{
  "cases": [
    {
      "x": "7/8",
      "covariance_magnitude": "1/5",
      "epsilon_max": "1/30",
      "negative_covariance_gap": [
        "113600279232030122197120353532187014156413095132357700352762029637958686171123159/115990915140831105658666077401574811118963378759044359282857025782537649798512640000",
        "11350616619182904009688314245672331326453119308354773321851250048509968424114332631/8281751341055340944028757926472441513893985243395767252795991640873188195613802496000"
      ],
      "positive_covariance_gap": [
        "-47440230048172355181480227516346803412032313954660526100204013856803702808003241/115990915140831105658666077401574811118963378759044359282857025782537649798512640000",
        "-147675743423552875143767241192983247933882900458328046890525457016066148995292329/8281751341055340944028757926472441513893985243395767252795991640873188195613802496000"
      ],
      "minimum_gap": "147675743423552875143767241192983247933882900458328046890525457016066148995292329/8281751341055340944028757926472441513893985243395767252795991640873188195613802496000",
      "certified_epsilon_supremum": "60304654034050944531055530958164298513677173296234457844325535057788586983002936/1661463877597975460787898687551945707476432298428705688439240594717591460494795751"
    },
    {
      "x": "7/8",
      "covariance_magnitude": "1/4",
      "epsilon_max": "1/16",
      "negative_covariance_gap": [
        "61008517487410100761573362477119428014069671359557166211639442643541688811433959/61861821408443256351288574614173232596780468671490324950857080417353413225873408000",
        "7595564830617034479190259084340505675889798850976815184175097337108594812632523751/4416934048562848503482004227451968807410125463144409201491195541799033704327361331200"
      ],
      "positive_covariance_gap": [
        "-46351822032724884157493691555236450364893934698454984757004586352966570507983641/61861821408443256351288574614173232596780468671490324950857080417353413225873408000",
        "-69963411120603444031128573569704040368202621565252394986086333242094902773892889/4416934048562848503482004227451968807410125463144409201491195541799033704327361331200"
      ],
      "minimum_gap": "69963411120603444031128573569704040368202621565252394986086333242094902773892889/4416934048562848503482004227451968807410125463144409201491195541799033704327361331200",
      "certified_epsilon_supremum": "108214205544911181551189203820103109240289682499622380214082932997480397704293040/1661463877597975460787898687551945707476432298428705688439240594717591460494795751"
    },
    {
      "x": "49/50",
      "covariance_magnitude": "1/4",
      "epsilon_max": "1",
      "negative_covariance_gap": [
        "91221516654267777243186960430195952871328207336736415870668765614158560874966806607977550443577250673871372914952265612179336422262121/55143468663788179674289891345650390287664522252914206275043577766795189337584994103001331259449768067902671319077392578125000000000000000000",
        "24560831904577830790110732868885197914943196937033133038208698952800450904884670444753776884312962716760801522916124310635173161265009897/1762193455125404872200133484306653776584061906777910504876392593851933224483694376769825151117199109996020148674864501953125000000000000000000"
      ],
      "positive_covariance_gap": [
        "-685723483590408482535552789264101086230259187450374285200859528832904196061166167663237457875034614409113185468313545998839200129260839/55143468663788179674289891345650390287664522252914206275043577766795189337584994103001331259449768067902671319077392578125000000000000000000",
        "-267627885849867076731602610476033551998835026815839365598835674094815458074361559130702729347025145673705016723022277803897463316267303/1762193455125404872200133484306653776584061906777910504876392593851933224483694376769825151117199109996020148674864501953125000000000000000000"
      ],
      "minimum_gap": "267627885849867076731602610476033551998835026815839365598835674094815458074361559130702729347025145673705016723022277803897463316267303/1762193455125404872200133484306653776584061906777910504876392593851933224483694376769825151117199109996020148674864501953125000000000000000000",
      "certified_epsilon_supremum": "11513927162931551030608131781474322216809128551432720709792935622791673690221773170837484494573980486264980138644986381460164374581277200/11246299277081683953876529170998288664810293524616881344194099948696858232147411611706781765226955340591275121921964103656266911265009897"
    }
  ],
  "reserves": {
    "7/8": {
      "log_interval": [
        "13416072405706609669337395393690757573848756813817218833828696705245496883/100471298486576181184283429105260903749692253815905724847163663524530647200",
        "1916581772243801381333913627670108224835536687688174589998470995658574429/14353042640939454454897632729322986249956036259415103549594809074932949600"
      ],
      "polynomials": {
        "A": {
          "0": "-11540424829/105696460800",
          "1": "206906567/251658240"
        },
        "B": {
          "0": "-79873/1228800",
          "1": "321391/655360"
        },
        "AB": {
          "0": "-6624078645151/54975581388800",
          "1": "10392084486973/10995116277760"
        },
        "BA": {
          "0": "-520588799010593/3958241859993600",
          "1": "6795050968489/6597069766656"
        }
      },
      "sensitivity_intervals": {
        "A": [
          "310271897992427509007155556125190365523630601125302327334822634055328592584429/516008778523396436382813947546831301601162308917226912672683194990522030620672000",
          "44324556856061072715307936589312909360518657303616606520934082879496277826627/73715539789056633768973421078118757371594615559603844667526170712931718660096000"
        ],
        "B": [
          "92812770843615211994569481284540464462396871708502038407299041472233481131/191967551534001650440034950724267597321860978019801678821682736231593017344000",
          "13258967263373601713509925897791494923199553101215018129968784168827511653/27423935933428807205719278674895371045980139717114525545954676604513288192000"
        ],
        "AB": [
          "154714980825291943531962972149238510608705099752521496891821289476204607929022007/27064546866193924653688751393700789261091455043777017165999972682592118286319616000",
          "22102140117898849075994710307034072944100728536074619442924377277900935168086041/3866363838027703521955535913385827037298779291968145309428567526084588326617088000"
        ],
        "BA": [
          "11630247143185828225515290812863619952335026089000874520009730455577807699441411497/1932408646246246220273376849510236353241929890125679025652398049537077245643220582400",
          "1661463877597975460787898687551945707476432298428705688439240594717591460494795751/276058378035178031467625264215748050463132841446525575093199721362439606520460083200"
        ]
      },
      "occupation": {
        "A": "737/49152",
        "B": "23/1536",
        "AB": "957367/18874368",
        "BA": "2552741/50331648"
      }
    },
    "49/50": {
      "log_interval": [
        "1031178829224385661261765570817888449410040978514175977500005796578815745331815178483322655319553830259583260702619772100883/51041616008076536501868219452770022403130056873928233429173197588156694659519172666683662974466643846670109863515078389847200",
        "21044465902538482882893174914650784681837570990085224030612363195486035619016636295578013373868445515568967781691512992347/1041665632817888500038126927607551477614899119876086396513738726288912135908554544218033938254421302993267548235001599792800"
      ],
      "polynomials": {
        "A": {
          "0": "-27532952944651/1406250000000000",
          "1": "113572265918671/117187500000000"
        },
        "B": {
          "0": "-3473351929/292968750000",
          "1": "22924025299/39062500000"
        },
        "AB": {
          "0": "-924821132260519051809/30517578125000000000000",
          "1": "457860035384932512659957/305175781250000000000000"
        },
        "BA": {
          "0": "-16912553966803531031685881/549316406250000000000000000",
          "1": "6977637300540554196562097/4577636718750000000000000"
        }
      },
      "sensitivity_intervals": {
        "A": [
          "1158637345294064532521296017510792904382540655602363145022112133619567445803853133803125758231618789458453496821965407727079212693/2491228394813189971392204067938978342510122257356711726356199122183303896464974196950017390595714213153541649158964285218750000000000000",
          "23645660108042133316761143214505977640460013379640064184124737420807498893956186404145423637379978477013617198107689307790722637/50841395812514081048820491182428129438982086884830851558289778003740895846223963203061579399912534962317176513448250718750000000000000"
        ],
        "B": [
          "206198627955109029412520418443222860849926953155012091994145559353612081471083985918084049162088944493540565629011141945837/584383859913954954584143576809518729183702148101504040899882505790125239611769691989213556320833735199048005901704031250000000000",
          "4208135264389980192092253437616793078569937819490042693758072639869634315736407875879266309430387074294768138883191418533/11926201222733774583349868914479974064973513226561306957140459301839290604321830448759460333078239493858122569422531250000000000"
        ],
        "AB": [
          "15945762379434970730642951275680325826175369739538168219826282291198405948657090020214492544196592431981329234362161940386733350770925231/2702029964525620804040204675936869124095561590392796107477135310572964277541664711047065231713038635327230894634792236328125000000000000000000",
          "325423722029285116951896964809802567881129994684452412649515965126498080584838571841112092738705973342317888612756149027976913577737879/55143468663788179674289891345650390287664522252914206275043577766795189337584994103001331259449768067902671319077392578125000000000000000000"
        ],
        "BA": [
          "551068664577002513739949929378916144575704382706227185865510897486146053375223168973632306496120803189329603329371629087774970519205955633/86347479301144838737806540731026035052619033432117614738943237098744727999701024461721432404742756389804987285068360595703125000000000000000000",
          "11246299277081683953876529170998288664810293524616881344194099948696858232147411611706781765226955340591275121921964103656266911265009897/1762193455125404872200133484306653776584061906777910504876392593851933224483694376769825151117199109996020148674864501953125000000000000000000"
        ]
      },
      "occupation": {
        "A": "29801/75000000",
        "B": "149/375000",
        "AB": "10881034099/7031250000000",
        "BA": "29016081047/18750000000000"
      }
    }
  },
  "scope": "Fresh rational/log enclosures plus the manuscript comparison theorem. Arbitrary type-dependent descendant kernels satisfy the checked supersolution criterion at these pulse lengths."
}