "upper": "1555245129259/1000000000000",
        "display": [
          1.555245129254,
          1.555245129259
        ]
      },
      "kR": {
        "lower": "14779318889221417744616361465529405659178991689120300808036000095828418137952409488810179996836279965074615141620021543913809080106435136079474940056421462552919620771714328700192778043460667056164225576155014203614303587280911459788957405525319868413565504734981056872684434831780007628836834465024873423855404503509353864364229599975424954700494927548365521583488943966930404157189560265805994276888668537139892578125/29854200327706605756190817804934612301779213631661875728983424558314003947169991173972712518746972450928476761586096534480649242766603627123243637799376858054914532819158583782238433152474470711076688194754573156881920420378194597313247468515926805719657222709526179289491358526443410120145249706653245043816961201565000564893270235332987470218982209406635617209809887593565242283899042850875990499811893013575400226816",
        "upper": "67536757941914454005026526777283640194330577020042485423857714024809341554542981477799274430014750907560684873418040735309329027677469938688948418425013373588191016311544901402095071565553629995916941251137097289483541282187131334143916567710617104588414173922466405945684845242820655628681954958152414429585206443823055026755023538292094192969100420236515911697674133465140055188231926752706613115151412785053253173828125/136424142153514322191950056306853599143194436948332640281220975535636337557303765267878098412305915512963755429523638819391663170820391854874635482264895165185339514245561970661240901710533195843390900190589939337380546037563705810232666921973340695380421139674398807767940527478256798815805344008201779399445318253411202328132700410395593118235092119985683562858041151866994346941294901440401489878322394866026352872701952",
        "display": [
          0.49504990008073557,
          0.4950499000823271
        ]
      },
      "leftResidual": {
        "lower": "-47376656595840498650114438153844144482757209660558945583648671096340354373730258842991182065130569085837176150907084671281940690845952814644590408517684937511786866005419927343422926226746512281416046891012918184085471746323335078544821741885697047227363398856349819849700119420766307114203013393304150178541469046904091803874574158613575755366417935973934453663853242509682437787145207254361811514601090465980108533014329352373656764280758927256992564225216862654239806490620099824528550059556662792135441731455632372838121741127211846841366523992922684627342431623973602510463321514617429781794971609694861965042685908845003220978279231611687807422505328523831/216478661700505283442606038551831191838829040527343750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "-1155528209654646308539376540337662060555053759035262684507591878740967230218747487175461375472654831289119350479607682648560456271688155182581106548579160433610241053580297993069776231072394122141434599911912359741288876283767720253538468053171627764585233243369071567289222579770617932125755583495192538731548211948507011070562820426808143615051788364589620665205667531848191653682519893244081542562895947147001013316633239795953312603293632540322535586402329196452863491012407048110758182517172075209873520410329174191693856795047174952189121712377176596619080751488483839626561993765590851884155790454891064149796283856337593094389415692397858355548650523809/5279967358548909352258683867117833947288513183593750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          -2.188513926669841e-10,
          -2.188513926669841e-10
        ]
      },
      "rightResidual": {
        "lower": "34149486405120605911324490250012310668884190564706515709213693674732572362771644056100735411884196390797753992696721807298898044953025734292330892199871339277741378410864581439393665524059906703905356473022142188476475883757457888025553496336936606136123252544183388906953967949220171544039710992295092144761037360921367797094955449110000691939772581857870025123945603266626474859971223552189529969901218899476537659884523832260098076417276886467540392889222311654056425621472617103287927557114144948352073320687254426008112900087230621402128854319646413676556551366344201039108241530674450278044218749427389510886509192130704131872415354725582565842276644836680693070901491738763/119316827175952483094172539728407939312558440001306624000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "upper": "34149486405120605911324490250012310668884193618257942959724536602951506666925670479907847166108606047147203975502130060702987476649774199329523897728100130956439104819859986751855438279747450189152674799811701781782811591351438115851384397839432531290554589373358852626223774377399167439533420832097602782587692180098702800674274930785383193453545742360792972631737446788261996280594123373663349162915221445134283545973339079877801361060258355144640189731943638697377765072946109339549884485642629806615922186315749336498990281603375688291167779022155834299714516403683350139757754644759598964821466008189657277257686376273443906876871527883514841112316055163319306929098508261237/119316827175952483094172539728407939312558440001306624000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
        "display": [
          2.862084687749995e-10,
          2.862084687749995e-10
        ]
      }
    }
  ],
  "fourProfileVandermonde": "72",
  "gram": {
    "M": 1,
    "leadingPrincipalMinors": [
      {
        "lower": "7723359075278550656797402147889455200182564/1208841956571836257373263747929111509765625",
        "upper": "3823062742262882575114714063205280324090369364/598376768503058947399765555224910197333984375",
        "display": [
          6.38905609893065,
          6.38905609893065
        ]
      },
      {
        "lower": "4089066108245009088165467894787435188675286951675449722720118274349235603703426100235990577130122118942181529183767842118638524797471023906315384029464746756764317954005333994846599651718034634018927961015846302090170397475056319/174853908227804943416095388724264066242248468173670812687945462044674229986629810409587603580640297039775941781787453859266215089755307678462431351781172875565086528895224379389824204800000000000000000000000000000000000000000000",
        "upper": "11469427572318590789203409454862375451985950772098786885601776884653434256482613934159617299468016105878432096504064666505351148471766710741266530778016015668921160486705850351014130564265504468974907079453039/490447985693335312030799453794515193273644253666087118127977697495401713512442148897675017612252323442280594646619068034548189663002633438666497511269085965661397340202475800494080000000000000000000000000000",
        "display": [
          23.385614595000362,
          23.385614595000362
        ]
      },
      {
        "lower": "38817790812138614692291389430373671799519626087392447576831616294389024401673918635276210880161813837605804335012918753109107069248341207891884598488412179648740700039927753481464411296381994665829012528496349947132848436746404590527798967776111656526845411084055514057591374141414769496758213813946660883127116212373696332186945261646490818608065461926230224393741108575811310552615530748461674017937865246066440665904095825201279/7543608876097566452199893533969211066827166508411359200372942259154529101930144451241806997357585705373262665070878607151212182603559198217544322139782556731621257450677716427793264006385033770215617097262515856694400488217180401303371309534670612960523087973058886610244412365691176222231616925438339475706100889747358873432782928433808410334288738279851381572994105104066030942866636800000000000000000000000000000000000000000000",
        "upper": "5766432760937735157549867704914650288570601780971897047018186996409989303313822295379020383064031334147148992109515198374823722657196273648342426303583902723623266854208822807909237813887080994921918097300728562251969014859465974360315877861445785955656008995511211853848542531704158601009829754004757603030906223002265718045073921412232428864382577389865118688483749581792068483496879053163273780341/1120612802757106114659341482915241765502030074391905110694768355457938606615158920683499826398354841317442858253638811272498365553441079188436938433266012158278191340585625854311295769197060628000731856200807612112892069542692503087362247097701225779935649504190056413753555450318445573420810893155154154282986198851154048925910793992802433183581415704390827809361646059520000000000000000000000000000",
        "display": [
          5.145785187131772,
          5.145785187131772
        ]
      }
    ],
    "lambdaMinLowerBound": "171630514017436816392461670477967804965918657038450061364550103700822048259118419290917926385958108898814236242558587074272999108927640970893173887968984346998403193071135357784949399724850751955196505165848741610905443795367599215309041160049026106772243924523183709215413861564975542886959115877876922327042780636715056520000217604308284887662306793237106403592348846380377871758538614334381579552793350346790000466556115485556037195480009935918905851106738021714812171232181/1551988199085214836700792556421527298699913703545208522291082498617730192057951157119047925559004345415978947574394692324736022981431905535261577586271533169623279468962456163223592507352065762170979285807001915587532482744129065783881489145717235008121140262811783502050443670756780062242411015102074449247368348538248320805242941394423634835559659807056183437811963926846866469739597852167844840840474372475437167850012403163448481970534383560014430208000000000000000000000000",
    "lambdaMinLowerBoundDisplay": 0.11058751227528704
  },
  "trace": {
    "representation": "positive half-spin of Spin(20)",
    "insertion": "s1 s2",
    "degree": 2,
    "nonzeroCoefficients": {
      "h1 h2": "256"
    },
    "all55CoefficientsChecked": true
  },
  "scope": "Certificates concern the specified examples. They do not certify admissibility of a full field-theory domain, global anomaly cancellation, a selected Higgs vacuum or Standard Model phenomenology."
}
