{ "description": "Derived-constant data for the gg->Zgamma E125 page evaluator (zgamma-evaluate.py round 3): everything needed to build ALL boundary constants analytically at runtime -- ZERO AMFlow-derived constants. Vendored 2026-07-04 from tools/rowscripts/row20_data.json (row-20 rowscript, all five derivation records folded; the 2026-07-05 labels-only provenance fold applied in lockstep -- all 7 A0 G-seeds derived, provisional set retired); subtrees are verbatim copies (byte-identical values).", "provenance": { "vendored_from": "tools/rowscripts/row20_data.json (2026-07-04, all five derivation records folded; 2026-07-05 labels-only provenance fold applied in lockstep)", "slope_tables": "FOLDED 2026-07-03 (slope-table record): /solve_row20/tail_form.json [slope_tables_exact_Qeps] + slopes.json + the derivation RESULT record \u2014 exact Q(eps) reductions {c8,c11,c13,B0,C11} over basis {K0..K10,K12,T1,T8,Z88}; vendored tables verified BYTE-IDENTICAL to the source record at fold time. Gates: 115.9-139d/order vs IC-extracted series (AMFlow-contaminated, gate-only); T t-independence E01-vs-E02 worst 133.8d. Derivation: /solve_row20/tensor_slopes/exact_expressions.txt.", "corner_forms": "FOLDED 2026-07-03 (corner-form record): /solve_row20/corner_forms.json + the derivation RESULT record \u2014 K0..K5 MB/Barnes closed forms (Gamma/2F1/3F2 at rational arguments), implemented LIVE in eval_row20.py build_constants (form-identical to the record's formulas); gated 139-141d/order eps^-2..+6 vs independent E01, two-precision dps 140/200, ZERO fitted constants (no PSLQ).", "tail_form": "FOLDED 2026-07-03 (tail-form record): /solve_row20/tail_form.json + the derivation RESULT record \u2014 exact polynomial-in-t closed forms (M8, M11 affine; g32=c13*D2q+B0; g31=K12), exact in eps; d/dt identity vs certified connection at 3 random rational (eps,t) points + independent E01/E02 structure gate 126.1d (gpl_tail/VALIDATION_E01_E02.log). Derivation: /solve_row20/gpl_tail/{solve_tcone3.py,final_form.py}; connection input = blog/files/zgamma/zgamma-cone-At.json.", "oracle": "FOLDED 2026-07-03 (oracle-literal record): /solve_row20/oracle_gate_literals.json + the derivation RESULT record \u2014 independent AMFlow literals from /F2-deformed/points/{E01,E02,E04}/accepted.tsv (independent oracle run, leg-B midpoints); vendored points verified BYTE-IDENTICAL to the source record at fold time.", "naming": "rowscript K = cone master index i of zgamma-cone-At.json (t-independent masters); M8/M11 = cone masters 8/11 (page names m8/m11); Rb = g32 = cone master 13; K12 = g31 = R_a = cone master 12." }, "slope_tables": { "c8": { "num": { "K0": [ -68616800, 100741800, 59182400, -52247400 ], "K1": [ 43961100, -128628300, 81412200 ], "K2": [ 48434400, -106243200, 18748800 ], "K3": [ 9497600, -35912800, 33835200 ], "K4": [ -22260000, 66780000, -44520000 ], "K5": [ -54611460, 229455180, -295669320, 110409600 ], "K6": [ -8697360, 25310880, -15832320 ], "K7": [ 18936660, -73735980, 71725320 ], "K9": [ -52247400, 156742200, -104494800 ], "K10": [ -13845561, 42320394, -29258544 ], "T1": [ -26123700, 52247400 ], "T8": [ 53726100, -162657000, 110409600 ] }, "den": [ 13302188040, -32591928120, 11975104080 ] }, "c11": { "num": { "K5": [ -300, 300 ], "K10": [ 1325 ], "T1": [ 5300 ], "T8": [ -5000 ] }, "den": [ -662924, 1258432 ] }, "c13": { "num": { "K5": [ -44512, 44224, 288 ], "K10": [ 18656, 2544 ], "K12": [ 5618, -2809 ], "T1": [ -29888, 49888 ], "T8": [ 134400, -89600 ], "Z88": [ -60000, 40000 ] }, "den": [ 757486176, -1262476960, 504990784 ] }, "C11": { "num": { "K5": [ -6908, 19452, -12544 ], "K10": [ 1325 ], "T1": [ 5300 ], "T8": [ -10900, 11200 ] }, "den": [ -12508, 23744 ] }, "B0": { "num": { "K5": [ -32, 64, -32 ], "K10": [ -32, 16 ], "K12": [ -2, 1 ], "T1": [ -64, 32 ] }, "den": [ -96, 64 ] } }, "corner_oracle": { "provenance": "independent corner-master oracle rows (t-independent, so the E01 rows ARE the constants): /F2-deformed/points/E01/accepted.tsv, indices per /solve_row20/corner_constants/RESULTS.md. GATE-ONLY: never used in the MB/Barnes derivation of the K0..K5 closed forms.", "indices": { "K0": "0,0,0,1,0,1,0,0,0", "K1": "0,0,1,1,0,1,0,0,0", "K2": "-1,0,1,1,0,1,0,0,0", "K3": "1,0,0,0,1,1,0,0,0", "K4": "1,0,0,-1,1,1,0,0,0", "K5": "0,0,0,1,1,1,0,0,0" }, "rows": { "K0": { "-2": [ "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0", 999 ], "-1": [ "0.84556867019693427878697581983519513791568132812015280238846553023026454644467065812610587341650650097073710550038583503807899197102691432755", "0", 111 ], "0": [ "3.0024272548575323426831190790269039183691468379463635288141559658350681506840555294083671847162036618515576611699136579446920484830508037536", "0", 109 ], "1": [ "2.2025304594201917143373855268547216282037052388204016402205342137731172660146343942545040011423681324825500010453149743242579096941322447222", "0", 109 ], "2": [ 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"191.44674176477612898483103388935799831931034841109688079162070141814498704545934679484371877773204001541358440219856958678835041379555562698", "0", -1 ], "6": [ "417.21591566250343766207761104970174005734469276706634921724208587630073627604640528518182278483285223243845992366142653690022050739817564920", "0", -1 ] }, "K4": { "-2": [ "0.14000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0", 999 ], "-1": [ "0.18184628049423746569684328144359398597486205260348805900105184089890370316892055880432148894497757680256986143672068357199772554261043467252", "0", 109 ], "0": [ "0.66953994259367326230704323188949774627935101466785849163421164899972898425783215958737504293361945177536567766002844642270275838412144503628", "0", 112 ], "1": [ "0.99167022675155247038915546224344649381885743906385705983268498537874159318150053701090576666334750345229222711314287700709193399289002045361", "0", 110 ], "2": [ "2.5821248272121722662529966234713619622064764823358410578072414295609774635512804705563160199535298624372115229136296804583597457690203004518", "0", 110 ], "3": [ "4.3004574858661101195159907656608120764445157781091157338140110345841806515574947610764740384411134643612309848441976084050341479621914937227", "0", 109 ], "4": [ "10.016100016373760382416351085376450619389128649619371354563968107439088139107919743906672386167244214596016367551927325236471492369367590137", "0", 109 ], "5": [ "17.653446450668948232720222254502555917697864640149904972319254676412591582316926362301682782700961941593910583629992525714268652022115094596", "0", -1 ], "6": [ "39.562957800389979147726374047077438192937658082819264278788885131994686242284258444433536181201110268510130483359415641489321701367903639673", "0", -1 ] }, "K5": { "-2": [ "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0", 999 ], "-1": [ "-0.10640315943542312610261659350001454690141839402440598727142110974038440139049023246644863308232317043040772557561548361624604032207035624517", "0", 109 ], "0": [ "2.1508313437505964900220825861208758027236282794202215749861201411936279431836352206116983588508147357738423767223660159249659043279767489704", "0", 109 ], "1": [ "-0.69649268762022904097043369506172578636893432199284389924258372339120340120530370274610180355996210969460192451045172929515345309543176616813", "0", 111 ], "2": [ "3.1539894887757406904448913098050338755371205500453547185441928020067860539589383774045964613246815281440692967149718888162802785190888947475", "0", 110 ], "3": [ "-1.5508776589931608581609197578446441062150255497415628073583755311057409402073187445479542918028767841289100841461258711461442571466874052490", "0", 109 ], "4": [ "4.1050390934774231652008174421755605862973171410954212822464075746377562581015787354117241517840021090507913600982446174305326832083227468280", "0", 111 ], "5": [ "-2.4817981882788082576059421827917651693700515619352111623744739080917670853051761446566470129299442812889762358522441251354817495030772855048", "0", -1 ], "6": [ "5.0532911681969368850317672690421414019874368541915783995036286638015264565814587289867930492755281092182783115818691808868540967576152833656", "0", -1 ] } } }, "endpoint_constants": { "provenance": { "source": "/solve_row20/RESULT record MAIN DELIVERABLE (2026-07-03 endpoint derivation) + s_transport/{RESULTS.md,endpoint_final_dps150.json} (tag 'final', FULLY ANALYTIC seeds, FINISH_DONE 2026-07-03 22:54); seed provenance closed by the 2026-07-04 seed derivation (seeds_final record): all 7 A0 G-seeds {G5..G11} DERIVED (cusp core_fast.py Gamma-sum closed forms; values gvalues_cusp_analytic.json), gated 61.1-65.9d worst-of-13-orders vs the dedicated independent AMFlow oracle amflow_oracle/ + independent second-config re-gate dps150/K96/r=1/24 (90.0d at seed orders; >=102.5d vs stored strings; >=159.4d vs the RETIRED provisional set)", "method": "region-seeded s-transport: analytic s=0 cusp boundary (exact Gamma-sums; cusp_boundary/boundary_data.json v2) + exact 22x22 A_s connection (As_build/cone_As_t13.json, V1/V3-validated) + generalized Frobenius/complex-detour march at dps 150", "gate": "independent E01 accepted.tsv, ALL 22 s-cone masters, eps^-2..+4: worst 136.8d (R_a 137.2, R_b 137.4); E01 used ONLY post-endpoint (s_transport/E01_USAGE.md); mid-path closed-form checks 149.9/150.2d at s=-1/8; seed certificates 5.0e-144/5.6e-146; endpoint max|Im| 3.4e-140", "mapping": "t-cone master -> s-cone index per As_build/cone_closure.json tcone_to_scone: K6->10, K7->11, K9->16, K10->18, K12->20, M8end->12, M11end->19, Rbend->21; fold-time cross-check vs retired E04-IC literals: 119.4-120.0d (old-literal noise-floor-capped)", "noise_prune": "|coeff|<1e-100 dropped (K10/K12 eps^-2,-1: true zeros per cusp_boundary v2 noise-key analysis); Im parts <3.4e-140 asserted and dropped (masters real at Euclidean point)", "caveats": "TWO-PRECISION honest note: the dps-190 full-march leg was SKIPPED at refresh time; alternate evidence = B0 seeds dps190/250 bit-identical to 213d + the 2026-07-04 second-config G-seed re-gate (provisional-vs-analytic >=159.4d at seed orders; provisional set RETIRED) + the independent-oracle gate itself. Cross-run 'two-prec agree' column low entries (masters 13/17/18/20: 12.4-29.4) sit on noise-floor orders (caveat-2 pattern), not value disagreements; gate column is authoritative. {K6,K7,K9,K10,T1,T8} hypergeometric CLOSED FORMS remained OPEN at vendoring time (not critical path; K6/K7/K9/K10 were closed 2026-07-05): these are analytic-transport digit strings, not closed forms.", "T1_T8_c13": "not vendored: solved at runtime from the transport endpoint via the exact recorded slope tables (T1/T8 from the M8end/M11end equations at t=-1/3; c13 = (Rbend-B0)/D2q per the endpoint derivation); Z88 eliminated (its only consumer was the c13 lincombo)." }, "series": { "K6": { "-2": [ "0.5", "1.2679195e-185" ], "-1": [ "-0.02918749453389026549610450341761211585925905808448238846565387485551667461282556152950156979057642091577627832580840113528553630758381340894527376990643050511447944077803251853312702905", "-2.9691443e-185" ], "0": [ "0.9811822540925868028984570510976164864928943756101853779061128887704062977925338566361384442064430919021903669056187554686612508128294632109220655223789454951284333531805181469845601226", "3.7801597e-185" ], "1": [ "-0.12470519477310011755003889526703808286105150732353306808771006856567499218807868830748260217998603850086299602877518632298629643332795142221156007712752783312967622146486828515875496765", "-6.4143761e-185" ], "2": [ "1.0119106242106664162218363881229498469186111934128121743878835762798539721746224330510079811480257351409419092899681386007807596261078236555937931882039273037858952982487693456770042911", "1.2514619e-184" ], "3": [ "0.41126610803246772287633049004973665425907616381014494830278152337997748203968633330304040920741053626445637832231542406259101611884434194952204203444730411146371186283740884115191234223", "-1.4790748e-184" ], "4": [ "-0.50348864146454083546978668338841408412427453178547277789797548531818755984252038186510405915619736501590250512975161934211496872650612538213115613342971901402887049869786944426822697053", "1.2353674e-184" ] }, "K7": { "-2": [ "1.00375", "1.6991621e-187" ], "-1": [ "-0.17099706564442730309383737727564663777036283696003960518491351380180077645008642417791989485575249358727604766305904662476068184437723484573653732082565227015633837032680510015979942454", "6.8542982e-187" ], "0": [ "2.1335580851380321193784527014285313415017176415960287158454838212558911077734921618605403074952746120761399242968892265273791447103101180051377088413752962870386104918782407386794141502", "-3.1838112e-187" ], "1": [ "-0.84484453022636940201141236766037441815685849067222756681602931943178476946921234486166622055257079444987220206020541438633631052034398785701510079265524973609793084205355507855753399519", "4.4678963e-187" ], "2": [ 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"0.0" ], "2": [ "2.268915080991675654694835526139752176461943610719119778601338581302572165596103615236423233446245156482499452858365429551480628894981360115323735", "0.0" ], "3": [ "-1.214906436151158276943813232039419738677778801511630536228420315195156183960441022041786649835152566379518037561128391117491536897362788639561904", "0.0" ], "4": [ "-1.948371036731285614889471493860154520167336483317602025596318468871112947110895151868115166409237139321388264979130385519047325693377047242492519", "0.0" ] } }, "series_pre20260705_note": "SUPERSEDED 2026-07-05: the original dps-150 tag-'final' strings (certified 137.2-145.0d by the two new legs; NOTE their printed digits beyond ~137d were UNCERTIFIED for K12/_Rbend -- the dps165-leg gate measured K12 137.2d / _Rbend 137.5d, so trailing prints past that were noise). Kept verbatim for provenance.", "refresh_note_20260705": "REFRESHED 2026-07-05 (chain vendoring step): strings are the dps-190 region-seeded transport endpoint (/zgamma_probe/probe190/endpoint_probe190_dps190.json), TWO-PRECISION certified 152.3d mutual vs the independent dps-165 leg over all 22 masters (gate_endpoint script); vs the OLD dps-150 strings 137.2-145.0d = the old strings' full certified content. Old strings kept below in series_pre20260705 for provenance." }, "oracle_E04": { "t": "-25", "header": "# point E04: s=-1/4 t=-25 Msq=7/25 msq=1 region=euclidean u=2553/100 im_expected=1", "masters": { "g31": { "0": [ "0.55129454202113704604185775543436541404184708727908803560545722607310576856872183860477957086157596612593368222815665191208909410043107265185", "0", "110" ], "1": [ "0.90052626519318063053394458091777285943209305940493450449830238938444182430662963855442427923337643404557663561247139085904624707444187762248", "0", "110" ], "2": [ "1.8773840408060890990544239069248336963358645966504007077387736360252441724383999035881397035871780933948849469515251285320428373645000119751", "0", "109" ], "3": [ "2.0783744878542038416072543153949065805072197459730127626299017085781187134226823957738859397584053234320340750042216055301094135577316230826", "0", "110" ], "4": [ 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"1": [ "-2.2594305578132744308181088264423305790832278249059706507063506335539030639150972493684425522169647771559699848576757722052311951981993978816", "0", "109" ], "2": [ "6.8145678448818549003919756455634178089198246645875181986305577541532179159502961243628593261701633476878960166800792646217668435449250997749", "0", "110" ], "3": [ "-2.7906575105655987419913661180997199993561171510850023419204948674448172148952182811466027316152645141611446710744030651760030109955201347768", "0", "110" ], "4": [ "2.5105645406912434513398121859523029847405958517213967683065404313717631030089307224164320764138018887810278228286564431981853792289119276667", "0", "109" ], "5": [ "6.1224796355429742530628583026582878130131988837476096474787212875261210125111426933353046722199524353618653812313484330165319566095825622058", "0", "-1" ], "6": [ "-20.677772976247289389293524489524287384228765394225800927408254021552532367502459086018920536464936291723876481915018032547430776212252324872", "0", "-1" ] }, 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"110" ], "4": [ "1.3001223380758969198580797842175312215330240540915099930027674791469636472418950775089188953656594354823521021889245924986730475597605116187", "0", "110" ], "5": [ "15.350117686789770399109963709244054038766430339071981806490182000664594885854118618696620082208402802437259858118355226162384083406286467215", "0", "-1" ], "6": [ "-44.310597473569764763372974460916912709980117170589868601718897455373682653830464927984431519318904546441790871531260409864665872141755573359", "0", "-1" ] }, "M11": { "-2": [ "1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0", "999" ], "-1": [ "-1.1064031594354231261026165935000145469014183940244059872714211097403844013904902324664486330823231704304077255756154836162460403220703562452", "0", "109" ], "0": [ "2.1763475820862902466954319228668457217977784733216696159102282313068792127868492967551406555810176516238684203771613869992976118338247150620", "0", "109" ], "1": [ "-2.6815146244630013144348499622086023357465363824549276653536920124600857090560300575044304925120067346312865308674888923118031374777703957453", "0", "109" ], "2": [ "3.3655411278446810063451219226864064023210604978090037997276916527420507568822798560727699171894053714940284075646542846931936586831761878411", "0", "109" ], "3": [ "-3.6605337097270579730788176292292500390043807822063222756638386028464927840417713920331840838714075219276688359888929192632902313539301285189", "0", "110" ], "4": [ "3.3688915483055914087108375630782350472641164091518822085594833696917876141977882777848719343904974397490687380752141234852910852351890093906", "0", "110" ], "5": [ "-1.8407888547461154710723483409607440319538125178656725407388870522998616420801953904809496086784523402701844267513532874396887015232615446183", "0", "-1" ], "6": [ "-2.2079077693789144617670528183375958281864056772293735251250008805519618304395361027907272131667779076369253951390651203714635125637455077856", "0", "-1" ] } }, "provenance": "independent oracle literals; source: /F2-deformed/points/{E01,E02,E04}/accepted.tsv (independent AMFlow F2-deformed oracle run, leg-B midpoints, amflow convention no exp(eps*gammaE)); GATE-ONLY: never used in any derivation of the closed form" } }