back to table · edit · history · where entries came from · files · download
18798 bytes, as of the version from 2026-10-28 18:59 (current). Recorded here, not run.
{
"controls": {
"series_at_origin": "I=1, harmonic sum=0",
"nonzero_control": "K_(1/2)(1)=sqrt(pi/2)/e, finite tight overlap",
"origin_limit": "kei_0(2^-128) differs from -pi/4 by less than 1e-73"
},
"independent_series_bits": 1024,
"series_radius_limit": "1e-200",
"rows": [
{
"n": 1,
"number": "3.914667606843246082248522786841159362118245140033896876481409624718963835262054932638562117525876313",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
-1,
1
],
"series_terms": 95,
"series_max_radius": "7.2996638e-244",
"series_tail_sum_bound": "6.248430687702347381974334988722179760533062641258523280065688827053288453934637251758290425351933597315203136713908545311088009083152542053460602026017779791593638367114639382580938906503367800170190537782138054762911910683151049484047805784471326792500203122392188779686255771659998703177045487263805888488e-244",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": "3.91467",
"AS_error_in_last_decimal_units": "-0.2393156753917751477213158840637881754859966103123518590375281036164737945067361437882474123687"
},
{
"n": 2,
"number": "8.344225062937332035330306995680109871104448891136815893175819047092013252661186877211103702704340229",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
1,
-1
],
"series_terms": 117,
"series_max_radius": "9.4206565e-243",
"series_tail_sum_bound": "7.348957975947961252834960799435784513185088137033463551006343111216938829597248112924821547584549690328972636000151344252501580623103508241585673142976669825107025227364289582443450621206821775437392136036986502599896515204074221068486780668731527955428051834124479858816821825912719066311846477650803710812e-243",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": "8.34422",
"AS_error_in_last_decimal_units": "0.5062937332035330306995680109871104448891136815893175819047092013252661186877211103702704340229"
},
{
"n": 3,
"number": "12.78255714860019849323674616307008350157749908713178247759248107566022491834210454618259218821337034",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
-1,
1
],
"series_terms": 134,
"series_max_radius": "3.8887591e-243",
"series_tail_sum_bound": "2.898228544672708471047130341578986256356850046790295065512255729158779337479388969389164520096587604357009428067251001448116407332977790830094585767517783416173539632426968766936479970098582219194764498130334144414936111953559831872297653591578632149145256034767410643056518252538878505393388156519913025705e-243",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": "12.78256",
"AS_error_in_last_decimal_units": "-0.285139980150676325383692991649842250091286821752240751892433977508165789545381740781178662966"
},
{
"n": 4,
"number": "17.22314372343476945553233733582037505929493832333115158170731820298792882608575312173488920306326503",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
1,
-1
],
"series_terms": 148,
"series_max_radius": "2.8418687e-242",
"series_tail_sum_bound": "2.056531683616967230673529348503922194778939885550401166232578798312053352064318327924546881931875284453385373528169455097179185446964327567814731574985375111413676411536915893498191847826613526789945718316861910847779983866894951592859060345683659683127686451619962446149517668479186265029262542903759046664e-242",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": "17.22314",
"AS_error_in_last_decimal_units": "0.372343476945553233733582037505929493832333115158170731820298792882608575312173488920306326503"
},
{
"n": 5,
"number": "21.66464214063516449913316958499225512146845366272185563598952929066578604229752630639047276027519252",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
-1,
1
],
"series_terms": 161,
"series_max_radius": "1.1118251e-242",
"series_tail_sum_bound": "7.877336272849189606105799821278325260800806196998100792229001415058721902882666242910987932902892280311344942273313709373915453852425048417232446930971707074985663049602884252840245933026827908121689936831108107999391462805598767815794721114872750706803669760975949532519927591412684595265807728914798462292e-243",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": "21.66464",
"AS_error_in_last_decimal_units": "0.214063516449913316958499225512146845366272185563598952929066578604229752630639047276027519252"
},
{
"n": 6,
"number": "26.10659928055842432482534866691990083750505445880136552118581501356547049663846942635504033127414684",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
1,
-1
],
"series_terms": 172,
"series_max_radius": "7.8060337e-241",
"series_tail_sum_bound": "5.439651284222237697942829228996625193298786824351891452782455855388342258797538601270096723183978587638624162781256733054385870346515856104122589052220439936203022118179039312082149730664478801561618930066566953808413142061293363634435378885610795977389322830737726426396829640268660393527031652530151771347e-241",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
},
{
"n": 7,
"number": "30.54881957534176276623116858512292019252028483693620716701376281421984822185777673229783560095678302",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
-1,
1
],
"series_terms": 183,
"series_max_radius": "1.0025879e-240",
"series_tail_sum_bound": "6.894814440387643510956631480275128161539861382431303653698103625360663219214079361991277972154472358120210596009595511594512723362756607695706225057110662827320857600193667149933693472874579712720967993065598340952384910249252976399490203541249335098989266659596605495297578899595299375267747427321038854210e-241",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
},
{
"n": 8,
"number": "34.99120479023713671166738599458398054906369570316370304603480589476735014664362740553919586851520903",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
1,
-1
],
"series_terms": 194,
"series_max_radius": "8.3599026e-242",
"series_tail_sum_bound": "5.687018042926700058599561966857618895735227171403856530535626767044441959356036584185722166178580892691463157707929980589803868158468902540345910529801519251368758832171522472957961571072758568621645287853856906528961888215515898569649764113652696847210005609102296049219137504590518416346641561872495791929e-242",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
},
{
"n": 9,
"number": "39.43370017261625990952801121478285546060557424678615714767574096393268574055096568650914468741778385",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
-1,
1
],
"series_terms": 204,
"series_max_radius": "1.0708572e-241",
"series_tail_sum_bound": "7.216916508747774580527859986786831593682862882834690285199749630805639165237487582516057215375465814122514654143756267107047228075378014284525619034892549773763588901632151297076447467353557839010275225975828514318068560090004121765978538492077162558293510962923148602441870269875401148009244746534161845915e-242",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
},
{
"n": 10,
"number": "43.87627279110208307389416096754234474464038793981541630158416632365915265166045935390772139174965917",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
1,
-1
],
"series_terms": 214,
"series_max_radius": "2.5411683e-242",
"series_tail_sum_bound": "1.698905828983819037575340647968943137795534070844637874846763670158851488879304365590878062581068305807399443678300581966055282184773032406688872090442485764197947664179656055273580797944958241470232719600554553376035901364057134335153406381741650699736454886375216809126894476234953245548840144499999230453e-242",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
},
{
"n": 11,
"number": "48.31890164989348503351879028460588372842478117645921891710904499015501958976257645501349420937247469",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
-1,
1
],
"series_terms": 223,
"series_max_radius": "1.4300698e-241",
"series_tail_sum_bound": "9.492309992027256619551964490494192090748632510336512283583726354592070994268323617820286297332061487145624653874173535029818378248826005208765937697687490859037878929040201697861156604127340703150558920170963215491366864522088466804077993829509553618081001714037608111094031255667426615053673349712146624924e-242",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
},
{
"n": 12,
"number": "52.76157273073524710735013864653861983972744937699333482982544643013324793386556965423508275327482553",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
1,
-1
],
"series_terms": 232,
"series_max_radius": "2.4081012e-241",
"series_tail_sum_bound": "1.588320187596985677468432291269666156419482444610413254657062616860304976060164870473290593611552952302416558712492336605921089652041814649022321892663872747561065242412105063630754952120070312822817743364072920687489600790478372753185898657428754752403263441833161114087901738387034373850765074400415513579e-241",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
},
{
"n": 13,
"number": "57.20427631674848858496381430361508026326128867217941589690617718411196358273560894086117274017457561",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
-1,
1
],
"series_terms": 241,
"series_max_radius": "1.5342235e-241",
"series_tail_sum_bound": "1.006243376128791850795822842801153929968755122262734542724206174981691331377035272559227101317076137177152465874953925133279504739210329368237803150573601128141924637665439440646047559093952535830805899705239596386693749444142807131939124729353121877803886401491077981320795605373914942235825157344407012557e-241",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
},
{
"n": 14,
"number": "61.64700546019694678704954194815370276436090652467559867662835450221503556503971101218881803464484884",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
1,
-1
],
"series_terms": 250,
"series_max_radius": "4.4120391e-242",
"series_tail_sum_bound": "2.879094287744836807848937491803969668976889227188220629412314565630475226900001770626280795573402239611334613533335413816732445575557063044241939528608517978154814839262418402200879160397864904425754975207276131495513655198628087814283316723715093259478212520352333315185594044456510811040207773106733341946e-242",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
},
{
"n": 15,
"number": "66.08975506165933815220329865337526933758717426896201893636364660807851164323711726307384250831352504",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
-1,
1
],
"series_terms": 258,
"series_max_radius": "4.0590636e-241",
"series_tail_sum_bound": "2.636189021149181886987455716795487110389553998994707649417717421882781803178468269568177125901700630757441256111825997233918382468444439092896178149350434502344123248680384913520153035997054148472189300669297624396075660708427634401986285327741305798195886694585696363127258030390245867540888452431231491572e-241",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
},
{
"n": 16,
"number": "70.53252129372920528008427257072071235994960772087805897950871690958796923933694733756114001780402466",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
1,
-1
],
"series_terms": 267,
"series_max_radius": "3.2585001e-242",
"series_tail_sum_bound": "2.107481975182706053120593286971362191412587262019154272459109886227019844693887141022787708972366841131143863260246106711546967762373357732461678308764494256818211024319438248108838053755809583093853882855249822676901001427596430513842488755189229612812679071871584418142726820887899545987321975929846420110e-242",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
},
{
"n": 17,
"number": "74.97530122768217821092244160484786053428706847194925257437723195357853480497994320023581587269825798",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
-1,
1
],
"series_terms": 275,
"series_max_radius": "8.9767181e-242",
"series_tail_sum_bound": "5.782810000172405543502112470622840432900243079110749425832863402070052603160927358733883413750572236236737940724293138496080630900677112573133316332984061957409896255203891376114091077521622683621053107884449051578753478410068188790855137179594322246397976083768497071114368549890560811907753111109318744761e-242",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
},
{
"n": 18,
"number": "79.41809258433820737907118234860465621870214385178784929383453495995453347375099545678891193189561653",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
1,
-1
],
"series_terms": 283,
"series_max_radius": "1.4900100e-241",
"series_tail_sum_bound": "9.563649020727075012692138308765988919285626001749580058175536037374479991184697653107193521856237778549303936048086996900526627927593418211991044012801163681059594788725229640274620179876152094897212720310109112433909761805280794337604271453264279574819783361230708445105036662488403669138852225423952599117e-242",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
},
{
"n": 19,
"number": "83.86089356344997016860349727627448518248301508703980885098610085456021054542019708173955325378656914",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
-1,
1
],
"series_terms": 291,
"series_max_radius": "1.5949604e-241",
"series_tail_sum_bound": "1.020277039358301908375215632784185024008319694637178012176695817362088303148708959737155239453136457691116626581046452181758691627580986763326364725029216547936087018627765591454430949068343252604642555488125227869294274546898436825552706246170065961593506170695955708300908067950690082591141344076296423716e-241",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
},
{
"n": 20,
"number": "88.30370272418294129413487914267720979440661205409591801421930924671381962629154266132153386723621304",
"ode_identity_contains_zero": true,
"phase_derivative_negative": true,
"series_endpoint_signs": [
1,
-1
],
"series_terms": 299,
"series_max_radius": "1.1646167e-241",
"series_tail_sum_bound": "7.426620928089216969360882837413902731367673320857726090842169766206066494051250494814417227910664985966226630181165179452753024368750175719149527642064938050921486168128447807209063599356819938657739077084506110063894076943329156656098866755677277736138344584266108809525757866762669576603966099857648050024e-242",
"displaced_interval_same_sign": true,
"abramowitz_stegun_5dp": null
}
],
"all_20_written_intervals_certified": true,
"table": "T587",
"skill_manifest": "agents/runs/20261028T182642Z-build-skills/manifest.json",
"skill_sha256": "e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c",
"versions": {
"sage": "10.9",
"numberdb": "0.1.10"
},
"working_bits": 753,
"count_bits": 384,
"cells": 353,
"scan_endpoint": "177/2",
"max_disk_ratio_upper": "0.5120956820189511715763940739223220703716157222344701909074577591143680212964685649174931397990701131286900143911803",
"counted_brackets": [
[
"15/4",
"4"
],
[
"33/4",
"17/2"
],
[
"51/4",
"13"
],
[
"17",
"69/4"
],
[
"43/2",
"87/4"
],
[
"26",
"105/4"
],
[
"61/2",
"123/4"
],
[
"139/4",
"35"
],
[
"157/4",
"79/2"
],
[
"175/4",
"44"
],
[
"193/4",
"97/2"
],
[
"211/4",
"53"
],
[
"57",
"229/4"
],
[
"123/2",
"247/4"
],
[
"66",
"265/4"
],
[
"141/2",
"283/4"
],
[
"299/4",
"75"
],
[
"317/4",
"159/2"
],
[
"335/4",
"84"
],
[
"353/4",
"177/2"
]
],
"max_returned_radius": "1.0000000e-108",
"written_measurement": {
"entries": 20,
"longest": 101,
"longest_at": 1,
"block_kb": 2.6865234375
},
"seconds": 4.210236191749573,
"program_first_root_matches": true,
"AS_note": "Controls use one last-place unit, 1e-5. The printed second root 8.34422 is not the nearest-rounded five-decimal value of the independently certified 8.3442250629...; it differs by 0.5063 last-place units. No hundred-digit claim rests on this reference."
}