{
 "what": "psi4 on the equilateral line (psi4 is the loop-integrated wavefunction coefficient, V_4 in the paper; column PSI of the co-author's table): the boundary vector at t = 3/4 in the coordinates of system_psi4_34.json (the exact 34-dimensional differential system of Sec. 6.5 and App. B.6, B.8), obtained by fitting the co-author's table INSIDE the 8-dimensional physical (single-valued) space (7-dimensional with the condition at t = -2/3) (16 real unknowns; psi4 = u_psi + two free log-free directions, whose two coefficients are carried by this fitted vector), and its large-X series.",
 "base": "3/4",
 "dim": 34,
 "vector_t0": [
  [
   "-0.392699081698724154807830422909934899349418852",
   "-3.66981723100344789124245005766922280005969102e-39"
  ],
  [
   "-0.392699081698724154807830422909934899349418852",
   "-3.66981727898279493642792985654045868436238043e-39"
  ],
  [
   "-0.39269908169872415480783042290993489934941885",
   "-3.66981701203495119116792553545278737617098851e-39"
  ],
  [
   "-3115237.19239032190481741984287596046177151487",
   "-2.91122431698074032896430655808571610517208596e-32"
  ],
  [
   "-64688915.9869367096200352301801772617251003686",
   "-6.04525221133859139445717980311947846479262585e-31"
  ],
  [
   "-1539055412.39992945382896779881103448778770945",
   "-1.43826465372805929474481372604762512741609852e-29"
  ],
  [
   "0.292468472071942211421224545380326078001082828",
   "2.72301925379131444478289054809640536368686461e-39"
  ],
  [
   "-0.0754021803433323923270376300891553120527271135",
   "-7.04461575060304272633027494635416727843081503e-40"
  ],
  [
   "0.041864773109493715170648654031721464651309125",
   "3.93845164908432029415273939291606149257127439e-40"
  ],
  [
   "-9.78631682256331096450917379884804897556220627",
   "-9.14532481314812584644314867647603912605337401e-38"
  ],
  [
   "-1.34992335556533001246711402701219663141616711",
   "-1.26343619370196980703781313563689099315825576e-38"
  ],
  [
   "-0.00146345806446622490585753155619793241226212223",
   "-1.36838614329043140530204617724511747756031777e-41"
  ],
  [
   "0.0721632038327998102774679398140317804103763596",
   "6.74394550030432478749658777610232222526245095e-40"
  ],
  [
   "-0.31912787486321454631354723154334000791694597",
   "-2.99031719019919162542169055109945585039749209e-39"
  ],
  [
   "-0.00137471086776731423993799117153142944495574009",
   "-1.28628218745272634184577787929958685193103693e-41"
  ],
  [
   "-0.000947547803415609806738328407386329552232397329",
   "-8.87096181667110195125432390947090915390253102e-42"
  ],
  [
   "-0.310641514959841122035124111986572434729205141",
   "-2.90315758549055471288392243062227629390143974e-39"
  ],
  [
   "0.0741348924280755294410525492727882925294628175",
   "6.86851570749513544959721291406929431601600872e-40"
  ],
  [
   "10.7474833475665542672506945318253078893753848",
   "1.00449128735248892410959873503008674332249917e-37"
  ],
  [
   "0.0238696676973608012576075455115620856577671897",
   "2.23087222259650666913452670974067484946042253e-40"
  ],
  [
   "0.0747641504967966324894145406569295240683521549",
   "6.86205781696813697092789891103831540634829582e-40"
  ],
  [
   "-15.3557414005503675216441828844190975339842007",
   "-1.43512131649590306372209231091906718091470741e-37"
  ],
  [
   "0.0228465421186489707149310635873196582296989833",
   "2.1193434943951925039684632917543070586689469e-40"
  ],
  [
   "0.0507312031056374821808313809132330640174097721",
   "4.71229262982046962254188442608749642208354699e-40"
  ],
  [
   "-0.0478586688540278099946836659361239200812940166",
   "-4.43784124656131175195760095526280411001255868e-40"
  ],
  [
   "0.0939138149160748039124781342842653904407867927",
   "8.75305594516738258490116425039829865357704343e-40"
  ],
  [
   "0.0809593949349217231690774524601567797995157943",
   "7.26446126663939055810109267947503585084227956e-40"
  ],
  [
   "0.540475198101179506554040747231029288736125625",
   "4.94354341886940092689958450594774231956143796e-39"
  ],
  [
   "0.858306475079370463754573794471598985653048597",
   "1.60944934404081606123248186939992613085171513e-39"
  ],
  [
   "0.0292322039702289731734582152964947616511900771",
   "2.66137803304952035392584434665445986557209143e-40"
  ],
  [
   "-0.217791480662605840682145791991919386960824787",
   "-1.19772933304418232683351586578790105727441933e-38"
  ],
  [
   "0.0678356268939582764957530041011040371433957864",
   "-1.43099662245604242341927929018424636501218746e-40"
  ],
  [
   "-0.706222289049880721399909558700974000888515022",
   "-6.58043142296894652203521903160424512550363593e-39"
  ],
  [
   "-0.706222289049880721399909558700971867433738788",
   "-9.21448787145309152336737491548630275685667827e-39"
  ]
 ],
 "series": {
  "X": "1+t",
  "nmin": 5,
  "nmax": 44,
  "coefficients": {
   "5": [
    "0.018064380381180636793847375785690180971574904435789",
    "3.0235153559032105513150663168616050505648504652773e-54"
   ],
   "6": [
    "2.1775541931444351472847435276771806792915519319487e-34",
    "-1.301588624096180136899001481237175314853894391686e-34"
   ],
   "7": [
    "-0.039283956272370600837994655881621463874559485256143",
    "4.0606419082795648548784818752852686498547802230598e-54"
   ],
   "8": [
    "3.4073900212868083853800504910219908215716019103475e-35",
    "-1.6011586376211271611809642894362275154276866304426e-34"
   ],
   "9": [
    "0.27215921058448833879774397402903635827133448740709",
    "3.0898515813367541206038740242245861781825930874196e-54"
   ],
   "10": [
    "-0.69392998222811585215836371850833761256922303243978",
    "-7.0199718342357603537799219517899465208515054659369e-35"
   ],
   "11": [
    "4.4918834043261657213607288072362486448281113808953",
    "-1.6455961518803678868137655817178224353689932845714"
   ],
   "12": [
    "-7.4155462855631563872189251020192175741961004069071",
    "1.8042673858844044985927825560282686564817087386499e-34"
   ],
   "13": [
    "27.820010884698402772826252226770105177021676527487",
    "-11.051674156378379785306084759036739310262216263429"
   ],
   "14": [
    "-46.290356229034277622302436770270639290141525296929",
    "7.2094928180822710158798365250267852958175331537822e-34"
   ],
   "15": [
    "116.42683340036766959472712252163755337968267486866",
    "-36.760515704590243603520046831695928302136691876401"
   ],
   "16": [
    "-193.39494644940855063538909322264582922630950848265",
    "1.9817094278036336999953947260795947588354054496807e-33"
   ],
   "17": [
    "388.40179623356105578116363389388052996965636531378",
    "-84.255751114428555590974433772648866490402853536708"
   ],
   "18": [
    "-640.36275071808679585642589820414477616531677067347",
    "5.1624753712999246231954611664355546817797865039818e-33"
   ],
   "19": [
    "1136.6757568854311310506016661502838712356680103804",
    "-147.00679008033115894221089035950446808472019965845"
   ],
   "20": [
    "-1863.8508542720547313582467412680918888914453246679",
    "1.3493200962083713514680304116330357965999829976551e-32"
   ],
   "21": [
    "3127.5326056870436504672449061076215469389331071192",
    "-204.9937065349816228049215085705729854687805596382"
   ],
   "22": [
    "-5130.1633363223830118335121593101930808673212243861",
    "3.594212181687345861031241474500829076291463952007e-32"
   ],
   "23": [
    "8553.131090803922898056635454016744591656790989763",
    "-274.51846065777070213389191951625406648040527057259"
   ],
   "24": [
    "-14154.351064877604419190951653924833271368898340205",
    "9.843119795978111751376397916519350311412368030286e-32"
   ],
   "25": [
    "24143.22872905056518537102607984833602003950109759",
    "-582.63696010813314554582797091055593243927119986738"
   ],
   "26": [
    "-40638.494680697276901339960786918407748271695204579",
    "2.7841324483405871336787810003765660698543239260654e-31"
   ],
   "27": [
    "71115.927068125351264821727670693808894720713454446",
    "-1810.8276102194409724196903284678641750247828937104"
   ],
   "28": [
    "-122165.824045860779619145606129324940130996074998",
    "8.1354047944522004238562017718131299246900621715828e-31"
   ],
   "29": [
    "216235.88002195534029759202890403306904759235257132",
    "-4719.8370057963157749603965481325849346623119368529"
   ],
   "30": [
    "-378202.04609806287528809936752582511942725655449262",
    "2.449318686375520831879935544818554075616745748846e-30"
   ],
   "31": [
    "668778.91974629819372551512646757006213236050520935",
    "-7296.1601019506250344194575594092561041166870117712"
   ],
   "32": [
    "-1185053.6570201597911829239570981228399578999664264",
    "7.5687518930467462844990811385903094437237400367907e-30"
   ],
   "33": [
    "2092163.5099971813190609462287225970450307037177212",
    "1637.1130950049574087923227727803407599781729163537"
   ],
   "34": [
    "-3740201.3464170387779155607278237560891698057190122",
    "2.3912751171234229995561390570465961750125124321372e-29"
   ],
   "35": [
    "6645478.4725065640011921094136948764206564230915605",
    "41694.731213417165128141701236139524151660104426731"
   ],
   "36": [
    "-11962885.698248296018945202611977622524996038447883",
    "7.6978531042796448559322657654800392727508832603998e-29"
   ],
   "37": [
    "21556201.377605040099259212716302096471676245745036",
    "89003.898541534848061768815184810280438857176517175"
   ],
   "38": [
    "-39071448.184968594914877064425451958183797159202669",
    "2.5177126880736973878415516511157171793829903138014e-28"
   ],
   "39": [
    "71445934.025997657039799369798053333297075106360947",
    "-90892.166661163868956691162796891608115077044184957"
   ],
   "40": [
    "-130430598.09047789743975724676843949950620532954187",
    "8.3471730234447942497876514557071426503461504423395e-28"
   ],
   "41": [
    "240626115.91291215776940230624276649888287583987243",
    "-1082684.2085280064780080597355237106524449804584764"
   ],
   "42": [
    "-442250242.08093366872296909091449232421469504368924",
    "2.8000682091546585102814881866368882930504659891728e-27"
   ],
   "43": [
    "817736908.65719073919848925052491528686334138184526",
    "-2910965.3548870766804648924106450662569793851386616"
   ],
   "44": [
    "-1511175813.302699670411472907805571664079967243147",
    "9.4896445648621846879814795197427961835764925658264e-27"
   ]
  },
  "note": "psi4 = sum_n X^-n (alpha_n + beta_n log X); |X|>2, use X >= 14"
 },
 "accuracy": "~27-33 digits (asymptotic checks: the exact coefficient c5 is reproduced to 31 digits; a second held-out set of values computed independently before the fit and compared afterwards: 32.2-33.1 digits; far held-out points >= 28 digits)",
 "provenance": [
  "the fit-and-test record of the psi4 boundary vector in the 34-dimensional system (8-dimensional single-valued space) of the authors' equilateral-line pipeline, kept with the derivation records in the paper's repository (not shipped in anc/)",
  "the large-X series record of psi4 (alpha_n, beta_n for n = 5..44), same location"
 ],
 "PRODUCER": {
  "produced_by": "authors' equilateral-line pipeline (reduction, structure and solve stages); see the repository records",
  "emitted_utc": "2026-09-27T23:35:13Z",
  "recut_utc": "2026-09-29T04:26:38Z",
  "recut": "plain-language metadata only; numerical content byte-identical"
 }
}