{
  "summary": {
    "status": "PASS",
    "checkpoint": "RMO96",
    "sector_degrees": [
      -4,
      4
    ],
    "compression_exact": "39/25",
    "certified_sector_root_count": 2,
    "admissible_roots": 2,
    "classifications": [
      "fast_shock",
      "fast_shock"
    ],
    "independent_original_inverse_solves": 2,
    "descartes_upper_bound": 2,
    "max_scaled_RH_residual": "2.08286558833092971163823824618088206552427209344411444158969268467751687256241564144001523E-68",
    "max_reference_state_and_z_difference": 2.6275164736999785e-66,
    "root_interval_admissibility": "exact rational positive enclosures at every isolated root",
    "R95_sweep_rerun": false,
    "external_solver_checked": false,
    "full_uncertainty_propagated": false,
    "new_solar_classification": false,
    "native_browser_tested": false,
    "source_sha256": {
      "results/shock_polar/RMO_shock_polar.json": "e6022879d71a77bc6e340c733235443123fd329f4e13e0237479ae04511a0354",
      "polar_inverse/PROTOCOL.md": "c69beff089966fdac69af571c768315efbfa7f24aac05496dec9de97144afc9e",
      "polar_inverse/audit.py": "32bf797b620f156928fff987bd9dec851fcb84b8255df5c6c92b6581d86d1346"
    }
  },
  "fixed_upstream_global_normalized": {
    "rho": "1.0",
    "p": "0.04056",
    "u": [
      "-1.0",
      "-0.0",
      "0.0"
    ],
    "B": [
      "0.05618818561896245",
      "0.6422339004220036",
      "0.0"
    ]
  },
  "gamma_exact": "5/3",
  "velocity_unit_km_s": 600,
  "proof": {
    "polynomial_coefficients_ascending": [
      "-2663326517667638025851885296089458394371337725396125026233/3125000000000000000000000000000000000000000000000000000000000000000000000",
      "13449920668989699280650458205548082532981031211347163302344761080169597/97656250000000000000000000000000000000000000000000000000000000000000000",
      "-2553216150952624612285440409506820932352700577302910863927759525688745893/625000000000000000000000000000000000000000000000000000000000000000000000",
      "7936195843814563007212910692458249875654350736842708947856092368137689/19531250000000000000000000000000000000000000000000000000000000000000000",
      "12578858516533615532505363819712094484476568173633701529528839425077463/4882812500000000000000000000000000000000000000000000000000000000000000",
      "-139886720584783194526064880530567705542332461361462790047879675616893/1525878906250000000000000000000000000000000000000000000000000000000000",
      "-199864066593229236604277526458573662123239641557195086132927376863213/762939453125000000000000000000000000000000000000000000000000000000000"
    ],
    "sturm_sequence_coefficients_ascending": [
      [
        "-2663326517667638025851885296089458394371337725396125026233",
        "430397461407670376980814662577538641055392998763109225675032354565427104",
        "-12766080754763123061427202047534104661763502886514554319638797628443729465",
        "1269791335010330081154065710793319980104696117894833431656974778902030240",
        "8050469450581513940803432844615740470065003631125568978898457232049576320",
        "-286488003757635982389380875326602660950696880868275794018057575663396864",
        "-818643216765866953131120748374317720056789571818271072800470535631720448"
      ],
      [
        "5517916171893209961292495674071008218658884599527041354808107109813168",
        "-327335403968285206703261590962412940045218022731142418452276862267787935",
        "48838128269628080044387142722819999234796004534416670448345183803924240",
        "412844587209308407220688863826448229234102750314131742507613191387157760",
        "-18364615625489486050601338161961709035301082106940756026798562542525440",
        "-62972555135835919471624672951870593850522274755251620984651579663978496"
      ],
      [
        "16122168301013203369791808263434683885922565657333442340971455080550337678282712914796",
        "-2338483088624944052164477046360363451972733411713482762485131539522426794120350036185991",
        "32937933887393005663719775144964517086917162032755142130811623667272342496382565621273272",
        "-1240265733926413341675425356357272964464830741754528983837963394734519327585247811128768",
        "-10394226261392766986692580399730463533561822479195826347886387523675550432746170298575360"
      ],
      [
        "-28602568016753190919408176518947200470002112828661217250293480809700568303323871413081363981247118973077854861226210969787530030910529898409646",
        "1689776058547653384760435210074835055744803656252533188757613834539692703197128754049780429534854176274986313799690306307962261065340224343800911",
        "-148816346766781492400514519933263987672794589453506937874827352564103611568287138289786794497819430621702396901188633279238343746599849889916592",
        "-1115735226002797463301084974241968973729082249857999602495530931433044628826432152470570717793772979928772948737101117901013152516523841686377792"
      ],
      [
        "-381715505399873556438891772840606792386665556811474645262620278127950946450698709599173763457909595578311861376237254262771687795560421389857083471415627856248996004927720818536816035774661090888262232881193532491892067206494227",
        "57080319487316458020631755685689899012941549307302167368224019826035618198213641877302583886248195026868175132042588604308454160593864046592643346734771392595108140946551818963178995794348679528884319329451938306864192218160002063",
        "-529755397147615225405295099931130674932410556233174590250500661988006347032868759194426914149627019555462143626524809287196618821316559218213305055116586916634117971765417290961692366778179973301709201807221882244665519398807325768"
      ],
      [
        "37569376492672198375755330754529421462071382844124788196678687382789907580898424795704947112343426109397642821421303098592479465983752193331675377682237150389391715109869910691221444781586492358456954973781308446496124110734109899687418919037478392315826516007169139842921695231136853907217694779985653699922029630404783147681321126976862590127",
        "-2197388092797856920868995904318336610669911092118247306571058478016616008902756610505570588845691707296083135313705220535448089226562472931423545106085035229093365939330297288201705445512122282047277163837899817439673820848444850202821345697695067340201052610963373972493052632719925212603430266216677351077295421279481668163439576725940592731144"
      ],
      [
        "-1"
      ]
    ],
    "polynomial_square_free": true,
    "outer_interval": [
      "-7/100",
      "7/100"
    ],
    "inner_interval": [
      "-699/10000",
      "699/10000"
    ],
    "outer_sturm_variations": [
      4,
      2
    ],
    "inner_sturm_variations": [
      4,
      2
    ],
    "outer_root_count": 2,
    "inner_root_count": 2,
    "sector_root_count": 2,
    "tan4_rational_enclosure": {
      "lower_outward": "0.0699267980801796400350091228427",
      "upper_outward": "0.0699837161521038974126338630238",
      "lower_exact": "468217178318139346259780933304379784758800854824348018504098580141367436605193843734051216763809323246077928145297256235253375024840322023458467167789927204362725765127618283484798669171998531324890890734588058288952200783002091681914448182406838779794686660267629065578212487614562727139827814206116286930215231870736925135390625720635025962606777962119947101263454095521878724090432589496981323203424481410817593287546245406728136676450565027735103208911473048843514882815045807403186757089298416857795878037304946682102485967769773122598015943669294719688804809604348686263937581147601890373003282630519743205784083835888508287157103932182975798792248344320107783644903705688487583759411281300064210162639647556663915096678737655041708052279405411032120538570204613820737775417292740959068888587785162158638740947935730218887329101562500/6695818930265775857368317841140351660078859166275443546438411588010336785304861464888892534908454321384576379539887238426436469367090172222174120461414161572751241673016219624689873062841273376960963967228600090580985291858024368511117717656785387371529500238168680211499888199180397585600235414893409827822453644071734103596356135065857353996558623601597542957215013133996613733659723806956185009459611799385081699860426867856676759385248213123119558240242803800577416451115560488469360765618015138162310473946260429555057088911345871987396912346950143311110262793734065934787953929080048357266815718164453306226349008083233631631942476511406842370420152349514482373438744967400904598441091451883101892791812254540732977366468066361646130848907587095991406456886685739759035197906772868198487084639979221036800243885777489688906174498440427",
      "upper_exact": "20003067504926559900275481263772990692711453526321294744010958421310418757303161090438565007825033853180709275886214656918735877704887592307051905939940662227634161513718571140402406857236270543198345671280470144806061369755597265600971740554939769346326221760307447180563333905266392072494089386219450830640048917653574331179158766380990576666715764494773343426738268328868297629696826334111392498016357421875000/285824597559974160774855287082015209211427806428966413005657565003562279067925742433997913824796477362190224790515580075952337001625005560459063199428327171883797493558702556808950774015383238699761701556473565064456945090426295122434803135331946747267557260332277942880972683006262801905175876156140357007188467778136901212988936592565006509786254833733311157138232411176536616747895614589013558602680083830434433"
    },
    "whole_outer_regular_denominator": {
      "lower_outward": "0.984040854079047371738474389057",
      "upper_outward": "0.999803200362091511350351235988",
      "lower_exact": "6150255337994046073365464931612317161/6250000000000000000000000000000000000",
      "upper_exact": "6248770002263071945939695224922275761/6250000000000000000000000000000000000"
    },
    "descartes_transformed_coefficients": [
      "-362982341661901826613166817415473900372334377624908577319254677610128592845884617/12207031250000000000000000000000000000000000000000000000000000000000000000000000000",
      "-480482055195460980323151300881440814636089421374646065484483823995370990622362849/6103515625000000000000000000000000000000000000000000000000000000000000000000000000",
      "-67946116772316932308209014009367314626145828881452086216318054918830967906735451/2441406250000000000000000000000000000000000000000000000000000000000000000000000000",
      "49021538306729292934007411626181019371386103433839420802854452519667853427607917/610351562500000000000000000000000000000000000000000000000000000000000000000000000",
      "165382146832400919247727843996173921318226855619385521329699548680500610104972949/2441406250000000000000000000000000000000000000000000000000000000000000000000000000",
      "-9727308337260326456703985055427278777186769036125423166057715105569197636279649/6103515625000000000000000000000000000000000000000000000000000000000000000000000000",
      "-124209847708327184834281902674906305013262808518596871435007794646254560180176217/12207031250000000000000000000000000000000000000000000000000000000000000000000000000"
    ],
    "descartes_outer_root_upper_bound": 2,
    "descartes_bound_tight": true,
    "known_root_control": "PASS: three prescribed real roots plus complex pair; empty interval control"
  },
  "solutions": [
    {
      "name": "A",
      "tan_phi_interval": {
        "lo_exact": "32583953692468256470236359477731439781211057052822637/5265614583427859334895901384183521615944754770027455562715548876800",
        "hi_exact": "25456213822240825367372155841977687329071138322517707/4113761393303015105387422956393376262456839664083949658371522560000",
        "lo_decimal": "6.18806279423064945556854872766114651753270543187189664797180701493659509963351116888582489E-15",
        "hi_decimal": "6.18806279423064945556854872766114651753270543187190195789329044381605468667058830793226553E-15"
      },
      "sturm_variations_at_bounds": [
        4,
        3
      ],
      "exact_endpoint_signs": [
        -1,
        1
      ],
      "phi_degrees": "3.54549881471347386427952164871375856960519337006232692223699934839417711442308825193340765E-13",
      "theta_Bn_degrees": "84.9999999999996459764170741231357707093457420931709722466578839194469389518895419127592703",
      "compression_exact": "39/25",
      "state_global_normalized": {
        "rho": "1.56",
        "p": "0.102094867397826744362781946230247608720075265700164116075944679198131965697025907409005957",
        "u": [
          "-0.641025641025640899972881957088140119095720027006353272109737285479500788200055045344675814",
          "-0.0203081558579370543818548862680407901350072876232170010189301185124166085655307165236573225",
          "0"
        ],
        "B": [
          "0.0561881856189602134418641642036492381352876627960035215170171586929701173669570416168629747",
          "1.00366496701056809736725997883287754477474310948800512608190920379170528227734491814828404",
          "0"
        ]
      },
      "u2x_km_s": -384.6153846153845,
      "u2y_km_s": -12.184893514762233,
      "flow_deflection_degrees": 1.8145648164675718,
      "p2_over_p1": 2.517131839196912,
      "entropy_over_cv": "0.181977058843855138748596390443756089110385950222098145539591747478854761552117290580205433",
      "upstream_fast_Mach": "1.43921481860313817226908154042403114587919498143539680841653099010082803623385477909913167",
      "downstream_fast_Mach": "0.736986052125468549512689525097399498469294381174150893180730101951483305544026664805131964",
      "flux_residuals": [
        "-2E-90",
        "-8.03075048033633259416381599910014288251103685820358886374508017606992700932054055767577373E-90",
        "1E-91",
        "0E-91",
        "1E-90",
        "0E-91",
        "1.30487961447332841026175375924940967396392203142287509255598495929868554906269059410191423E-68",
        "1E-91"
      ],
      "diagnosis": {
        "case_id": "R96_solution_1",
        "status": "SUPPORTED_LOCAL_CLASS",
        "family": "fast_shock",
        "scope": "one planar discontinuity, ideal MHD, exact supplied states",
        "candidates": {
          "fast_shock": {
            "status": "SUPPORTED",
            "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition."
          },
          "slow_shock": {
            "status": "INCOMPATIBLE_FOR_EXACT_PAIR",
            "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition."
          },
          "rotational_discontinuity": {
            "status": "INCOMPATIBLE_FOR_EXACT_PAIR",
            "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation."
          },
          "contact": {
            "status": "INCOMPATIBLE_FOR_EXACT_PAIR",
            "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump."
          }
        },
        "coverage": {
          "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded",
          "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check",
          "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model"
        },
        "global_uniqueness": false,
        "uncertainty_propagated": false,
        "checks": {
          "front_speed": 0.0,
          "evaluation_boost": [
            0.0,
            -0.010154077928963449,
            0.0
          ],
          "rh_scaled_inf": 2.2204460492503126e-16,
          "rh_components": {
            "mass": 2.2204460492503126e-16,
            "normal_momentum": -1.7831848176577867e-16,
            "t1_momentum": 0.0,
            "t2_momentum": 0.0,
            "t1_induction": 1.1102230246251565e-16,
            "t2_induction": 0.0,
            "energy": 0.0
          },
          "characteristics": {
            "left": {
              "slow": 0.017081680979062402,
              "alfven_n": 0.0449865521441132,
              "fast": 0.8697934501974934
            },
            "right": {
              "slow": 0.02102538603704246,
              "alfven_n": 0.05618818561896642,
              "fast": 0.6948233071770148
            }
          },
          "front_relative_normal_velocity": {
            "left": -0.6410256410256411,
            "right": -1.0
          },
          "upstream_side": "right",
          "characteristic_transition": [
            1,
            2
          ],
          "compression": 1.56,
          "pressure_ratio": 2.517131839196912,
          "entropy_over_cv": 0.18197705884385507,
          "tangential_field_ratio": 1.5627717041269125
        },
        "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.",
        "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness."
      },
      "root_interval_physical_certificate": {
        "pressure": {
          "lower_outward": "0.102094867397826744362781946230",
          "upper_outward": "0.102094867397826744362781946231",
          "lower_exact": "10850324842163834551890018246557374168946990833939775658005544926334193644941994784725777705510319006035091211325759119469466604558940947111801551600848110438852402605601536273745485195921445723105704465854397212849148732643368153162118499069833292879136395763666093175309673592303960575447668332871523442488273514116875481254895847847248236202497960642304804406850169996787488132703951445284130326807516354795498285236550153922925242449793204664175233642463929704392189894737991294814187440753962271729049629008336783736964336607295500191126038893272050263843822229377381115047810444018978335903663875418704185318553644490140016890121529/106276888532349486150553945480418464696536892427324336471940260393229054840740073286684827866062939649300070184806723592208617157783052810201279209841069685848964589797831373353537400235202050590276170568484716652883807577256428931009976915671181870875696781716151632511787761229833365300123288472581768878673984752354611802030071407334970904245230510200273372872259654524509828764635850447509270712396461779678501325985274010839378180493630750908533888583296152547421050256107681752477756789645208109508386850398828079291379812452698233317804486534314997784273161666758821283800869082605312383529111466803200000000000000000000000000000000",
          "upper_exact": "10850324842163834551890018246557374168946990833939775658005544926482078026802819361593565190269245199896124615593158371587809651641438053920789854233605415154728661814312407345556075662321872077846468046806930630901869688299589974437290996539198011991494578411569629042146301989797949948240884271540926846432914711484394985640267624784713250824152525838081139234291827102034696039622679837319697789103564011548279575346004871961405805587133991355118673307826878960354726375529667181758753625019073985123030435805331640132485424917475748606745431251928434143149264159733895154797525608205639648164041846274934938060506864102179580384604871/106276888532349486150553945480418464696536892427324336471940260393356755747451597918726638999843876356143701540716706830974192402085846961012718037480983467077367142709835201924363860324721917483562017756950731232736155192158466059458092497632205960061956977133613654973049998244594717489989449087998590396170837771407681728089450799187601498866196833673029510453073989451285323484865403913811019411848175033456216582012329735030695462894314301843860126503068841546184349165887222285944489898295229998789838107958571038865750952030030028324454179557652779661967980389422746721201326776691400600873162187500000000000000000000000000000000000"
        },
        "entropy_cubed_margin": {
          "lower_outward": "6.70947028489244896019282567039",
          "upper_outward": "6.70947028489244896019282567040",
          "lower_exact": "537401118568396631765085384791277082049265189350043098968700524675162771969851176578418412010788681535588620848754378067493619542056107434170558429469737806104678433367826451188478791197447160581705569849862789882584824037178602922207951468639934117627889621660469067478222966240756368733911660890063550000604352488219635475608232465561212190101008996584067604689267757211804199766368095183292540163756252023667727474171402745844738770372292066202639530117469210430815248294053188126575810048535650845634422662409276393088010493504405199609126041686558489424343351933034028976385351457099897332277721008305119863405747101884332964122138986323403155766368058731077404829548832975516562319001864944162148059238794217057149964574566019952296564211581375246483455403047212082808848315846285875468444140750349186725263679635216848879549544245903764311337782312467442141833966109259802679749688850295152514040719489553623476255935687994840068514061414248922240887417986568736938033758056512235778530282856061565748552595839437831419205729812511118140605527000583529644398507386770464000709551330565997595056293381960082331794029171783412754786677736638772880592516525731240698126989920747810690717643606709870699503959481047309791185778671985438221679734202321588390066887031361526758135652886416932388346459050236108392923147517993292931765280989701260481375280138846114781541757884853352089678575825487053629631622715473731570316274343863176510003676088566600941576706970236667353924734923644540631494020286264749293529822975604868461881647357928498984938366284662611615110289817844900215633204603884746642660009550750288843668767743220003415586839325478903397234137200508218393482929835155200522379275474283499145762766272912883604177450150569374646810013943131257919612545701147836201805257718270787071434106606896146337236897068715357703107473618852170839499788922278669387407926941408968735390848036501467318889/80095908581404654066116909962454046677994250178824813122231619137716803012086264168542222864326817908765650999407379634440630824941539092093829669838461174074454698722697851334645180808703623101756817533011386748421103955322834156194487365193220252505695400085270138408366524336845897494590305525743204467628522435001028880280625390529494746183396827950858045610490130944825360412786121366198739544286986159599390361947617000459102591829456848640811805165616942332549654438625032845844061946426463768177656647180574383055555659475405197362699326758674394782641574906210537600421578526706530248775707190193909364271679898956162867492669200617148141176019442904943903889630398503953191578410355888531504146137913135388602974181165806365911758528471060923860512073272162004597694384819153658715959605345879061978782321391010306001194303737648175676255708362333643657449394506517167753838972349679717336180663445248142588325483496108075476087068432802248770622117702618572659518198179255092935883605445725290113332702100328164054873063265811652591925336604470024962153974566252743356338599039665412281241766291858860801948795180293332946141878715626190739959429418405765369092037938722774716092409799491972800339381964579908768126574649242429617615030770714109602768863487744815338940187515558307559871120544905806054081300398353181806320618347495412137426943322834724296752458759605733009832188910365567570558885794134135574349819302836089773091595242742845473552545626517307653050660211796285104555022674183878425408427144564371350106678238484332132517012237420403131971369924507192270853763452928402000437857483419090773237226577821014921312551113425091551199879962224508336393539527697248324026372710826333537059278534178311117945634584747860966620818827604823768065176741022899815439529594037645805935077224333274597679419097088000000000000000000000000000000000000000000000000000000000000000000000000000000000",
          "upper_exact": "537401118568396631765085384791277082049265189350043098968700524724726324235551507029310020986150331172431426901612337371586999068923240060767010363720761944662621322159217598833231240807661855445479325625395970735503969665165062825276013002911238023665757911175501719117502750441701137585199366041732210624916375500309283713131592149912825561121818560753242919300601995872857653417452407177615814386536718629323117708701517982539703989022328831716177146975738713704548025570116650851791651612564798564596736638327144217657118839520680714767065699915444447535227619276699067644777855975494571294366053254506058615527749603689646471997227426420186374219477032160961612731432765196274821004408325770534118633807039868581304644028482575471777298264457929334597665703890344657629618067729048655426219435520478159152606664755433209670302290224742071453728479763660286644028315067930979227375424976651680929678692305186914611587264636540580567551995928759578920561986114513600489032634375459952225790922750408596637984397077493567012936895259172768869627644122524358805911439607407904733682034698261557873390209060136360969060886998521693758714962375656986716636789387758651444526249196835223365965260142227406017910002347287354572665448096261574458596095371431107013068835020816970871351018337885616123024541695067346242634210063588118626931647477351739028025324508422164895653935845129369476118109041930089845051789774360696903032480795810178362486679957386552299519554812353144445684850785672798481112517629991385402725031452241693290696960537787597754724448195477760054357151348532840342430487905760983487519409807275487597070506259691628717470344692523352258786692865581542711463572455226747189612829219391305710309143255164019016765706755132519676201314680445851069894449473386403902042836307138730427045808390849488491872625502545032534241473744275213615717075257067160850185189074872873103101681407333958268311/80095908581404654066116909962454046677994250178824813122231619138005529572234344971793130864657597952428715705228954577482844019598353474457488698392457429903408600472072940577738160239409658323041537560831971373479849250253437935120294651737723189631575438256255456334943954074454236492516645552376351053713281575860640912241187638312367015903220354361775398503737140773211444109708868950420586053403058359755171945180300165775410677434732287805814638527489402590160180334003415900659621111407566921593252525652244060468419784439053719316192756215876324230119191951664489219835075403361315108344042631708332623730127022207897049020314833604886002905409776147914177535514588773214696276033625525357189095918516051701373235428856876746280324419084463726487143585445612979562034834056750355815976834070491641009369078951989579271898615212742232594280225802440112142839565325764578867446841477146673642427545746838320413523115537572293814601313040351054954371520961830608963401156697810897224279017205145076290441885651320907393092360582917542298707227031992700829502084966421707983354644777788509384676200135614531462294335134374319320483198038586979395096743922674158613795589629630372675314545886323213557757237702188558540111507615777759225662339557231635138102906104520385406656314191388185367365421625837748545344290542035676052561183671939540535840410461558933056435466460166177271565932583499184437914826866546941515813593778543517127925193344873864415294191365092231869357298885255945382094093564136836273109482779880425619352163916084974478542949742320160082812898310869330660813042984741536418100176132279127726054854065877740809026069147757082481120498565401060181701481231186704388391041078007360798724648208472792995384398945939198647252415245316361154547999098661311719487224714459567260205188078125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
        },
        "upstream_U_squared_minus_trace": {
          "lower_outward": "0.516778504945588985457411947038",
          "upper_outward": "0.516778504945588985457411947039",
          "lower_exact": "699636767204930772200252434840578676621939925489483877359005871237220885257201420982849016360050078429428690360799192768978433208964779423429204285744435893139003387/1353842624082429130653522550902956595341664378852866545061564799748173411544628518509177534122973783950748561402047824951020554283027920000000000000000000000000000000",
          "upper_exact": "1146284879388558577172893589242804103777386373921970384664995219435062698405398878576325465669501374931114462497398481900825712995431586543104821148210250289635478347/2218135755296651887662731347399404085807782918312536547428867767907407317474719218957861233281088102375528683421746151173967244629901520000000000000000000000000000000"
        },
        "downstream_U_squared_minus_cAn_squared": {
          "lower_outward": "0.408890082578518974587346983120",
          "upper_outward": "0.408890082578518974587346983121",
          "lower_exact": "44527897804567749357989660961514925096502764298200603036651892942782780433720116813931065597302930800979933363729505768064818990572860594457303184709921924522698301291410309014127433816818730055407770591617492524324390984226574905668086458896675831729978910759371805218672244566948739303839481565641/108899432150001039979802425916138553858062915765302603827467781503933431889977084641912278971047064927879252444813565782552254490224688980906985283343217699810399268663665931337466158588672609128899538885851690106020169778552351668703986321506346417439018285381205865783843994140625000000000000000000",
          "upper_exact": "119528665518905426818056618834896573690855635396479988556186355953662587780262014895776221391008211150306107601207034148464714450917380409613060267263248943175027730001258411658836882419652790569110484006259108911533886781187094328288353307026666325003817897539539800748531501626794247497291937932201/292324687273265895674524949907048704640696780701485934364136592533167365830309405454023193175922296713768742429626443658254112779115119290479418881195258477558756412257976749102374181653186482662259104990133303819802126197031195400609154972313187074592092256286421304115609600000000000000000000000000"
        },
        "minus_downstream_magnetosonic_polynomial": {
          "lower_outward": "0.141921987642297260210795052127",
          "upper_outward": "0.141921987642297260210795052128",
          "lower_exact": "10643831039892389115373681927735482289887008281615190844000601801662539346105268556640006735950844962083498702652809953024160774678576817314081176097760499288872724328530804934662416837706966855429211625217446460664393699543182446974414211282423317757832027229967514675643893927480938569777586260268189312999331275807149372115171411873811515261872676659330007372152562792181273428225382132754600247010961686106050183748218124049861928680261258179080780582094298163552264068191597962774191106009739953505124333064655276236449134311962683453665405476675350536598697138103804036342730784083458955014509982828644766469332015847835799935803182144462789462230087383387561378976090103371490501201310732396730000916204955395332266961023247155100336899271988362531989821162036324354690554536875398018004142399150544599399574353847029926635754869619275429621740837114475778010493598980930079867272748723725800504768786532616816316936065036947984368338186444857729200641715518390522825148700005425998944221159160600001031373835476318816115843016682598881661657128593030094557900325292888306826944262420308854255502791795206075836387923889250753627796157736146267633569396357532309797540900242195970727937994212875286019695991231137139532886773262882505868088177760559186893772191/74997759097901679778780188005423013063546913266883993822643184236829369650566346837524458517511378050889315115055499676683276598553834423154780282550324645503120824071158193079454406264668578159322874020135658426321205543719719671957806900407052450021340331534041370334041282671548174376846885990530302799105820970096334321456052077058389113360529718556512867263073202537117041045069282731952655146409277109874782933856095808023810832954387327829561708335714081786779731326055221830959725104752493047103992504593430763649750571105690494295230907962449128995435575768079542953670864443999274255740656721288261759120729174036348381922038285331547464164667873381479189696576018550836034357908883449799141536705234631140990657979060222911984035905812039999785107666335426860812325828929586110926465498415854431636773704893993943098885798040969963673920907797091920615276842409619064934673173546940662154598819779933921083728802557163714529703667398561038869987279257697724017731171695118854506783362319291060723820647543333358059220591602719196625196572714638836999381719876195236589258623851855145179835290222921182840126018462415146002788630915866404051741011285548205835788644212313872216705212300347047042846679687500000000000000000000000000000000000000000000000000000",
          "upper_exact": "76696885608086212104146791188889034647837634585123298340608363534678184935553554132518472632906554799681948363651536759018462953532259048182816102365651333248410459069066386539725343806910736157576724263479259720663540620845161104499468722272260683167693906374214597296856545253962169782544965543269620935178451108730902072484261086569308492952232480724085222831239840098309079012058238679002435598092001506174361108209999447936583703919382378044239961509551020322279153936666679202178049042921689159427961713133178423356627942591398645719369322850320997901081874946900339080904259193315561246491097409075812331961808731684195916949787094155307896173810409993615925548976507679516231353588888839524776457779709674944109078964412980755056160330129272651759116279443443106716344889754930676794188030679289564065912195993058001882494840492309416625798209504647774217904233198769146952504730897059713870601253994520574999455082779180427354116820558284383657338026141785016632481035831026620073776654111608958452902253934077740564243065557721094664776611512593628146531691810788225127665214381702539736751234307352985706143882479794337165537228220882757569974692132078689514852919161828531528183666753254853204652327538273633857687141174781652255623672029790610015763577889/540415807883091570062598524748051040232741136853971173135445761373425660812710486550854416353210683105832003348466716993723243991355719510715888131522800252448843600772999860233108274112373458528610386469387886897830030677127620922079556441588651499934009221855794497137589404136747009121242408955180897744316074112499423440501737139031868701589067663931438633652785243342968526324975083423701612278537570723993219151552714128886793835042444633588815226633193638728219865562971609210705008802030588682668821980604178209288303287814084280444514320564740956522838553964713867571604770779081495231149246933413998352743832935784496533327865752011942764011185776676585113347370422701620597506317087023951514771588294778459505154534708269656892886853389036547361645660837523387498850928629237261996650526156516592810802336556315691598090374584439122801697532230108105636585225916761297691643374135911848283250541857889397456823790386298139785802951192141831916967172827019382049380835504133694505234519408496455337729726599979571719005017728375197461465592243479477047379429468758853391700353537795357108086375740692546520994790300581271029696609737577251630491114178802444815723887031598101197063516296958699790632222720000000000000000000000000000000000000000000000000000000"
        },
        "tangential_amplification_minus_one": {
          "lower_outward": "0.562771704126912341315290762809",
          "upper_outward": "0.562771704126912341315290762810",
          "lower_exact": "1516303738972320626331945256953248900316801525596149689546356020647002280220725143731590671562514995844737301836627503120895760763493674560232668015068343472991926528591/2694349640987590245070667365003102081892356353653787271978780294475677126071570247481948376115724407255548169815494189938854002883785885617649415898265186537986915080625",
          "upper_exact": "1516303738972320626331945256953248900316801525596149689546356020650239775191677881468381335113887667699284335152407653567044724356506325439767331984931656527008073471409/2694349640987590245070667365003102081892356353653787271978780294474058378586093878613553044340038071328274653157604114715779521087279560177882083913333530010978841609216"
        },
        "regular_denominator": {
          "lower_outward": "0.995074904963083776555767618159",
          "upper_outward": "0.995074904963083776555767618160",
          "lower_exact": "2631200821276943598701823598635841876848004251615026632791777631322322635337982303333547894863318429031518215974222768277128438561796445486212972571614775401346525009/2644223875160994395807661232131084159313618731857124877138595181097623164945245383300756841758861139390364848100093433217024000000000000000000000000000000000000000000",
          "upper_exact": "4310959425580144392113067784004963331027770165846059635166048471161083401714512395971117401785159051608877071704790703902166404614057416988239065437224298460779064129/4332296397063773218091272162723568286619432930274713398703874344710345793446290035999960009537718090777173767127193080982772121600000000000000000000000000000000000000"
        },
        "normal_field_numerator": {
          "lower_outward": "0.0561881856189664241837043950322",
          "upper_outward": "0.0561881856189664241837043950323",
          "lower_exact": "739663324028952810742540396833842343122529920733333511134589590243325711804629133/13164036458569648337239753460458804039861886925068638906788872192000000000000000000",
          "upper_exact": "577861971897619383392609685026439330564476500572916805573898117412670204253224363/10284403483257537763468557390983440656142099160209874145928806400000000000000000000"
        },
        "upstream_tangential_field_numerator": {
          "lower_outward": "0.642233900422003252303979095972",
          "upper_outward": "0.642233900422003252303979095973",
          "lower_exact": "52839940500528999201365930429936688417606236187159056980772705573114991431122457957/82275227866060302107748459127867525249136793281678993167430451200000000000000000000",
          "upper_exact": "67635123840677118977748390950318961174535982319563592935389063133618609465234869987/105312291668557186697918027683670432318895095400549111254310977536000000000000000000"
        }
      },
      "independent_inverse_reference": {
        "z": "6.18806279423064945556854872766114651753270543187190095627699977010547348851884971279812436E-15",
        "state": {
          "rho": "1.56",
          "p": "0.102094867397826744362781946230247608720075265700164116075944679198150154162545378896908017",
          "u": [
            "-0.641025641025640899972881957088140119095720027006353272109737285479467211823256456130091135",
            "-0.0203081558579370543818548862680407901350072876232170010189301185122077415055866260723551201",
            "0"
          ],
          "B": [
            "0.0561881856189602134418641642036492381352876627960035215170171586923725473185791061305934913",
            "1.00366496701056809736725997883287754477474310948800512608190920379172061399837224938655325",
            "0"
          ]
        },
        "iterations": 5,
        "residuals": [
          "0E-90",
          "0E-89",
          "0E-91",
          "-2E-90",
          "1E-89",
          "0E-91"
        ],
        "agreement": "1.65334445104072914859536679997438907915E-66",
        "seed_saved_phi": 0.0
      }
    },
    {
      "name": "B",
      "tan_phi_interval": {
        "lo_exact": "4456363618402390864817327462873183995334740741195777848463324780911/131640364585696483372397534604588040398618869250686389067888721920000",
        "hi_exact": "445636361840239086481732746287318399533474074119577784846332478161/13164036458569648337239753460458804039861886925068638906788872192000",
        "lo_decimal": "0.0338525621106233364979116258617758606294342455181441218181520486934561203374173826332237451",
        "hi_decimal": "0.0338525621106233364979116258617758606294342455181441218181520486987660418208462620928107822"
      },
      "sturm_variations_at_bounds": [
        3,
        2
      ],
      "exact_endpoint_signs": [
        1,
        -1
      ],
      "phi_degrees": "1.93886851568487453572442229896150914802406582055341573501314697149904617371370361357867137",
      "theta_Bn_degrees": "83.0611314843151259905741231715606895134865476484745170309817431806401164781106777168920412",
      "compression_exact": "39/25",
      "state_global_normalized": {
        "rho": "1.56",
        "p": "0.102126170373843180457973116445250070653650101493609420938401137862355574690718806474085338",
        "u": [
          "-0.640482609273312342604112511555188209992899395837068849660313937910918598827523507144622592",
          "-0.0160410828153616537158549377960826842017497342397411777964988585208471569715582289770299507",
          "0"
        ],
        "B": [
          "0.0439470619994876698754809574400563032356239643373914593614926202571151106771608698597141961",
          "1.00383499813133680245023862286931064848403322244991270771715832972937551858731069728393734",
          "0"
        ]
      },
      "u2x_km_s": -384.2895655639874,
      "u2y_km_s": -9.624649689216993,
      "flow_deflection_degrees": 1.4346903915565223,
      "p2_over_p1": 2.5179036088225635,
      "entropy_over_cv": "0.182283618604819492206014727607050927675712234189234926540412839706340721562505574696825597",
      "upstream_fast_Mach": "1.43899909387829941776561947706629625653815270667456960089172781818111002152930243272291570",
      "downstream_fast_Mach": "0.736955388676929807576219005460884316602401962867767229852960808142314157731125577494815243",
      "flux_residuals": [
        "-1E-90",
        "0",
        "5E-91",
        "0E-91",
        "2E-90",
        "0E-91",
        "2.08286558833092971163823824618088206552427209344411444158969268467751687256241564144001523E-68",
        "-2E-91"
      ],
      "diagnosis": {
        "case_id": "R96_solution_2",
        "status": "SUPPORTED_LOCAL_CLASS",
        "family": "fast_shock",
        "scope": "one planar discontinuity, ideal MHD, exact supplied states",
        "candidates": {
          "fast_shock": {
            "status": "SUPPORTED",
            "reason": "Requires compression, nondecreasing entropy and the 1 to 2 characteristic transition."
          },
          "slow_shock": {
            "status": "INCOMPATIBLE_FOR_EXACT_PAIR",
            "reason": "Requires compression, nondecreasing entropy and the 3 to 4 characteristic transition."
          },
          "rotational_discontinuity": {
            "status": "INCOMPATIBLE_FOR_EXACT_PAIR",
            "reason": "Requires unchanged density/pressure and Alfvenic field/velocity rotation."
          },
          "contact": {
            "status": "INCOMPATIBLE_FOR_EXACT_PAIR",
            "reason": "Requires zero normal mass flux, continuous pressure/velocity/field and a density jump."
          }
        },
        "coverage": {
          "intermediate_switch_limits": "NOT_IMPLEMENTED; never automatically excluded",
          "full_fan_and_compound": "NOT_TESTED by a two-state discontinuity check",
          "smooth_waves_and_image_alternatives": "NOT_TESTED; require their own spatial/observational model"
        },
        "global_uniqueness": false,
        "uncertainty_propagated": false,
        "checks": {
          "front_speed": 0.0,
          "evaluation_boost": [
            0.0,
            0.01973542318357527,
            0.0
          ],
          "rh_scaled_inf": 2.1971417258590307e-16,
          "rh_components": {
            "mass": 0.0,
            "normal_momentum": 1.7890086858236587e-16,
            "t1_momentum": 0.0,
            "t2_momentum": 0.0,
            "t1_induction": -1.1102230246251565e-16,
            "t2_induction": 0.0,
            "energy": -2.1971417258590307e-16
          },
          "characteristics": {
            "left": {
              "slow": 0.023693853582616546,
              "alfven_n": 0.06235777302785497,
              "fast": 0.8693316581556901
            },
            "right": {
              "slow": 0.029156505548112662,
              "alfven_n": 0.07788483354870718,
              "fast": 0.6945296201305124
            }
          },
          "front_relative_normal_velocity": {
            "left": -0.6406586500252864,
            "right": -0.9994274940394469
          },
          "upstream_side": "right",
          "characteristic_transition": [
            1,
            2
          ],
          "compression": 1.56,
          "pressure_ratio": 2.517903608822564,
          "entropy_over_cv": 0.18228361860481956,
          "tangential_field_ratio": 1.5653561150765734
        },
        "result_sentence": "For these supplied states and front speed, a fast shock passes the local ideal-MHD checks.",
        "next_action": "Next assess uncertainty and unresolved spatial structure; this exact-state result does not classify an EUV image or establish full-fan uniqueness."
      },
      "root_interval_physical_certificate": {
        "pressure": {
          "lower_outward": "0.102126170373843180457973116445",
          "upper_outward": "0.102126170373843180457973116446",
          "lower_exact": "68987594125720351937162721131664687302276662616783691848750019663439938412516317391821917554306176442943709142361869696809428787794856623629167117877802696378603699910647656655313046011658801535135357734948116048136247197958887830411328093963725250580865587249827702786038938409625652492948843764268281706335764301200288552905287815215244221959366878657031746338671117943645196719901377575701954766236756757687345414450211619979842633187835971220253927941140092242218203270107948037064495990737675486375738765996510856106117089574265297235060837172896816398712313575970661741560561864353690038032975457674024459607342393314512669452123607321/675513375985648761887234071581052999734874382002212072952464603663293439967943838830951791880425001296766533371231384332143349113785746872463298997321082242255488330814761081902586022415854375614073482376289124825867797324890333611837440007002750293534314948317121212562644359514819870448793822667986741963160081972872003513315482877927471916888290494320824402424986255944905374484694675698401496165079964471911150031639969421528252856934012972213958112329671279295212284086219336455021012385646871213460989423983180906342215014158765487958164832969524833194951969474264248135185078207599176699665857493432000000000000000000000000000000000000",
          "upper_exact": "5306738009670796302858670856281899023252050970521822449903847666525492958902636387955602990002793183402757531700279790551325257620610578513605676640470858909801243643690118867786643652929567309562256566445370480214455064157461014888167062394730285241306193465320568374936426339638815844505150910687332344833100051213543050484528262780629094412488624470385886043800396536362778794398667623509982938356720502854614112235712052706560974569389170131005436991033161460973666300352510189255908372959209253254749329208065882908760225093903025703692478047420376580794631533134121991662831765373392322715726030518276165984854448940723340486388857283/51962567383511443222094928583157923056528798615554774842497277204955720729491592046080464628631236617011642323758592144898705479874900280669131316492592611781448018676929133177950049797343084944021708668894406893181658883819894882866564228581779089866035453997498850843956468504870916812100674749277945209526484618255025212260210520911031827151613978921516242933943742786365887798650718379402884851471103330355637283362584816643392680292813564857932188257631144172656709282842398817744745953454471471558546813942774139916018668151591621421692580376173395117500419504864024942964647807542543709781099729449026400000000000000000000000000000000"
        },
        "entropy_cubed_margin": {
          "lower_outward": "6.72414447069821115078211135417",
          "upper_outward": "6.72414447069821115078211135418",
          "lower_exact": "138303360845049756491514208864150615343195854675749251250689338608225252650160858952717209466811597791147169988265112822797681505229392932769023997690686077747649848880403101400793236622246423051570805140075460660044044511359732257676307474370931865628430910617561170452140299660011629174191849734416360043378197523037948518976340326711088011447702018282599101240067599799518995655266164061347707703339972196420310536569667798753940573391936077449479826949091734010231567034096867385127140555417121040242921389641516003184227015693600940809032058795376118297574963675274359483910011874726087575263370911498439589665108299263894801615580325656771653629399698631905682952194723713527066486124367610666951507839200226139706096871609468454810235093398874982989470876385266165946626451503488410842452641661269619945647187979668883578114411886473180986207300919199883634155849397949552942736031772917437358723066944816995475205059031658964087611493773000559359033089619689177100785675293779610127356130772215143357283141219855515275463042465009760863477553754667291452839991360603900873688265261914428872831478915780072511187119961987098197473690359447717787836668052037305358504833043206964202071356192497286301022877277817536414263023790519596177430452001743009278214889443599751830133553024606976654208993316591045895224887416535867575676501960880846401570941742813595503692483637754008574946307463130911290071641237775559702369886560214464649008187942835074555640475915733255752955394217985387682366158158912879258401676016324592520638565701574472451600331796624360430878545189277436204449652362562710650238161778244622256334761750200805629006885449872582096719130758797988427591531529179226400210750141579346487622450587364501706884648720474829347333468260915576441588920996650317694639711472591557803097565081241642763021229185631512070673446748580497637248075167999476326832633459376719543294473299835279745821251186737161/20568172121782033836176668883936936394237775926988436533375300466597861179534673087069895735973768940686778251306075728312630375882278840930638631844810922336677852208555524060087350913106316789009882706222285246803005316657794528848528013717550146685510165768432003061839140858774702919419329266187349597922506470295789593133956939133716295924350711494197645231076785721595663373874938392504154100208533605651531183257936486943159267112939058356982929127860792777386801695702226941466674265486286233445072082256667592215289665325630998983121547553453226775028800777811876037442609971000786406626366785844228744501215038256736219911710667262811274973724919143138880179073242298853266413220491301077340949323258278851058827256277384028368155972072536146102976841019917790201741675443172040586537492744096576651006140973889840530180378989822258001709713422047454252403247289556830479832269455839866196952306134674493894388673387874480654484167399175949067073018471321005985165804056463808773442944018020472754205897220293234111686098755456452522133394358737961066722678660719782608398569134587603150817423218402230844251056134615769130323919811091284252470291329793012513968846601692839578807958131707071732627175931550173063071648250071894955517421240276294909450691569745449581688846205988139935086689560353707888569913451576654677444405856780499492812433665404326902002365967144361938523868442717354401810684243259231224003720595725445051970820662013555379819914656088577635420005157705468944324147667806110904783436565613214895339481049695325198415574163355171622148614137043009895784646115092853985553573612140828829775448439282676760960459179814348160778273746287799058932998600646766500979017217857262271597648937938510152292910521512992143773302415583507925875833566300077311985758718737286061309175523858842463931276197888000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
          "upper_exact": "62951006301797795398959585281816392964586187836026058830536795005524828873846024994352712692450551303002947846296240368309653553150460592762125760797415698850398010634719965298866362654550316904624688860331156918632372074209365904284644268094197937362502702914306058305268802604114214362528675807159235072646917535712996916840577232796604507221141234392135288500586542115588205146502843536476180524905728693814467380376921845433084105897578588564786870654924811225252671413567246422886649786591246551726838398774341473925054713925796395167170736654828615604991572654757930800435628235456238669810021473420325470738585676685439608381372368855847058579369430735244709684260931043784845497601947260538776724278837898306806523423166430398487533920196477653865351216417825890155937231240621777272381096647338602893418272937370999062418915717437517475776445636636155965811730831029760332289754178184441399364784702972532750888758483714012506295307943503820109939424576670446633304108937383421894124465510113900086497382372352774648562806924862286658742071917193341892346355980887014664404206810151752232857906562547551994796258061311819233493199749147151707373667430713770069230389924309434721212580508402134398737610748154141765096753421525536050678897160478748459811217467025472636675874606554315747957731298156536409299370536917662332197258342746877756686461167773960451273400406618140595044849130392298451985466522857674792557220067996075372443346891515811144634074207789828640365658030539076737330221275517814121255751664203279148091392245991339788103598738702375175895198370366844700645992131309756352533334977895538050660545837311663605178358088058287196472514238935601559393286478574749936227250897856190858388816934693353721553162364491553495082990429236151283761773288975303979482280993378970655624929446972000211771079573428008350974075576203354302184646861141680927678253566027525962563851412042944189699728484187/9361935421839796921336672227554363402019925319521363920516750326218099914709304146226978537810380102785440822210557741109087140151832490507044889876517852899289524811176090519976190650744425626977526783762505125215298325816300104915698967777560897620481270103268633916226146250708746131556821333487393274666545837429265106659717520903856627977995256591519892057624571227822725252785271234679893289281800996570625446019345254029303234210064029965015737494900475284342595553105697759359257909985172617834245316517316935117533857274088561198324443019154713945261697107226734930706875201084601880087627739887295815269209569854330490391738350195473159480224608304569810867956441724008625828450971212409800490854239959062638425956877133776648073317818451205830381745821911531651732490516571019741483180083412864174975033602934731920150201870699533714568188609187148678292806356835371869778977634627753388796955560919091307916904408564518053249076749931207584855044852260629509400765052693847139051329990507570945650776838172742972046625165054435888314281411188593003179182528564638997744722750684351512369776299994133107254331115793700227849758993722786512892532722414790360883767062187343818805218962639758813961904957430157514969059612262306386428168006725483133692875779791868767484541261409363724833725968034730048841588414789904806693479502613075520274930683883913681551674877924766331057107478005879116200997538878804245975139529464214644521440533876417037896817871544521764228081307565179876913075394270088471711946839490280759648362024633333930370141017245806234640729040501082307932815575205457524243103881310231718923446806884910546763376695422706339281811869535732014176111213225118339571172053525314726445701038850980931765433706678661529779075541897874776868485268989657540981315724951190877924272956489559391194123094417641570304000000000000000000000000000000000000000000000000000000000000000000000000000000000"
        },
        "upstream_U_squared_minus_trace": {
          "lower_outward": "0.515633820787557618603428816122",
          "upper_outward": "0.515633820787557618603428816123",
          "lower_exact": "7156603391334296168604210706448245531099733322692080019525000818460904085429123786175815431663348136137916067885724540304726262741144611317858419715997833696235019123/13879235811963610657847700446356353751193257538305681747046502280418648510260780315384891015289008107868786868973075476267921952475353680000000000000000000000000000000",
          "upper_exact": "715660339133429616860421070644824553109973332269208001952500081846331245994503282805669960439029035564337315648568973445930078901930128093565127588364525409044482843123/1387923581196361065784770044635635375119325753830568174704650228041366451318995908144167931625453073888840449492812211832220057003999193680000000000000000000000000000000"
        },
        "downstream_U_squared_minus_cAn_squared": {
          "lower_outward": "0.406555013995229005388931162365",
          "upper_outward": "0.406555013995229005388931162366",
          "lower_exact": "4653071001299009622625443953392175794101663269864055281967282042693227355074394751920635421433917289765968136365368895285995493495418109193006238635941491065346006188988292353480708363354574924308202276492862213870580723735747354192037814033676530808718251630282418032736384180705270592019591981486681/11445120195599442857693261695147854991206514155894991081123551128158949559737563661794465666987340097701590006909147066390242593797143011004136958503388591604886899171147225809244403547092633632652612467213519287472445417714002634537039313086640583536424586855142085890761402500000000000000000000000000",
          "upper_exact": "3579285385614622786634956887224750610847433284510811755359447725152942505770301954923999602763136565418996581780259807069157110162117705813989168919323282532753401497464134689017223929294879748195182749687899002056074228001208597683339893782768916932960133049610479621362437538105354849578691482551533437/8803938611999571428994816688575273070158857042996146985479654713968422738259664355226512051528723152078146159160882358761725072151648470003182275771837378157605307054728635237880310420840487409732778820933476374978804167472309718874645625451261987335711220657801604531354925000000000000000000000000000000"
        },
        "minus_downstream_magnetosonic_polynomial": {
          "lower_outward": "0.141529842972777251267612915525",
          "upper_outward": "0.141529842972777251267612915526",
          "lower_exact": "736726697781923976905822513689945922890518828799543695453815830101941676034594689460627614475660715080825577149928273425345602168726925368572142526897241927171712098892003409422198987703221847268896913868159230434264463940164183045784017560012554595959315729316904147675747180466820880198649273196942296958290513536777833078828240944141583265937049140276728895305252654548000258172639259350173122195576628193108687899409099833800518440176264212757521176480634040627345483417924181632087733089389405024939508021656431052625814767966767246498244659803359168168197760743100856847857213927400685706598504581260900810710335918233975626154163149989059598757477389694864413315506471060192616769127685469702995747592556948446562703880451512249707951761546292515104749002895595569806015656366541871578463879385159511389497739503032768234611678000161636461144246898148147248646051578294112594872721155682129493720625868812536833497266781840228728270283798044568511154336301732519649658390506134502792974590799708792610579672532305044910310484002704258986403113231703500421476110905894885662153258510635253267148314178838895463840276351652982573479540611846029815267219825456178127254207263484548400547430000013981696051285406265283988901080894564847389714754326054989393388026266635679/5205451248353541014515515563680909636790787339280158970191189181047741558199933949928796631041883397626641853654102206720749008704539933582141375775359298920888710295231082159482689052850881627940955117472024354271074857952739823153447638434805959682236617565489557252544759214640180110264868342003148006745854749303940335168555557084966398752174149219806811921189937359064436787233873905757522066406173559302044120314813527523162781030579624430045814992224717664880926492400962007250739867831983733842784819177597461392854427352136335523717402929569050329568833004545955287043061730289451265280024052600795567532523463392933738490390459675997630048827999152593098448135085329808811175166112242498163766750081750555902537082016001078691267778939710453979523028866021973138116348965415786081687687136880013602290215205367295598076011624634830920704859504909774000580664269014588160284693785537794762035684099227618100219625957946720851037107967071489022249471877157924452125360996342937224973478743711608293216061342927899502845739829929213527691656489415396242694308021346208689073957274990115389951947862911643928959121671858249397030627742159210345462592723463322939382631778977369532389518821996205580334037847905328000000000000000000000000000000000000000000000000000000000",
          "upper_exact": "73672669778192397690582251368994592289051882879954369545381583011397383005230338945570369488113913113547942155634476990928108043000551344418034560334891968192250720824867719614275411271213727387123188204833059299008490998976973087792831974189479331451289649978570323003908376306533497507117954276774453977924762115571727677619316808099994709416042837945736253761225261861928279608103938804309056823026742954235596249871331776451803490908319203463851110877682866037225798266958496364403014724838288114730060656063633885991578467286153328988701383017295753992107551165252245566939036244756692239858030705950268168423093071083116115350290431875284829585418387892856875630813169889026905372907959231983844925004637230750839622287645860813892558096642677986323143502452979103164590868891064676141661104010301760709422171169784694047298114271428230595842130747168163654407706333563477731398014858006455973486034663511573038512343296638605439989548543020069145072521801605393258457148201323503680269305249899705243189540420081216761928543255003214116216534273426677838356402380239451817830126923463051614492233611594236798132775985941739545791641246806436794847745573267933667701442675058547343549808252296323186356416835914667503211091544397180514758657607152739462508424336644841414324321/520545124835354101451551556368090963679078733928015897019118918104774155819993394992879663104188339762664185365410220672074900870453993358214137577535929892088871029523108215948268905285088162794095511747202435427107485795273982315344763843480595968223661756548955725254475921464018011026486834200314800674585474930394033516855555708496639875217414921980681192118993735906443678723387390575752206640617355930204412031481352752316278103057962443004581499222471766488092649240096200725073986783198373384278481917759746139285442735213633552371740292956905032956883300454595528704306173028945126528002405260079556753252346339293373849039045967599763004882799915259309844813508532980881117516611224249816376675008175055590253708201600107869126777893971045397952302886602197313811634896541578608168768713688001360229021520536729559807601162463483092070485950490977400058066426901458816028469378553779476203568409922761810021962595794672085103710796707148902224947187715792445212536099634293722497347874371160829321606134292789950284573982992921352769165648941539624269430802134620868907395727499011538995194786291164392895912167185824939703062774215921034546259272346332293938263177897736953238951882199620558033403784790532800000000000000000000000000000000000000000000000000000000000000000"
        },
        "tangential_amplification_minus_one": {
          "lower_outward": "0.565356115076573378866652709750",
          "upper_outward": "0.565356115076573378866652709751",
          "lower_exact": "1516303738972320626331945256953248900316801525596149689546356020646375927644459617970500275928081677756680317790372567780081024285283695814186411117208850424661578646539/2682032967427880920301423297849097736105646324166662547610087874631484101070896362403075163700313874898262056992917162225790031646417451024196478054396596059860940309561",
          "upper_exact": "1516303738972320626331945256953248900316801525596149689546356020650866127767943407229471730748320985787341319198662588907859460834716304185813588882791149575338421353461/2682032967427880920301423297849097736105646324166662547610087874629239001009154467773589436290194220882931556288772151661900813371701146838382889171605446484522518956100"
        },
        "regular_denominator": {
          "lower_outward": "0.990526121618322051777938417495",
          "upper_outward": "0.990526121618322051777938417496",
          "lower_exact": "26820329674278809203014232978490977361056463241666625476100878746292390010091544677735894362901942208829315562887721516619008133717011468383828891716054464845225189561/27076852481648582613070451017022301791371455814216958741899214654439661209039312724999750059610738067357336044544956756142325760000000000000000000000000000000000000000",
          "upper_exact": "2682032967427880920301423297849097736105646324166662547610087874631484101070896362403075163700313874898262056992917162225790031646417451024196478054396596059860940309561/2707685248164858261307045101702230179137145581421695874189921465443966120903931272499975005961073806735733604454495675614232576000000000000000000000000000000000000000000"
        },
        "normal_field_numerator": {
          "lower_outward": "0.0779294486225462099099727715786",
          "upper_outward": "0.0779294486225462099099727715787",
          "lower_exact": "25646652571585714221861167675220276874933569592442972506416293159077573638463893199/329100911464241208430993836511470100996547173126715972669721804800000000000000000000",
          "upper_exact": "2564665257158571422186116767522027687493356959244297250641629316019987737945134449/32910091146424120843099383651147010099654717312671597266972180480000000000000000000"
        },
        "upstream_tangential_field_numerator": {
          "lower_outward": "0.640331786378454440720769498066",
          "upper_outward": "0.640331786378454440720769498067",
          "lower_exact": "168587019629340119614649141135493968820164206045748939986905566914123995059635742911/263280729171392966744795069209176080797237738501372778135777443840000000000000000000",
          "upper_exact": "1685870196293401196146491411354939688201642060457489399869055669142025461431310524161/2632807291713929667447950692091760807972377385013727781357774438400000000000000000000"
        }
      },
      "independent_inverse_reference": {
        "z": "0.0338525621106233364979116258617758606294342455181441218181520486934835646054318441341477386",
        "state": {
          "rho": "1.56",
          "p": "0.102126170373843180457973116445250070653650101493609420938401137862379696288469997230509854",
          "u": [
            "-0.640482609273312342604112511555188209992899395837068849660313937910949588700139481872523868",
            "-0.0160410828153616537158549377960826842017497342397411777964988585211767686808770635540356134",
            "0"
          ],
          "B": [
            "0.0439470619994876698754809574400563032356239643373914593614926202580652965315881691927591838",
            "1.00383499813133680245023862286931064848403322244991270771715832972937336194516368086393047",
            "0"
          ]
        },
        "iterations": 5,
        "residuals": [
          "2.11844068284690621E-73",
          "1.8516566235995013E-73",
          "-1.97291484481042004E-74",
          "4.9276087930799161E-74",
          "-1.3175509480834333E-73",
          "5.4226923183551076E-75"
        ],
        "agreement": "2.6275164736999782288695250E-66",
        "seed_saved_phi": 1.95
      }
    }
  ],
  "velocity_contrasts": [
    {
      "pair": [
        "A",
        "B"
      ],
      "delta_u_km_s": [
        "0.325819051397134421261667319771145461692378701570653469654008541149313623518922920031933200",
        "2.56024382554524039959996908317486355995453203008549393345875599494167095638349252797642308",
        "0"
      ],
      "max_possible_LOS_difference_km_s": "2.58089257825579712355856498609291316193620159926313738841599261880750617308863638395648416",
      "best_LOS_unit_vector": [
        "0.126242779006837796997872035366497417301631197235638560425693933290801103394796945954348878",
        "0.991999375377137379177896254267769958070201745407163179645980785271121652846342152708990397",
        "0E+89"
      ],
      "blind_in_plane_LOS_unit_vector": [
        "-0.991999375377137379177896254267769958070201745407163179645980785271121652846342152708990397",
        "0.126242779006837796997872035366497417301631197235638560425693933290801103394796945954348878",
        "0"
      ],
      "hard_half_width_for_disjoint_prediction_intervals_km_s": {
        "x": "0.162909525698567210630833659885572730846189350785326734827004270574656811759461460015966600",
        "y": "1.28012191277262019979998454158743177997726601504274696672937799747083547819174626398821154",
        "best_direction": "1.29044628912789856177928249304645658096810079963156869420799630940375308654431819197824208"
      },
      "criterion": "strict 2*epsilon < abs(l dot delta_u); exact fixed model predictions, equal hard error half-widths",
      "full_observational_uncertainty_propagated": false
    }
  ],
  "sources": [
    "https://farside.ph.utexas.edu/teaching/plasma/Plasma/node102.html"
  ],
  "scope": "One exact fixed-upstream, fixed-compression, coplanar regular model within the declared normal sector."
}
