{
 "what": "C4 = u + Omega v on the equilateral line (x_v = 1+t, X = 1+t): the boundary vectors u(3/4) and v(3/4) in the coordinates of system_C4_28.json (the exact 28-dimensional differential system for the correlator C4 of Sec. 6.5-6.6 and App. B.6 of the paper), and the large-X series of u and v. Omega is a PARAMETER: the default is the co-author's 34-digit value of the integral that defines Omega (Sec. 6.6); the authors' independent determination (the fit to the co-author's table transported to large X and matched to the exact asymptotic series) agrees with it to 29.7 digits.",
 "base": "3/4",
 "dim": 28,
 "u_t0": [
  [
   "-0.39269908169872415480783042290993786052464617492189",
   "2.4923477597862298414232540967555210286986853224625e-53"
  ],
  [
   "-0.39269908169872415480783042290993786052464617502324",
   "-3.0354509449720435721341647006951484596921677847596e-48"
  ],
  [
   "-0.39269908169872415480783042290993786052464617494723",
   "-2.3078212841081490287590062705256435143969223079063e-48"
  ],
  [
   "-3115237.1923903219048174198428759839524381123984112",
   "7.0153022817457994761180316820329481302651863843131e-42"
  ],
  [
   "-64688915.986936709620035230180177749516451125608409",
   "1.4580633382551072109746934821651327306231172181923e-40"
  ],
  [
   "-1539055412.3999294538289677988110460931440065971556",
   "3.4698483198794293485379062514548778778830888090802e-39"
  ],
  [
   "0.29246847207194221142122454538032827816407341704664",
   "1.5036966435111894001931556063095373970516405777934e-44"
  ],
  [
   "-0.075402180343332392327037630089155880551787101192044",
   "-1.6057431719211499641541422365161145816969628938354e-44"
  ],
  [
   "0.041864773109493715170648654031721781699247559405204",
   "5.8653667370353914078184051017103281216935300810529e-45"
  ],
  [
   "-9.7863168225633109645091737988481227694601624223497",
   "2.7453690451312282153017010085964632429230253180292e-44"
  ],
  [
   "-1.3499233555653300124671140270122068205520930302349",
   "-4.9938634191929201136212641093318717802272448252586e-44"
  ],
  [
   "-0.0014634580644662249058575315561979434515932584749983",
   "7.3155488411150666083377347427810844665041156334617e-46"
  ],
  [
   "0.072163203832799810277467939814032324562122704596746",
   "4.6362424371611104176501963378014867123840029800315e-43"
  ],
  [
   "-0.31912787486321454631354723154334241847109257636365",
   "1.6351470125192811805334671263536043789169195417457e-42"
  ],
  [
   "-0.0013747108677673142399379911715314398195025394778963",
   "-4.1066173231010730813520287443052900647973655750885e-45"
  ],
  [
   "-0.00094754780341560980673832840738633670572587006772508",
   "-3.0388962838963129646296308167842093177837967249048e-45"
  ],
  [
   "-0.31064151495984112203512411198657477723131930509776",
   "4.2436925804327198515511603283722004461701618950601e-43"
  ],
  [
   "0.074134892428075529441052549272788848478046596683836",
   "4.7760393934161495495392188990777858566792989345574e-44"
  ],
  [
   "10.747483347566554267250694531825388937950887525979",
   "-1.4826596745174325796485051383048464103343891028694e-41"
  ],
  [
   "0.02386966769736080125760754551156226566020552826656",
   "-3.293243526566104216850007517707448072167329346816e-44"
  ],
  [
   "0.074764150496796632489414540656930081422815566129448",
   "4.3967975738466200172686608325728320409006464665058e-44"
  ],
  [
   "-15.355741400550367521644182884419213330418724978724",
   "2.264104880939222524640486065624261466460232360196e-41"
  ],
  [
   "0.022846542118648970714931063587319829706690227210885",
   "7.519918955153077774815392802619739340269654028663e-43"
  ],
  [
   "0.05073120310563748218083138091323344504282631846251",
   "-1.8608761309619761117527561777452342498201677754592e-43"
  ],
  [
   "-0.047858668854027809994683665936124279125095448259049",
   "2.7918403455180852833746203782364980202711330436776e-43"
  ],
  [
   "0.080959394934921723169077452460157374753332599822484",
   "2.7603354519856679620085925259572040351781688080167e-43"
  ],
  [
   "0.54047519810117950655404074723103330886282135984373",
   "5.6565452016863685925236788226277263649978898975599e-43"
  ],
  [
   "51.910089688827729198980527078413865819487277740924",
   "2.787921941017219504143165666721292889553665304267e-42"
  ]
 ],
 "v_t0": [
  [
   "3.4528083712229481740735586850110106321988068893691e-67",
   "-6.284055889419973798847063879525092029605275987297e-67"
  ],
  [
   "2.1448640776783835153425671446016838287202946545454e-61",
   "-3.9035441033600131760511457481747370806015408078987e-61"
  ],
  [
   "-2.8851005371099204982697263044056567924032210696922e-61",
   "5.2507625877603783415660007556709320587990491393109e-61"
  ],
  [
   "-9.5527372910162803927023573282780998364983790753899e-56",
   "1.7385435332233072536269039969171158957966744962599e-55"
  ],
  [
   "-1.9779690712542476390221767645252709682371215147427e-54",
   "3.599903863598014410017400974765281902259987154762e-54"
  ],
  [
   "-4.7014842417965147296997642799727403932378110564954e-53",
   "8.5567118254938430174596601570012245252759040345049e-53"
  ],
  [
   "-1.0535439383968786490421441087903653116042403722776e-57",
   "2.1686325625067469884426155594463083628564998596368e-57"
  ],
  [
   "3.9872080779501013525954514399146247618907561725385e-59",
   "-7.3195828421741381780199602917232046713480936851114e-59"
  ],
  [
   "2.3804489679439826298286056055870496204978979918028e-58",
   "-5.0312391334589456578621611377174227591543357664975e-58"
  ],
  [
   "1.2100750551091367914135452198311181963055940457233e-58",
   "-2.4489676750967971374168765213843580956770152089242e-58"
  ],
  [
   "-1.9125776919470962742465122467344620241007553864434e-57",
   "3.977238551420350797583137586478032824785738070784e-57"
  ],
  [
   "1.0769133978514778157358992024545114639616859852812e-59",
   "-2.7967707119564466754410497245376465305689834353273e-59"
  ],
  [
   "8.2319817644813939556186849137995435454931940284831e-57",
   "-2.1245012798616181165842302254859601435695731784794e-56"
  ],
  [
   "2.552940890487275143408946352072960226978654705674e-56",
   "-6.6182827916553839241768405674299900493058705551584e-56"
  ],
  [
   "-6.4554643365506182374623232444371363164820466115247e-59",
   "1.6604022753069525932079291381648611925506618992327e-58"
  ],
  [
   "-4.8912896964147751210562582718152020320675488465676e-59",
   "1.2524955370566906639079972380431122046058310273315e-58"
  ],
  [
   "6.6513295058551402396576307274381397210631085012246e-57",
   "-1.7119768410150396889950497945754234643131022363972e-56"
  ],
  [
   "-5.3592552813876140163376107936331109745959060104326e-58",
   "1.1252207643607946079139633534101871832288581323483e-57"
  ],
  [
   "-2.3060551215018698586510130278492278135218917963627e-55",
   "5.9411611323565169390599434097925795394066299471516e-55"
  ],
  [
   "-5.1323898186945218207156173096617832974629413008659e-58",
   "1.3266760303385942449349780638744560220144529762995e-57"
  ],
  [
   "-1.2033591400557779699939835105969126902749949795001e-57",
   "2.5008192428170327990939538617368910012344020821004e-57"
  ],
  [
   "3.4800789366708342392120690366059419962332524023209e-55",
   "-8.9700472411727843988704247609410407200333098741093e-55"
  ],
  [
   "1.1260830083796533011457412612357933648842088546973e-56",
   "-2.9037699809941384661235020194521916374140240657979e-56"
  ],
  [
   "-2.4588803066429150208487889879991338858356196143944e-57",
   "6.1820344864074648799579976342507153930028625697839e-57"
  ],
  [
   "3.7116050396132218943216207607820112429696375190746e-57",
   "-9.3820799447512566328762296601174133157543515092073e-57"
  ],
  [
   "-2.9069893192426286124985858621340776535806067633191e-57",
   "6.0400760605236149884431657227836704479729012710853e-57"
  ],
  [
   "-9.6841345891746097330645360465494664788230182601985e-57",
   "2.0391845820511547547295328285984358343905609753928e-56"
  ],
  [
   "-2.3806547607420421597479706450918921174726147930815",
   "2.9521941018857518245789006195954258055471378716856e-55"
  ]
 ],
 "Omega_default": "21.4444295139357745195031667653426535",
 "Omega_default_source": "the co-author's independent closed-form check: direct 34-digit evaluation of the integral defining Omega (the value printed in Sec. 6.6 of the paper)",
 "Omega_from_transport_and_asymptotics": "21.44442951393577451950316676534 (the coefficient alpha_4 obtained by transporting the fit to the co-author's C4 table to large X and matching the asymptotic series; agrees with Omega_default to 29.7 digits)",
 "Omega_direct_evaluation_30d": "21.4444295139357745195031667653 (an independent direct numerical evaluation of the Omega integral by the authors, 30 digits)",
 "series": {
  "X": "1+t",
  "nmin": 4,
  "nmax": 44,
  "u": {
   "4": [
    "-6.08287309127536315519816454586161263756186979e-42",
    "1.0727476496978084455742541141798451639600469e-41"
   ],
   "5": [
    "69.8575748780115329691121286094624733232548317",
    "-75.3982236861550377231034411987080692207320656"
   ],
   "6": [
    "-133.771430829253589277504768249528433599937413",
    "-7.60875325514083634323382401510462545459226143e-44"
   ],
   "7": [
    "344.166337293370745349025203075554803800104866",
    "-165.457213089062443892365884852720485234384255"
   ],
   "8": [
    "-595.7980601710132791530682937651058671218538",
    "-3.4175429967692651811971321689480611127267984e-41"
   ],
   "9": [
    "1022.30698630221774037855896228739035393666102",
    "-196.977859380080036051607740131624830839162521"
   ],
   "10": [
    "-1732.89610373998324617331137844156033609879375",
    "-1.14471099936892378507750833616134799123008198e-40"
   ],
   "11": [
    "2495.88060272471001325544958883684074702382315",
    "38.3236903825412039458651270815060310171052319"
   ],
   "12": [
    "-4165.29684210316421390290873017246371972648776",
    "-3.36200817930487304889988691617606710007082362e-40"
   ],
   "13": [
    "5807.18970084156400886592856993201053492441727",
    "771.447684353070062081253466804104507894575138"
   ],
   "14": [
    "-9535.86589175488341284877205682859694011521697",
    "-1.04182809943893173793261215916228908951024346e-39"
   ],
   "15": [
    "15479.3645327181214420685249423717486496035775",
    "1245.02610983737285926693810356896743414137825"
   ],
   "16": [
    "-25820.1892507448518492151823079702698398465406",
    "-3.41404772775277174583832310068055216298641462e-39"
   ],
   "17": [
    "52116.7921424916582058962922720587219048674256",
    "-2943.30728517589193185031221334841158454444297"
   ],
   "18": [
    "-91881.9939695056768487946663528459786122916756",
    "-1.15859332376048246090649836615568805465629178e-38"
   ],
   "19": [
    "195732.92335456799852083417601625530474950739",
    "-20777.384279457090912025543584705883225112026"
   ],
   "20": [
    "-362048.862131380713934474439730608798715537701",
    "-4.02519531895543178585715077630844849241705302e-38"
   ],
   "21": [
    "711649.550641669438348754495504874500524536281",
    "-46242.7679014801906937892424251567896296210721"
   ],
   "22": [
    "-1346540.68579982907509917410896439214804269445",
    "-1.42353314414682874116516789780410566879206474e-37"
   ],
   "23": [
    "2409488.78627642327202503129267191755576336137",
    "19773.9194985101531489077181483657834880366513"
   ],
   "24": [
    "-4574329.87078400023829808476671238606771767432",
    "-5.10552204251067556600331446012613884352248549e-37"
   ],
   "25": [
    "7864950.51891603843575113071998032504383212882",
    "471294.89251106353310172988567409763990697358"
   ],
   "26": [
    "-14832725.8334535166513330869383907484500407613",
    "-1.85171040494075360470907366216887266178196314e-36"
   ],
   "27": [
    "26466142.7620016290407815301481868191785656215",
    "1437662.83087175262999124170881353426118345265"
   ],
   "28": [
    "-49680156.1858319147643949332005861934203809889",
    "-6.77705868351773188553704298729664263058387078e-36"
   ],
   "29": [
    "95854704.7073694200639127805558794577526284095",
    "613571.433464780171749862803437526389031600561"
   ],
   "30": [
    "-180983917.049517999096052665030043028197843789",
    "-2.49893613319217472314458128868157719739163789e-35"
   ],
   "31": [
    "366186525.783070717456109062715971436218042347",
    "-11550098.7173070231399174202148278775812587591"
   ],
   "32": [
    "-700122957.871008281779263073929608941700929438",
    "-9.27244512473892010253380298868550071060639479e-35"
   ],
   "33": [
    "1403613472.07584651823502685196784829322918064",
    "-47257991.6384774225098599920661025679483894336"
   ],
   "34": [
    "-2711823432.39816610659778838751836178264371877",
    "-3.45905169983267522795491147882033776998107814e-34"
   ],
   "35": [
    "5239868614.96474144077092538673560368198058827",
    "-56835268.1883621008804158443278842608912872073"
   ],
   "36": [
    "-10167374454.0052059996462016157855766463737146",
    "-1.29636393949881254819341526205320768461004216e-33"
   ],
   "37": [
    "19101605936.8719055810363353779566256672543671",
    "263735069.9413313743294586428652982154097675"
   ],
   "38": [
    "-37030499479.5160089620303401500484839255833796",
    "-4.87808693326704971971965684053195637779125185e-33"
   ],
   "39": [
    "69549040234.7273188013839969350806182690561988",
    "1533335811.91919812617142696950635676992206165"
   ],
   "40": [
    "-134493708428.52008118063150630974530828647511",
    "-1.84211600346779580020600220557492574858774869e-32"
   ],
   "41": [
    "258429285982.600045970811706866437700395049803",
    "2945138951.07950341525723943812249253544937799"
   ],
   "42": [
    "-499642885678.953205442917076789214477530576514",
    "-6.97841833872392631967345679576261280039923028e-32"
   ],
   "43": [
    "983569570519.404525060958305562273566428775669",
    "-4854372215.06652659395337344270436016251586633"
   ],
   "44": [
    "-1907485614641.00501999597955321065861330110687",
    "-2.65109379566151306786659588891265976342101037e-31"
   ]
  },
  "v": {
   "4": "1.0",
   "5": "8.17032333048043367959865662322241167947249756e-65",
   "6": "0.3625",
   "7": "3.25165791964975470587911030962085409713120885e-56",
   "8": "0.072109375",
   "9": "3.78908217334885219502464793970020008802332053e-56",
   "10": "-0.0074755859375",
   "11": "-3.99428372050397296374882999863151644321691191e-55",
   "12": "-0.0140147857666015625",
   "13": "-1.83468358607469149311948037453143783427120028e-54",
   "14": "-0.00670309497833251953125",
   "15": "-2.76769560052643531290923954594507235470040806e-54",
   "16": "-0.0016401435968875885009765625",
   "17": "6.01204443829246201125054672690031167911093468e-54",
   "18": "0.00012574156928360462188720703125",
   "19": "4.34023066804886917837866720643596238944302969e-53",
   "20": "0.000342128922131075523793697357177734375",
   "21": "9.67486862419778650407692568241561274075787574e-53",
   "22": "0.0001806934611948029487393796443939208984375",
   "23": "-4.2532169674133634888023528550268511429803192e-53",
   "24": "0.000049477620178885986751993186771869659423828125",
   "25": "-9.93386725565504603561125301359743355625920008e-52",
   "26": "-0.00000128577773823999727483169408515095710754394539",
   "27": "-3.0301855741606680300451070732030001441231256e-51",
   "28": "-0.00000926746685098213419281876213062787428498268154",
   "29": "-1.31422961742973528103601787087320545533270493e-51",
   "30": "-0.00000534311332855640833880972451197521877475082973",
   "31": "2.42001146968840427006384329732811343318945793e-50",
   "32": "-0.00000160555775678242213219484857411600842169719184",
   "33": "9.90467660181193841237041251817764902783177396e-50",
   "34": "-0.000000034890454325509079761437267186430233323349108",
   "35": "1.18289677585441188653756601959052594089425138e-49",
   "36": "0.000000261006323203118824674852313202141201875454481",
   "37": "-5.59105568922519800912204067990633942396883735e-49",
   "38": "0.000000164425572679673754532325999916110006657062021",
   "39": "-3.24095967379213938599697632828383723783888866e-48",
   "40": "0.0000000536710191918417435671982854605968748914167428",
   "41": "-6.25493825421248332648028545246425981728237555e-48",
   "42": "0.0000000034521140870036239234745220730112177024313935",
   "43": "9.97437506452559934123992022196493098395361597e-48",
   "44": "-0.00000000745489788664863575613351094548692035405597298"
  },
  "note": "C4 = sum_n X^-n (alpha_n + beta_n log X), alpha_n = alpha_n(u) + Omega alpha_n(v), beta_n = beta_n(u) (v is log-free); converges for |X|>2, use X >= 14"
 },
 "accuracy": "u: fixed without any C4 data (the exact large-X conditions plus the exact -pi/8 double-pole boundary constants), components good to ~28-33 digits; the model reproduces held-out C4 values from an independent direct numerical evaluation (computed before the model was built and compared only afterwards) to 28.0-29.4 digits and the co-author's table to ~28.5 digits; v: exact structure (even rational X-series), numerics ~45 digits",
 "provenance": [
  "the data-free C4 model record (u and v at t = 3/4 from the single-valuedness and large-X conditions) 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 u and v (alpha_n, beta_n for n = 4..44), same location",
  "the record of the alpha_n/beta_n functionals evaluated on the circle |X| = 3 (monodromy at infinity, n <= 44, 60 working digits), 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"
 }
}