{
 "description": "Named puncture-cusp seed constants of the zgamma E125 t-cone at (s,t)=(-1/4,0), M=7/25, mt2=1: the boundary data of the VoP-word form. amflow convention (no exp(eps*gammaE)), raw J values, eps^-2..eps^4.",
 "provenance": {
  "short": "11 t-independent masters = verbatim E04 accepted.tsv (A_t rows exactly zero => t=0 value = E04 value); m8/m11/R_b derived 2026-07-03 by exact-word transport E04->0",
  "t_independent": "masters 0-7,9,10,12: VERBATIM strings from <archive>/F2-deformed/points/E04/accepted.tsv (>=109 agreed digits; their A_t rows are identically zero, so the t=0 constant equals the E04 value EXACTLY).",
  "derived": "<archive>/blog-evaluate-fix/zgamma/r2/derive_seeds.py 2026-07-03: exact-word (VoP one-fold) transport of the certified cone connection from E04 accepted.tsv (s=-1/4, t=-25, leg-B midpoints, >=109 agreed digits) to the puncture cusp t=0, along -25 -> -1/3 -> -53/236+0.18i -> -0.12 -> 0 (detour around the apparent eps-dependent singularity t=-53/236 of the connection).",
  "derived_checks": {
   "max_abs_im": 8.477881873140514e-141,
   "rb_eps0_vs_stored_50d_extrapolation_digits": 50.34510495676305,
   "stored_ref": "<archive>/zgamma-t0cusp/clean_t0_from_existing.json['-1/4']"
  },
  "certified_digits_cap": 105,
  "named_status": "These constants are provably NOT closable in the conductor-4 Gamma_0(4) ring (three independent value-fit campaigns, honest negatives: <archive>/zgamma-cusp-ring/VERDICT.md, <archive>/zgamma-t0cusp/RETRY_NEWTOOLS_VERDICT.md). They are named seeds, not fitted answers."
 },
 "seeds": {
  "0": {
   "-2": [
    "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
    "0"
   ],
   "-1": [
    "0.84556867019693427878697581983519513791568132812015280238846553023026454644467065812610587341650650097073710550038583503807899197102691432755",
    "0"
   ],
   "0": [
    "3.0024272548575323426831190790269039183691468379463635288141559658350681506840555294083671847162036618515576611699136579446920484830508037536",
    "0"
   ],
   "1": [
    "2.2025304594201917143373855268547216282037052388204016402205342137731172660146343942545040011423681324825500010453149743242579096941322447222",
    "0"
   ],
   "2": [
    "5.3919438761143729388364413340626046649409248586455109351518088055659131955192182659161619678708537264049010628598082812263292814485555825075",
    "0"
   ],
   "3": [
    "3.6889342525480277326222929635514906228069327507886914717172017582791884434659610629991704645959985250112308153974155076862787145995455325402",
    "0"
   ],
   "4": [
    "7.8713551051336128782534595942880015672987096266650418072275660649488921744753556962435210595742521284413950603846230083044624194857854477846",
    "0"
   ]
  },
  "1": {
   "-2": [
    "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
    "0"
   ],
   "-1": [
    "1.9080686701969342787869758198351951379156813281201528023884655302302645464446706581261058734165065009707371055003858350380789919710269143276",
    "0"
   ],
   "0": [
    "5.7428791047024428200755184139071840915343041533580018757198647777350113128150780739256647620336039669995959423799411550227336188426902382718",
    "0"
   ],
   "1": [
    "11.250244914498540792506458995445587855426929538886987396814557112795232471133191123422974197644469146952208540489545404161794115506980289979",
    "0"
   ],
   "2": [
    "24.291785965788370351137540162729399421362049790446147354259631785954790370685374562513418569469684870958025171843076246748739509671877900660",
    "0"
   ],
   "3": [
    "49.847174564753361578701277214113632275284160790067626291122537033795230080385071673510238977681680308796686331024063970881098962891976670062",
    "0"
   ],
   "4": [
    "97.521733852011408990795873443920084708721559105856855018761194591096216593032757705983490283897441695126546962852970440425918561064977392245",
    "0"
   ]
  },
  "2": {
   "-2": [
    "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
    "0"
   ],
   "-1": [
    "0.71536033686360094545364248650186180458234799478681946905513219689693121311133732479277254008317316763740377216705250170474565863769358099422",
    "0"
   ],
   "0": [
    "2.7111173904358257532702542306053827514684401211362164859651561344972830483562818914928109488345004753661382048377285713440437893273254879031",
    "0"
   ],
   "1": [
    "1.3046824593859697433392739742401624722068521575986320431038343215455871150159028692958500701885496350041581046229364632889890961824036246127",
    "0"
   ],
   "2": [
    "3.6127211195005854817578049029885472139797294301584401729255084437772977092144785265084328622595231297999439303466707527533851558596638920709",
    "0"
   ],
   "3": [
    "-0.40248214063380141002825277926205460793451996481415820355048560144079092308231395625148633666873172915305802115733815880587541404182513325024",
    "0"
   ],
   "4": [
    "-0.061056621544068362867361196053492846951511122783898243401155890456484462994358052077185820290083287862931767588236029039040556621767891594676",
    "0"
   ]
  },
  "3": {
   "-2": [
    "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
    "0"
   ],
   "-1": [
    "1.7755686701969342787869758198351951379156813281201528023884655302302645464446706581261058734165065009707371055003858350380789919710269143276",
    "0"
   ],
   "0": [
    "5.9615970961128668076953474175602377162584629237771141797295761842992337156239525393897201928698377826772575376714276059771365511833135036623",
    "0"
   ],
   "1": [
    "10.503507270688625914328195964605682495215974062169544296681558828540711336985944890097582266705610298075790222863257054743929574270041036550",
    "0"
   ],
   "2": [
    "25.735478061438879720476539551289718126697603985698144784111672488115637822990892497009050855843807506029303993561542065510458204928303404808",
    "0"
   ],
   "3": [
    "46.511631049756620575392189485960621816359789569878960677933797415306281661334910698926442368734891245688651119053324952513405184321460410728",
    "0"
   ],
   "4": [
    "104.19292618199729207771812541046291480438324623998126459937865358095267861829787898060744473745498768662530622193913649373077644227080344732",
    "0"
   ]
  },
  "4": {
   "-2": [
    "0.14000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
    "0"
   ],
   "-1": [
    "0.18184628049423746569684328144359398597486205260348805900105184089890370316892055880432148894497757680256986143672068357199772554261043467252",
    "0"
   ],
   "0": [
    "0.66953994259367326230704323188949774627935101466785849163421164899972898425783215958737504293361945177536567766002844642270275838412144503628",
    "0"
   ],
   "1": [
    "0.99167022675155247038915546224344649381885743906385705983268498537874159318150053701090576666334750345229222711314287700709193399289002045361",
    "0"
   ],
   "2": [
    "2.5821248272121722662529966234713619622064764823358410578072414295609774635512804705563160199535298624372115229136296804583597457690203004518",
    "0"
   ],
   "3": [
    "4.3004574858661101195159907656608120764445157781091157338140110345841806515574947610764740384411134643612309848441976084050341479621914937227",
    "0"
   ],
   "4": [
    "10.016100016373760382416351085376450619389128649619371354563968107439088139107919743906672386167244214596016367551927325236471492369367590137",
    "0"
   ]
  },
  "5": {
   "-2": [
    "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
    "0"
   ],
   "-1": [
    "-0.10640315943542312610261659350001454690141839402440598727142110974038440139049023246644863308232317043040772557561548361624604032207035624517",
    "0"
   ],
   "0": [
    "2.1508313437505964900220825861208758027236282794202215749861201411936279431836352206116983588508147357738423767223660159249659043279767489704",
    "0"
   ],
   "1": [
    "-0.69649268762022904097043369506172578636893432199284389924258372339120340120530370274610180355996210969460192451045172929515345309543176616813",
    "0"
   ],
   "2": [
    "3.1539894887757406904448913098050338755371205500453547185441928020067860539589383774045964613246815281440692967149718888162802785190888947475",
    "0"
   ],
   "3": [
    "-1.5508776589931608581609197578446441062150255497415628073583755311057409402073187445479542918028767841289100841461258711461442571466874052490",
    "0"
   ],
   "4": [
    "4.1050390934774231652008174421755605862973171410954212822464075746377562581015787354117241517840021090507913600982446174305326832083227468280",
    "0"
   ]
  },
  "6": {
   "-2": [
    "0.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
    "0"
   ],
   "-1": [
    "-0.029187494533890265496104503417612115859259058084482388465653874855516674612825561529501569790576420915776278325808401135285536307583813408945",
    "0"
   ],
   "0": [
    "0.98118225409258680289845705109761648649289437561018537790611288877040629779253385663613844420644309190219036690561875546866125081282946321092",
    "0"
   ],
   "1": [
    "-0.12470519477310011755003889526703808286105150732353306808771006856567499218807868830748260217998603850086299602877518632298629643332795142221",
    "0"
   ],
   "2": [
    "1.0119106242106664162218363881229498469186111934128121743878835762798539721746224330510079811480257351409419092899681386007807596261078236556",
    "0"
   ],
   "3": [
    "0.41126610803246772287633049004973665425907616381014494830278152337997748203968633330304040920741053626445637832231542406259101611884434194952",
    "0"
   ],
   "4": [
    "-0.50348864146454083546978668338841408412427453178547277789797548531818755984252038186510405915619736501590250512975161934211496872650612538213",
    "0"
   ]
  },
  "7": {
   "-2": [
    "1.0037500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
    "0"
   ],
   "-1": [
    "-0.17099706564442730309383737727564663777036283696003960518491351380180077645008642417791989485575249358727604766305904662476068184437723484574",
    "0"
   ],
   "0": [
    "2.1335580851380321193784527014285313415017176415960287158454838212558911077734921618605403074952746120761399242968892265273791447103101180051",
    "0"
   ],
   "1": [
    "-0.84484453022636940201141236766037441815685849067222756681602931943178476946921234486166622055257079444987220206020541438633631052034398785702",
    "0"
   ],
   "2": [
    "3.1284931508817744680261756281717977826354677910859474236331302846035539329717948834738198481567156825780564503435243641378477292217933572923",
    "0"
   ],
   "3": [
    "-1.7487111475575828997524612944976314857945212281566748861777873161724416431430217498770135589068919903420564269382752414494752957368172037835",
    "0"
   ],
   "4": [
    "4.0654984675762099924986080982310323748554483564842985803309980407873668154758258443431774162058667252791391135029638885310714012907311002431",
    "0"
   ]
  },
  "9": {
   "-2": [
    "0.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
    "0"
   ],
   "-1": [
    "-0.077215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447249807082480960504014486542836224",
    "0"
   ],
   "0": [
    "1.0825091847673982214166581746034915968678256449903828142475051078192988918602482818990135498725703597498107374490492067362930530402359072982",
    "0"
   ],
   "1": [
    "-0.40581618674948482698741190988224965019528075253568805529159105021089595435492091746081998858016110776372385704512022039188965657642651943987",
    "0"
   ],
   "2": [
    "1.6166989899939454415959006194822169723556504625437675340899736110014337235671094124716478698326767308385500207606238896951240691241725149889",
    "0"
   ],
   "3": [
    "-0.89173619186228938714660778610980640110762422366415612377068858112013729663600259577660479262213309393852801867314980000769007000745683031404",
    "0"
   ],
   "4": [
    "2.1868964877589721609957914769175393216801114168656213675006416028606844867055000973594992671412698791498871732392990232970250590682645383637",
    "0"
   ]
  },
  "10": {
   "0": [
    "-1.0208975096520743232197358921848534714811215169253041875992081446235704145530583860351432897916433089719059075759498856454949094215331627422",
    "0"
   ],
   "1": [
    "2.1597041953236293678413553691009392855610690531507846954124492153744768756191254690114374304643473428319343896503519246647464551741128308757",
    "0"
   ],
   "2": [
    "-6.5104551601355789638276105182872836122900395787987626568461951012858655918433680670246201264996880510640081002533423202836196767508657171817",
    "0"
   ],
   "3": [
    "13.753092260387034419793080695217773778400386911340952372956162256390228516311077530282250209458933448671837128241073733357316563971572215423",
    "0"
   ],
   "4": [
    "-30.719003310415363911154916330245352103540935163562482528694968822077919356119357282329131952072818488683372825679100315363374057178655893401",
    "0"
   ]
  },
  "12": {
   "0": [
    "0.55129454202113704604185775543436541404184708727908803560545722607310576856872183860477957086157596612593368222815665191208909410043107265185",
    "0"
   ],
   "1": [
    "0.90052626519318063053394458091777285943209305940493450449830238938444182430662963855442427923337643404557663561247139085904624707444187762248",
    "0"
   ],
   "2": [
    "1.8773840408060890990544239069248336963358645966504007077387736360252441724383999035881397035871780933948849469515251285320428373645000119751",
    "0"
   ],
   "3": [
    "2.0783744878542038416072543153949065805072197459730127626299017085781187134226823957738859397584053234320340750042216055301094135577316230826",
    "0"
   ],
   "4": [
    "2.8545486087698869972482549799389882867047663730244598082243931283801499653892641524322028219755632409911241444076003995461224128265590639760",
    "0"
   ]
  },
  "8": {
   "-2": [
    "1.0975",
    "0"
   ],
   "-1": [
    "-0.160844720869531727874356971666448909493973910350880053022223615337210152939991216964701439191485572508984099849148121838",
    "0"
   ],
   "0": [
    "2.32395790907245582543037174960249104827122268238783622012174929705824910721962394762893294162811842824235405496499749884",
    "0"
   ],
   "1": [
    "-0.833488334833291540902129728343930189847902860004178129988116595607085111893213847151562924008250730535221573067261560898",
    "0"
   ],
   "2": [
    "3.32917696254480102616245343409170280348056541451064747738510718075252012735273296829499686779175205146585749187635807757",
    "0"
   ],
   "3": [
    "-1.62926845527313349181023969781530755845974991844463470457586679027651562316359813679120916942171632819972493857199509616",
    "0"
   ],
   "4": [
    "3.99377992987072380938698306005585845142400404441920229564346448379848199729779470608144401038124454438362394215573708811",
    "0"
   ]
  },
  "11": {
   "-2": [
    "1.0",
    "0"
   ],
   "-1": [
    "-1.10640315943542312610261659350001454690141839402440598727142110974038440139049023246644863308232317043040772557561548362",
    "0"
   ],
   "0": [
    "2.19334954353788434504743125255566239634770896671111322916304419580552872637971022166468709169770563862937731846184013219",
    "0"
   ],
   "1": [
    "-2.68047618910366373284954648122633311812508516799432807026859282731509586560532430389986968199852085812417920893011634881",
    "0"
   ],
   "2": [
    "3.39190103227343602977198843496512498172677371292282123598583715643882499708890241427949022272638587420196053802101493719",
    "0"
   ],
   "3": [
    "-3.6676408506354589350067590258083247907886756529171265235261035922701712413417622797679454491199298324302689358018210279",
    "0"
   ],
   "4": [
    "3.39490289883983033178493405396763631260504465038135663156821767065827226573773254648735004077097158228521065407533907554",
    "0"
   ]
  },
  "13": {
   "-2": [
    "1.0",
    "0"
   ],
   "-1": [
    "-1.10640315943542312610261659350001454690141839402440598727142110974038440139049023246644863308232317043040772557561548362",
    "0"
   ],
   "0": [
    "2.01385146580296326841643499768759448061154975691930909750868141115648510288823398464097832666162923450853845107705013623",
    "0"
   ],
   "1": [
    "-2.286806181771674436292256518836552885370491220840868760854755119735822708856500850192698974658727000363085498272976682",
    "0"
   ],
   "2": [
    "2.26686458676901608163645944798303316245065316302115104622988578234587964592523885511502324294172992079887799545749212134",
    "0"
   ],
   "3": [
    "-1.21419563208356573388057487205730721761676911157433103870039837152549852013671738234506453921700198101835864933876771818",
    "0"
   ],
   "4": [
    "-1.95038241378000050749570973240627432958442344854155311411012952778989759283526934835735294387410125023753189899218970423",
    "0"
   ]
  }
 }
}