{
  "summary": {
    "checkpoint": "R102",
    "status": "PASS",
    "cases": [
      {
        "case": "L",
        "status": "NOT_EXCLUDED_BY_THIS_BOUND",
        "minimum_G_decimal": [
          "-0.17229087389431999986145442708274361424961272132331504848361543172281485282450455",
          "-0.17229087389431999986145442708274361424961272132331504848361543172281113056194821"
        ]
      },
      {
        "case": "H",
        "status": "FAST_EXCLUDED_OVER_SET",
        "minimum_G_decimal": [
          "0.14537518511762285732381462585111038138826093541444565096017576264775202896391243",
          "0.14537518511762285732381462585111038138826093541444565096017576264775689069459826"
        ]
      }
    ],
    "threshold_eta_lower_decimal": [
      "0.75588009172991968993679370293665378",
      "0.75588009172991968993679370293665379"
    ],
    "saved_slow_inside_both": true,
    "saved_R101_fast_removed_by_both": true,
    "equality_fast_boundary_retained": true,
    "component_semantics_controls": "PASS",
    "historical_numerical_tests_rerun": false,
    "solar_measurement_claim": false,
    "unique_slow_identification": false,
    "production_API_changed": false,
    "native_browser_tested": false
  },
  "protocol_sha256": "40782c77e9cbf0484385baf4cadb10c0287aece2d19baccebc57bf0eb4bfd212",
  "source_R99_sha256": "34aa2f1d11bf10c6a5a5d9028486cdcf64737a1bed5129069241c84ae89f30c4",
  "source_R101_sha256": "9308a5849b12674fadb6c580ba39219320912b413f93e9c6ca6ca68d6bf816b6",
  "B": {
    "r0_enclosure": [
      "71341630932043758904042097882781131012672981763894774086362255349593/32910091146424120843099383651147010099654717312671597266972180480000",
      "285366523728175035616168391531124524050691927055579096345449021398373/131640364585696483372397534604588040398618869250686389067888721920000"
    ],
    "r_min_enclosure": [
      "69696126374722552861887128700223780507690245898261194223013646325593/32910091146424120843099383651147010099654717312671597266972180480000",
      "278784505498890211447548514800895122030760983593044776892054585302373/131640364585696483372397534604588040398618869250686389067888721920000"
    ],
    "r_max_enclosure": [
      "72987135489364964946197067065338481517655717629528353949710864373593/32910091146424120843099383651147010099654717312671597266972180480000",
      "291948541957459859784788268261353926070622870518113415798843457494373/131640364585696483372397534604588040398618869250686389067888721920000"
    ],
    "x_bounds": [
      "9/10",
      "11/10"
    ]
  },
  "definition": {
    "w0_squared": "3/4",
    "eta": "|B1 dot n|/(sqrt(mu0*rho1)*w0)",
    "fixed_sound_speed_squared": "1/4"
  },
  "derivation": {
    "mass": "w2=w1/r",
    "normal_field": "cAn2=cAn1/sqrt(r)",
    "closed_necessary_fast": "x\u00b2>=r*eta\u00b2",
    "exclusion_margin": "G=r*eta\u00b2-x\u00b2",
    "monotonicity": [
      "dG/dr=eta\u00b2>=0",
      "dG/deta=2*r*eta>=0",
      "dG/dx=-2*x<0"
    ]
  },
  "cases": [
    {
      "case": "L",
      "eta_bounds": [
        "7/10",
        "6/5"
      ],
      "minimum_G_enclosure": [
        "-567010836355913531782556115477822977181398745818464752375965168125943/3291009114642412084309938365114701009965471731267159726697218048000000",
        "-2268043345423654127130224461911291908725594983273859009503860672503723/13164036458569648337239753460458804039861886925068638906788872192000000"
      ],
      "minimum_G_decimal": [
        "-0.17229087389431999986145442708274361424961272132331504848361543172281485282450455",
        "-0.17229087389431999986145442708274361424961272132331504848361543172281113056194821"
      ],
      "maximum_G_enclosure": [
        "490276882975512572747582973854114595029399452270355224383351115682337/205688069665150755269371147819668813122841983204197482918576128000000",
        "1961107531902050290990331895416458380117597809081420897533404462729357/822752278660603021077484591278675252491367932816789931674304512000000"
      ],
      "status": "NOT_EXCLUDED_BY_THIS_BOUND",
      "direct_downstream_speed_squared_difference": [
        "186603783054832859410204463155265510548710129529886813593637745296617150351774619360035448054457281929736607452777766200837979661926400/4857550031641296659024483462667819216770665319167590652427595201900802996555393491960681522209620932801964383746848323520680190166801649",
        "2985660528877325750563271410484248168779362072478189017498203924745809901849746918483714694079360262735990395998511422882764409117081600/77720800506260746544391735402685107468330645106681450438841523230413405513897293651793799452383536715075491661916759265884667151839431129"
      ],
      "same_corner_acoustic_bound_margin": [
        "-525640186055590305583046244405697396033338835817329153928519514363947/7273130143359730706324963786903489232023692526100422996000851886080000",
        "-2102560744222361222332184977622789584133355343269316615714078057455567/29092520573438922825299855147613956928094770104401691984003407544320000"
      ],
      "saved_slow_retained": true,
      "saved_R101_fast_retained": false,
      "other_fast_existence": "not constructed or excluded by a failed screen"
    },
    {
      "case": "H",
      "eta_bounds": [
        "4/5",
        "6/5"
      ],
      "minimum_G_enclosure": [
        "7475485301014449392902356484773964538030545978991455640144367605593/51422017416287688817342786954917203280710495801049370729644032000000",
        "29901941204057797571609425939095858152122183915965822560577470422373/205688069665150755269371147819668813122841983204197482918576128000000"
      ],
      "minimum_G_decimal": [
        "0.14537518511762285732381462585111038138826093541444565096017576264775202896391243",
        "0.14537518511762285732381462585111038138826093541444565096017576264775689069459826"
      ],
      "maximum_G_enclosure": [
        "490276882975512572747582973854114595029399452270355224383351115682337/205688069665150755269371147819668813122841983204197482918576128000000",
        "1961107531902050290990331895416458380117597809081420897533404462729357/822752278660603021077484591278675252491367932816789931674304512000000"
      ],
      "status": "FAST_EXCLUDED_OVER_SET",
      "direct_downstream_speed_squared_difference": [
        "-157452097676889142343593097886146906641188339412423591359714574288565232964264599985868364648818975375475165129833909553177506191769600/4857550031641296659024483462667819216770665319167590652427595201900802996555393491960681522209620932801964383746848323520680190166801649",
        "-2519233562830226277497489566178350506259013430598777461755433188617127977261568445523252168803250542353457758153662992139843547850342400/77720800506260746544391735402685107468330645106681450438841523230413405513897293651793799452383536715075491661916759265884667151839431129"
      ],
      "same_corner_acoustic_bound_margin": [
        "-525640186055590305583046244405697396033338835817329153928519514363947/7273130143359730706324963786903489232023692526100422996000851886080000",
        "-2102560744222361222332184977622789584133355343269316615714078057455567/29092520573438922825299855147613956928094770104401691984003407544320000"
      ],
      "saved_slow_retained": true,
      "saved_R101_fast_retained": false,
      "other_fast_existence": "excluded by positive whole-set margin"
    }
  ],
  "threshold_eta_enclosure": [
    "37794004586495984496839685146832689/50000000000000000000000000000000000",
    "75588009172991968993679370293665379/100000000000000000000000000000000000"
  ],
  "threshold_squared_enclosure": [
    "159284841148692744880601016871551528882328831793330530772145353523200/278784505498890211447548514800895122030760983593044776892054585302373",
    "39821210287173186220150254217887882220582207948332632693036338380800/69696126374722552861887128700223780507690245898261194223013646325593"
  ],
  "saved_witness_eta_squared": {
    "slow": "10/9",
    "R101_fast": "11881/100000"
  },
  "controls": [
    {
      "inputs": [
        "-1/10",
        "1",
        "normal"
      ],
      "status": "REJECTED",
      "reason": "INVALID_ALFVEN_BOUNDS"
    },
    {
      "inputs": [
        "1",
        "1/2",
        "normal"
      ],
      "status": "REJECTED",
      "reason": "INVALID_ALFVEN_BOUNDS"
    },
    {
      "inputs": [
        "4/5",
        "6/5",
        "total"
      ],
      "status": "REJECTED",
      "reason": "NORMAL_COMPONENT_REQUIRED"
    },
    {
      "inputs": [
        "4/5",
        "6/5",
        "sky_plane"
      ],
      "status": "REJECTED",
      "reason": "NORMAL_COMPONENT_REQUIRED"
    },
    {
      "case": "equality",
      "r": "2",
      "x": "1",
      "eta_squared": "1/2",
      "G": "0",
      "status": "NOT_EXCLUDED_BY_THIS_BOUND",
      "meaning": "retain possible fast boundary; no endpoint state constructed"
    },
    {
      "case": "orientation",
      "B_over_sqrt_mu_rho_w0": [
        "0",
        "1",
        "0"
      ],
      "normal": [
        "1",
        "0",
        "0"
      ],
      "total_Alfven_squared": "1",
      "normal_Alfven_squared": "0",
      "status": "TOTAL_NOT_A_NORMAL_LOWER_BOUND",
      "meaning": "geometric counterexample to component substitution, not a complete shock"
    }
  ]
}