{
 "schema": "ghu-rs-fermions-reference-v1",
 "engine": "mpmath 1.4.1 at 40 digits inside SageMath",
 "conventions": "those of rs_unification.mjs (ruFermion): conformal z in [R, R'], R = 1, R'/R = e^{kL};\na left-handed zero mode of bulk mass c has density |chi|^2 dz proportional to z^{-2c} dz (UV-localised for c > 1/2);\na right-handed one has density z^{+2c} (UV-localised for c < -1/2). Gauge KK modes: Neumann-Neumann,\nf_n(z) = z [J1(m z) + b Y1(m z)], normalised by int dz (R/z) f_n^2 = 1; zero mode f_0 = 1/sqrt(kL).\nCoupling of the n-th KK gluon to a zero-mode quark, in units of g_s: int density * f_n / f_0.\nZero-mode boundary value F(c)^2 = (1-2c)/(1-e^{-(1-2c)kL}) (LH), F(-c) for RH; F(1/2)^2 = 1/kL.",
 "cases": [
  {
   "kL": "26.67",
   "modes": [
    {
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     "x": "2.46438272740085799583265",
     "rootResidual": "0.0",
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      "0.5": "-3.542298259149767510568319e-41",
      "0.45": "0.3800619147075925875735243",
      "0.3": "1.690360638741733140698788",
      "0": "3.436115802424837343693615",
      "-0.3": "4.480551671921089774500904",
      "-0.5": "4.959419152607401073567154",
      "-0.7": "5.326879885768001121739659"
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     "couplingR": {
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      "0.6": "5.154761285985145480693282",
      "0.55": "5.060243679580078189170301",
      "0.5": "4.959419152607401073567154",
      "0.45": "4.85171550842719822323417",
      "0.3": "4.480551671921089774500904",
      "0": "3.436115802424837343693615",
      "-0.3": "1.690360638741733140698788",
      "-0.5": "-3.542298259149767510568319e-41",
      "-0.7": "-0.2229632695959017920426745"
     }
    },
    {
     "n": 2,
     "x": "5.582420145126536853130632",
     "rootResidual": "0.0",
     "couplingL": {
      "0.7": "-0.1539203898537149605168465",
      "0.6": "-0.1485404409241836822195481",
      "0.55": "-0.118116827377647644687686",
      "0.5": "3.196566604684838789650365e-41",
      "0.45": "0.2227139202398550841029627",
      "0.3": "0.7028353657171157465400181",
      "0": "0.4632063676109227755261048",
      "-0.3": "-0.334005455721641040921851",
      "-0.5": "-0.9178782233794575627245384",
      "-0.7": "-1.480110211935730179455838"
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     "couplingR": {
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      "0.6": "-1.20337033272104007300035",
      "0.55": "-1.061566391275717451778085",
      "0.5": "-0.9178782233794575627245384",
      "0.45": "-0.7727105143911228350047856",
      "0.3": "-0.334005455721641040921851",
      "0": "0.4632063676109227755261048",
      "-0.3": "0.7028353657171157465400181",
      "-0.5": "3.196566604684838789650365e-41",
      "-0.7": "-0.1539203898537149605168465"
     }
    },
    {
     "n": 3,
     "x": "8.717338240387934018054755",
     "rootResidual": "0.0",
     "couplingL": {
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      "0.6": "-0.1208004173781039929749843",
      "0.55": "-0.09527994791183637596904883",
      "0.5": "-3.388219135400171635042618e-41",
      "0.45": "0.1720061373410655259578437",
      "0.3": "0.5086982935834415351387165",
      "0": "0.4496595596711815938792114",
      "-0.3": "0.3491415530044923491811288",
      "-0.5": "0.3910983736643046580045096",
      "-0.7": "0.5151059327296790829830906"
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     "couplingR": {
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      "0.6": "0.4440033305726061911955103",
      "0.55": "0.4151157518186316180134798",
      "0.5": "0.3910983736643046580045096",
      "0.45": "0.3722508868588156701709472",
      "0.3": "0.3491415530044923491811288",
      "0": "0.4496595596711815938792114",
      "-0.3": "0.5086982935834415351387165",
      "-0.5": "-3.388219135400171635042618e-41",
      "-0.7": "-0.1255137712563644097874054"
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   ],
   "zeroModeF": {
    "0.7": "0.003051464234187308593714426",
    "0.6": "0.03113879680082916939922133",
    "0.55": "0.08639743591957182742539244",
    "0.5": "0.193637065371958854644579",
    "0.45": "0.3278178105800179372268161",
    "0.3": "0.6324628933257448617081123",
    "0": "1.00000000000130718234017",
    "-0.3": "1.264911064067351732985259",
    "-0.5": "1.414213562373095048801694",
    "-0.7": "1.549193338482966754071706"
   }
  },
  {
   "kL": "35.0",
   "modes": [
    {
     "n": 1,
     "x": "2.449894284694982736386829",
     "rootResidual": "0.0",
     "couplingL": {
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      "0.6": "-0.1925256093012977801560575",
      "0.55": "-0.1714596052147019143511863",
      "0.5": "-3.522116146025388115759031e-41",
      "0.45": "0.4662444991129333834605865",
      "0.3": "1.987671699307079024440502",
      "0": "3.975128544050185304968279",
      "-0.3": "5.162602371561518494085243",
      "-0.5": "5.706633725867800027772276",
      "-0.7": "6.123907609570413761185913"
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     "couplingR": {
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      "0.6": "5.928477727054414812747741",
      "0.55": "5.821142949245640223446499",
      "0.5": "5.706633725867800027772276",
      "0.45": "5.584297887640402282877411",
      "0.3": "5.162602371561518494085243",
      "0": "3.975128544050185304968279",
      "-0.3": "1.987671699307079024440502",
      "-0.5": "-3.522116146025388115759031e-41",
      "-0.7": "-0.1939277520818646027203142"
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    {
     "n": 2,
     "x": "5.566892546997775797953464",
     "rootResidual": "0.0",
     "couplingL": {
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      "0.6": "-0.1315162119878617962790749",
      "0.55": "-0.1157313979004090221089872",
      "0.5": "3.639536074104471441479936e-41",
      "0.45": "0.2752867937564408719388146",
      "0.3": "0.8276484366549274600757735",
      "0": "0.5331464298424674582688373",
      "-0.3": "-0.3903884474100152427839992",
      "-0.5": "-1.062909855073260577723831",
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     "couplingR": {
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      "0.6": "-1.391164751673812324754068",
      "0.55": "-1.228159812370999746070621",
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      "-0.5": "3.639536074104471441479936e-41",
      "-0.7": "-0.1326774645677201774103079"
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    {
     "n": 3,
     "x": "8.70128300630550152745892",
     "rootResidual": "0.0",
     "couplingL": {
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      "0.6": "-0.1066591821721176659336461",
      "0.55": "-0.09342088749031637382913412",
      "0.5": "-3.777553025196213385332557e-41",
      "0.45": "0.2128259782590902404983757",
      "0.3": "0.5980055145370269341440798",
      "0": "0.5169705879069054548053524",
      "-0.3": "0.39911187620644933859738",
      "-0.5": "0.4477458381029245336132589",
      "-0.7": "0.5910675633554108399609349"
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     "couplingR": {
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      "0.6": "0.5089355457452626467632414",
      "0.55": "0.4755352730020715222777246",
      "0.5": "0.4477458381029245336132589",
      "0.45": "0.4259200847273494161549909",
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      "-0.3": "0.5980055145370269341440798",
      "-0.5": "-3.777553025196213385332557e-41",
      "-0.7": "-0.1076738165160686313909025"
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   "zeroModeF": {
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    "0.6": "0.01351084196652254285351868",
    "0.55": "0.05580112835579562560924762",
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    "0": "1.000000000000000315255838",
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    "-0.5": "1.414213562373095048801689",
    "-0.7": "1.549193338482966754071706"
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  {
   "kL": "12.0",
   "modes": [
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     "x": "2.542011739837238878696766",
     "rootResidual": "0.0",
     "couplingL": {
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      "-0.7": "3.507898523108601578510001"
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      "-0.5": "-2.604268675527712206602727e-41",
      "-0.7": "-0.321587417996069153118637"
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    {
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     "x": "5.669684695379269179286646",
     "rootResidual": "0.0",
     "couplingL": {
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      "0.6": "-0.1662997506707574636363937",
      "0.55": "-0.0981415050059242828578988",
      "0.5": "2.723435607823959768736972e-41",
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      "-0.5": "2.723435607823959768736972e-41",
      "-0.7": "-0.2276591916228234940464775"
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     "x": "8.810207673000521926359201",
     "rootResidual": "0.0",
     "couplingL": {
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      "0.6": "-0.1347469344412752240986576",
      "0.55": "-0.07821954237139421747296709",
      "0.5": "-2.382158398644158914661025e-41",
      "0.45": "0.09000927977960831759179098",
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      "0": "0.2943708838454749075826791",
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   "zeroModeF": {
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    "-0.5": "1.414213562399789281163958",
    "-0.7": "1.549193338483207408881693"
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 ],
 "benchmark": {
  "source": "arXiv:0807.4937 Sec. 6.3",
  "kL": "36.84136148790473094428786",
  "x1": "2.447594241900291355680274",
  "masses_GeV": {
   "up": [
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    "0.5569074024211838858020611",
    "141.0372430508850029281711"
   ],
   "down": [
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    "0.05014533981811492575512196",
    "2.20897527186249218552372"
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  },
  "coupling_g1": {
   "Q_1": "-0.1852951726949277007141639",
   "Q_2": "-0.0922711740591769149546076",
   "Q_3": "0.2327794634506084643915493",
   "u_1": "-0.1889028361967027534475229",
   "u_2": "-0.1766524454595441082659901",
   "u_3": "5.42279864550494859628422",
   "d_1": "-0.188902231275475299566646",
   "d_2": "-0.1888889337442152020591918",
   "d_3": "-0.1727222463304290523711191"
  }
 }
}