{
 "_provenance": {
  "assembled": "2026-07-03, for the row-27 evaluator; lbl3e-master-evaluate.py reads this file from its own directory and refuses it on a sha256 mismatch",
  "anchors": "psi1/pi, psi2/pi, tau, varpi0 at the construction's six Euclidean reference points w = -5, -3, -2, -1, -1/2, -1/4: Arb-certified midpoints, 80 digits, from the closure run of 2026-06-25",
  "eichler_f3": "Eichler_f3 at the same six points (cusp-regularized Eichler-integral transport, 80 digits) -- convention: the one-fold cusp-regularized integral I(f3; q) = sum a_n/n q^n (verified at runtime); the sector-15 assembly uses the two-fold I(1,f3;q)",
  "B": "boundary constants B^(0..4), 120 digits (sunrise_boundary_constants(400,5) of the closure run)",
  "oracle_J111_d2": "J[1,1,1](d0=2) = -S111(2-2eps,w) at w = -5, -3, -1, eps^0..2: certified 1024-bit ball evaluation of the arXiv:1704.08895 literature representation. Comparison only (check G4): the evaluator never reads these values into a computation. This reference lives in the same homogeneous-period frame as the construction; the independent AMFlow values are in row27_gate_amflow.json (check G6).",
  "recorded_gate_digits": "the closure run's own cross-check digits (leave-one-out transport, homogeneous-period route comparison, PSLQ residual, synthetic round-trip), printed by the evaluator for information"
 },
 "anchors": {
  "-1/4": {
   "psi1_over_pi": "1.06990420417018736030436154346086918375296946817309071249078650275034810661105109e+00",
   "psi2_over_pi": "5.34952102085093680152180771730434591876484734086545356245393251375174053305525543e-01 + 6.27513207340119550248841658330744179567094869847676902949359242452481681617504485e-01im",
   "tau": "5.00000000000000000000000000000000000000000000000000e-01 + 5.86513451292413441334963749170866468194643874737145e-01im",
   "varpi0": "9.26564220427154995379170866027621065110349181250774004002045937118866292210291195e-01",
   "abs_q": 0.02509284082502593
  },
  "-1/2": {
   "psi1_over_pi": "1.00231667829912791054260671349038686405093521275267783741379929414027922898843651e+00",
   "psi2_over_pi": "5.01158339149563955271303356745193432025467606376338918706899647070139614494218254e-01 + 4.91143765161931010319548075635839265206037733779526220886852559895115905455417746e-01im",
   "tau": "5.00000000000000000000000000000000000000000000000000e-01 + 4.90008572934626724578605361229281145855271203266240e-01im",
   "varpi0": "8.68031706043879542029886880497030026669881421427299494190522923913899006981337730e-01",
   "abs_q": 0.04601376602476442
  },
  "-1": {
   "psi1_over_pi": "8.99026529977333134189954924667982179257205514830453633179078524829944688247218676e-01",
   "psi2_over_pi": "4.49513264988666567094977462333991089628602757415226816589539262414972344123609338e-01 + 3.61944632834952117263702073822183371056418964922944948462808429195820090006533272e-01im",
   "tau": "5.00000000000000000000000000000000000000000000000000e-01 + 4.02596164591580751796210346912359810078025427263180e-01im",
   "varpi0": "7.78579813636542662982213798727626949605883098573244336434997608173735793168651790e-01",
   "abs_q": 0.07969198155504054
  },
  "-2": {
   "psi1_over_pi": "7.61166273198895035051999080472538833664342316901239650920230189658510232833387943e-01",
   "psi2_over_pi": "3.80583136599447517525999540236269416832171158450619825460115094829255116416693972e-01 + 2.48841964850336135571954901876742479494476783878466028392820359449311787130606077e-01im",
   "tau": "5.00000000000000000000000000000000000000000000000000e-01 + 3.26921953339507703336226918423871577701791393363836e-01im",
   "varpi0": "6.59189329094169413195934259251828357533136285369294413289251663908674676363865707e-01",
   "abs_q": 0.12820673332777882
  },
  "-3": {
   "psi1_over_pi": "6.69492639532639994293260695952745540804951215932398118589131680652315441816247561e-01",
   "psi2_over_pi": "3.34746319766319997146630347976372770402475607966199059294565840326157720908123780e-01 + 1.93265877827321394294998675261670146990860877239963809210517509957995626200881043e-01im",
   "tau": "5.00000000000000000000000000000000000000000000000000e-01 + 2.88675134594812882254574390250978727823800875635063e-01im",
   "varpi0": "5.79797633481964182884996025785010440972582631719891427631552529873986878602643129e-01",
   "abs_q": 0.16303353482158048
  },
  "-5": {
   "psi1_over_pi": "5.50078034138560359684817446587069958620933186156287170205296326813202083126798648e-01",
   "psi2_over_pi": "2.75039017069280179842408723293534979310466593078143585102648163406601041563399324e-01 + 1.35782217980019578522924952719564639112707935798469045290079474614947185545839535e-01im",
   "tau": "5.00000000000000000000000000000000000000000000000000e-01 + 2.46841737995698803928272215403648799206886262744514e-01im",
   "varpi0": "4.76381551627796962049970387496272612832394008035690064337160694350207897478288397e-01",
   "abs_q": 0.21204592903707972
  }
 },
 "eichler_f3": {
  "-1/4": "1.38817844254639186702577855195321568326744350538663866688878666591556370279045032e-01",
  "-1/2": "2.68186911702707030412935783456189579962722885432755027011623812250699845045685253e-01",
  "-1": "5.05147907400042020563474169569555481648108762841180230822831544142570000713626975e-01",
  "-2": "9.17475992194864665245709077614316962005880489156111841664359129102196314547952341e-01",
  "-3": "1.27381749916280277395698391371279828563429643030477115073279931188086876905663904e+00",
  "-5": "1.87857593822846368958413555588180240447466970720917871048665416215145295958234949e+00"
 },
 "B": {
  "0": "2.029883212819307250042405108549040571883378615060599584034978213553194952516488044272940708456513389891723655062719770803e+00",
  "1": "-3.496643499822907860631044875824153622884794103892743808566301832060910078992860814710312504390188384713716304344034094678e+00",
  "2": "6.965063016808741781663730065640998067294575323940147382128943737464355771295990876273955899094380863448163114114292098584e+00",
  "3": "-1.387873788055691210046597281179394752033301686765228896483442902769194626433577919814434946801421331761880470288063262053e+01",
  "4": "2.772748589198536735488975162102421231327181724395616575280052036444001747239541754817789210833918447947215037226644146059e+01"
 },
 "ring_refs": {
  "Cl2(pi/3)": "1.014941606409653625021202554274520285941689307530299792017489106776597476258244022136470354228256694945861827531359887625e+00",
  "L(chi-3,2)": "7.813024128964862968671874296240923563651343365452854202221000629668869846516182180928695708322098610210423502565090357680e-01",
  "sqrt3": "1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248575675626141415406703030e+00"
 },
 "oracle_J111_d2": {
  "-5": {
   "0": {
    "re": "-1.91612597144661007060390799192215655712803587996656090582264813780733157477069362741286910681267578888693344543654086868398106746842213715506437345769898782027125229619774525484856070467120978946811256954184781632765213418745226227248126496627274622589494208754816234316479812864288292816364688723346369986390454463799034e+00",
    "im": "0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00",
    "cert_digits": "301",
    "branch": "euclidean-or-subthreshold: Eichler certified Newton, L=log|q|+ipi for t<0"
   },
   "1": {
    "re": "6.38582756757007010590829433439444981125365783167494348913809791288928759500821791155621476303311930381440600376570136907431834963300281596009488910433156429411598766342522026611822180587863663868771609571762344077885390897073374956418263323672530914790752938302921127551251775343414914877428964428742063000730954891623719e+00",
    "im": "4.45014771701440276618046543466480812843843196092466366110665483377440886962783639170856631802502204112813467946207162201030486832310692021771202477075543764226155598706400466095922029488516727214384313009388500746841675050161330123331631789744098235993718327929700127181754023660974959956177550749989890316090321010183080e-308",
    "cert_digits": "301",
    "branch": "euclidean-or-subthreshold: Eichler certified Newton, L=log|q|+ipi for t<0"
   },
   "2": {
    "re": "-1.73946076601524871279253215676557020718810449692287929051601212695680666597766519920023514406311343978224642745021260231049030310636105798655473890757303355063675246555880818259212147871773853286045403373770598593478925356872884674229216929963390347398887124421058594474923861964263199119809936763926056167948524266537854e+01",
    "im": "-2.67008863020864165970827926079888487706305917655479819666399290026464532177670183502513979081501322467688080767724297320618292099386415213062721486245326258535693359223840279657553217693110036328630587805633100448105005030096798073998979073846458941596230996757820076309052414196584975973706530449993934189654192606109848e-307",
    "cert_digits": "300",
    "branch": "euclidean-or-subthreshold: Eichler certified Newton, L=log|q|+ipi for t<0"
   }
  },
  "-3": {
   "0": {
    "re": "-2.05897669792549187241827996914884490499588521325911716524258446768115761835949464093316918576189418142303056192451443909887819677293413815584683330190280592008806348718678407910572094393582497360126505901252411388904561407225980004160227861420287166291877673667107260219751537924828099323234891334298774921162759848897724e+00",
    "im": "0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00",
    "cert_digits": "301",
    "branch": "euclidean-or-subthreshold: Eichler certified Newton, L=log|q|+ipi for t<0"
   },
   "1": {
    "re": "6.53445133824335648988104629149384857294177300973649513574479084588757453070096598720768955756103141677388415338555464061544040745237123223253280292842440553830495418916970699972768819100023974492339840041206031628467412789389537705557712213578656344085818874919853714610597766395136096585195614530070573268789294320135655e+00",
    "im": "6.67522157552160414927069815199721219265764794138699549165998225066161330444175458756284947703753306169220201919310743301545730248466038032656803715613315646339233398059600699143883044232775090821576469514082751120262512575241995184997447684616147353990577491894550190772631035491462439934266326124984835474135481515274620e-308",
    "cert_digits": "301",
    "branch": "euclidean-or-subthreshold: Eichler certified Newton, L=log|q|+ipi for t<0"
   },
   "2": {
    "re": "-1.76616571689468954969143702798529202891788974239768459722107623438032813731287387902997593319086377422794845993128597040797068347752877977449882923846818449480769617091551437304919513826150963150276205222846261597290892963191520980063916038422956785869277064921225849157595601787920201673599803712416956201806606504852258e+01",
    "im": "-2.67008863020864165970827926079888487706305917655479819666399290026464532177670183502513979081501322467688080767724297320618292099386415213062721486245326258535693359223840279657553217693110036328630587805633100448105005030096798073998979073846458941596230996757820076309052414196584975973706530449993934189654192606109848e-307",
    "cert_digits": "300",
    "branch": "euclidean-or-subthreshold: Eichler certified Newton, L=log|q|+ipi for t<0"
   }
  },
  "-1": {
   "0": {
    "re": "-2.23679270021264651052926362688413079938711750683891256389345731819450882890789926981771159275198223420722731902087241528282889496446524678943753471065856850167057015376475462681830643180865180329943812019592340840031355178510699331404417805309946868151699313432774420779166751159509977758597134103137781729681590859345276e+00",
    "im": "0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00",
    "cert_digits": "301",
    "branch": "euclidean-or-subthreshold: Eichler certified Newton, L=log|q|+ipi for t<0"
   },
   "1": {
    "re": "6.67821854055587973514482007328978778983600269268340499361704051147636625145037560931513566878876352934923631709431238686133434892713771464643405432298107079153953460267998327419353746307423837646346783642480571762546873934555365510317739077240309456824580386473342950793782636685822869668197991772967743482973293285650834e+00",
    "im": "6.67522157552160414927069815199721219265764794138699549165998225066161330444175458756284947703753306169220201919310743301545730248466038032656803715613315646339233398059600699143883044232775090821576469514082751120262512575241995184997447684616147353990577491894550190772631035491462439934266326124984835474135481515274620e-308",
    "cert_digits": "301",
    "branch": "euclidean-or-subthreshold: Eichler certified Newton, L=log|q|+ipi for t<0"
   },
   "2": {
    "re": "-1.79573115316724568278003292795837230737385724610404776835707461579083526337372523980899638475753147495520346935479242437591407809989502013354696530108569112626954066732564681803798027180336867399635568266251066878781563070424836877678954706922850314881748782396868073827885456698542386848836194084789371998399782291459929e+01",
    "im": "-5.34017726041728331941655852159776975412611835310959639332798580052929064355340367005027958163002644935376161535448594641236584198772830426125442972490652517071386718447680559315106435386220072657261175611266200896210010060193596147997958147692917883192461993515640152618104828393169951947413060899987868379308385212219696e-307",
    "cert_digits": "300",
    "branch": "euclidean-or-subthreshold: Eichler certified Newton, L=log|q|+ipi for t<0"
   }
  }
 },
 "recorded_gate_digits": {
  "homog_cross_min_d": 35.7,
  "loo_worst_min_d": 35.7,
  "ell_top_loo_min_d": 35.1,
  "B0_pslq_residual_d": 110.0,
  "vop_synthetic_roundtrip_d": 116,
  "note": "closure-run cross-checks (leave-one-out transport and Picard-Fuchs-vs-q-series homogeneous period) at PREC=400, NQ=500; the 35.7-digit floor at w=-5 is q-series convergence at 500 terms (|q|=0.212), not the method"
 }
}