back to table · edit · history · where entries came from · files · download
190800 bytes, as of the version from 2026-10-27 01:08 (current). Recorded here, not run.
{
"tid": "T190",
"count": 72,
"all_passed": true,
"controls": [
"pi_interval",
"displaced_value_rejected",
"integral_t_equals_half"
],
"minimum_accuracy_bits": 660,
"records": [
{
"params": {
"nu": "0",
"x": "critical-1"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 696,
"argument": "[2.197141326031017035149033562698966273053018331500334192764665950435275022098636536525158765756194518799607871882913548431266445350 +/- 2.64e-131]",
"root_certificate": {
"lower": "2821597160603357578366640225043820834437994548079645379804084832851408848884747901180042970072624722824448935057428940951623509767656643521426814668210607303690476518474935187036927616126212297199254228980484186949619766775511770797267150371126079515677661026007193571843172472412545077260082087217831483008850256630991469184906715569261959882165801758088194614817014424248230339197759401426050093185254934834411197319/1284212866588958375791257295625031412487875928423626430541572486100764686107685747586344369208395617975337638880902885183842634826705030240021439152991181848133599529084092919480386659639727225896311829037056000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "2821597160603357578366640225043820834437994548079645379804084832851408848884747901180042970072624722824448935057428940951623509767656643521426814668210607303690476518474935187036927616126212297199254228980484189518045499953428522379781741621188904491429517873260054654988144673941917292631577259906569899800086207306269230990677083254531613292226281800966500597180710691447288507383598362199369372639706727458069271431/1284212866588958375791257295625031412487875928423626430541572486100764686107685747586344369208395617975337638880902885183842634826705030240021439152991181848133599529084092919480386659639727225896311829037056000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"2249/1024",
"1125/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "0",
"x": "critical-2"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 689,
"argument": "[5.429681040794135132772005190852584196583757476029145836503698537020178091745765031265337718255338710520653709127342240204657673721 +/- 3.82e-131]",
"root_certificate": {
"lower": "1743216563515488830424781146121189196151269672881958838878139151032318559752383908023086082908665775061052120668384933315835392739048117319171888843418552140393694458166055453548002316666346787967955166814201173287006672740584925873522302740467796820871307256975901242795239100719728203178653822794232583147099328029031627488046621506120501176368707848131670735983247569160130370135985137650087325175317377698165787611/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1743216563515488830424781146121189196151269672881958838878139151032318559752383908023086082908665775061052120668384933315835392739048117319171888843418552140393694458166055453548002316666346787967955166814201173929113106035064113769150950552983503064809271468789116513581482151102071257021527615966417187344908315697851067939489213427437914528883827858851247231574171635959894912182444877843417145038930325854080306139/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"5559/1024",
"695/128"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "0",
"x": "critical-3"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 685,
"argument": "[8.596005868331168926429606180163967851102921566974879929406738222195834040570007721510180695677527440690275319450632742936707473668 +/- 4.91e-130]",
"root_certificate": {
"lower": "2759775334346269684661187317298194372576979260277873752482976721190436283480448917430821198487268182002182474995609294754170132507542095284923764602501426559722893823942250959959684227161545253006764833189029943589936416828072278701577071228427345382383356625952473260796431297852455162241711880159961988799102735429379613990979922583541927265604493976896053685641070338983703734059137750292385079239519686352950943861/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "2759775334346269684661187317298194372576979260277873752482976721190436283480448917430821198487268182002182474995609294754170132507542095284923764602501426559722893823942250959959684227161545253006764833189029944232042850122551466597205719040943051626321320837765688531582674348234798216084585673332146592996911723098199054442422514504859340618119613987615630181231994405783468276105597490485714899103132634508865462389/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"4401/512",
"8803/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "0",
"x": "critical-4"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 679,
"argument": "[11.74915483083988124339942193992235071430116598327881055256304314603486276382203886431321315597433116674894848970430618154712859308 +/- 3.46e-129]",
"root_certificate": {
"lower": "3772103951327598056194269012961650675044482001728226017532539451376185498312168683690966874092853360053897206049548881799739209231229396382422704432941746754462573716500164461926359581501889806063251582442002372996898214769221369086357953639519522749202184140772564441931067946423444427235410573421232215545150414136466329949599403783306029374635191194687839206633136373083480753409656719823934452881129831921798600111/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3772103951327598056194269012961650675044482001728226017532539451376185498312168683690966874092853360053897206049548881799739209231229396382422704432941746754462573716500164461926359581501889806063251582442002373639004648063700556981986601452035228993140148352585779712717310996805787481078284366593416819742959401805285770401041995704623442727150311205407415702224060439883245295456116460017264272744742780077713118639/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"12031/1024",
"47/4"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "0",
"x": "critical-5"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 675,
"argument": "[14.89744212833672537884481915642987087980715063087504210888140840233261623783396895982028191036541922058077201669844057387657616754 +/- 4.94e-129]",
"root_certificate": {
"lower": "1195717928779651201948168123767146271653761494298550288934572229116131791690175762491891292812981668548041239628110095167848090331933167236284922083846438962219513722499799997640955852849118036705119383905433372213977793623528185236520743146686423658544945309960915431062043059288658896531988717900566059242697116169114244554247616252763501430454221539765889768356764219257424674328035633475563131108187698039348575809/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1195717928779651201948168123767146271653761494298550288934572229116131791690175762491891292812981668548041239628110095167848090331933167236284922083846438962219513722499799997640955852849118036705119383905433372374504401947147982210427905099815350219529436362914219248758603821884244659992707166193612210292149363086319104667108264233092854768583001542445783892254495235957365809839650568523895586074090935078327205441/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"7627/512",
"15255/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "0",
"x": "critical-6"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 670,
"argument": "[18.04340227672785556430455550788950890216308832483431968643648938810081344042962450081037190590247454203968725547042855147897532220 +/- 7.29e-130]",
"root_certificate": {
"lower": "2896446170101802174364939043173576063959470898466442710323526586588813566747828149041953628319293750426764050257021878940953930634286341366547229091194590472039626370835151143124471146408800545967796984610743237459310426641300863464157183540012133393798786198392694584275008964693469526633738537284411568429571092857684173870350916221064556523419976159047608559789232394227605171627065313223734364515648410147300667243/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "2896446170101802174364939043173576063959470898466442710323526586588813566747828149041953628319293750426764050257021878940953930634286341366547229091194590472039626370835151143124471146408800545967796984610743237780363643288540457411971507446269986515767768304299302219668130489884641053555175433870503870528475586692093894096072212181723263199677536164407396807584694427627487442650295183320399274447454884225257926507/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"4619/256",
"18477/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "1/2",
"x": "critical-1"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 693,
"argument": "[2.975086321688279377698573140759028816301866312181541496898731127443183745874509844026313367392537774932218684747824327258308516851 +/- 3.79e-130]",
"root_certificate": {
"lower": "3820644133524905226103296133190226867879931929486993706415706308917857450775965423372380272321892057120452899287088079436598352831545333802881010679737721868108830300265562167982351302783956416826809653161157922938189735473827431455175358161278976546018407224677066778300696806595194827034248306441542695696851453438343352483145232754361774443306397389940903384202921847316150410966392196254640797313401106404235416069/1284212866588958375791257295625031412487875928423626430541572486100764686107685747586344369208395617975337638880902885183842634826705030240021439152991181848133599529084092919480386659639727225896311829037056000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3820644133524905226103296133190226867879931929486993706415706308917857450775965423372380272321892057120452899287088079436598352831545333802881010679737721868108830300265562167982351302783956416826809653161157925506615468651744183037689949411341801521770264071929927861445669008124567042405743479130281112488087404113621114288915600439631427853366877432819209366566618114515208579152231157027960076767852899027893490181/1284212866588958375791257295625031412487875928423626430541572486100764686107685747586344369208395617975337638880902885183842634826705030240021439152991181848133599529084092919480386659639727225896311829037056000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"1523/512",
"3047/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "1/2",
"x": "critical-2"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 689,
"argument": "[6.202749816793042774075154551879217409846188666624236200750922993735415655367979908719597134479987526590283225691844879851597495456 +/- 3.68e-130]",
"root_certificate": {
"lower": "1991412780739482461823398488865218177004344932161952815838214236696628491648726400134258532963662346927366131361565216689797845708773646340815340778728875318952787391329577068409312624932574187701874559497192416271843179929741786308162308703674775251784536214552149501595426294569486052062534572627932077140388945891014813642200202124281031142513658968539947887040362240211139544987372366605078185250075907361251725111/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1991412780739482461823398488865218177004344932161952815838214236696628491648726400134258532963662346927366131361565216689797845708773646340815340778728875318952787391329577068409312624932574187701874559497192416913949613224220974203790956516190481495722500426365364772381669344951829105905408365800116681338197933559834254093642794045598444495028778979259524382631286307010904087033832106798408005113688855517166243639/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"6351/1024",
"397/64"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "1/2",
"x": "critical-3"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 685,
"argument": "[9.371475105855952708110690442709909615960146234769454405309152036276967932864197572378820464889964288843249162935289519786407673185 +/- 1.35e-130]",
"root_certificate": {
"lower": "3008742227464583791889103539498477379938824972437542911052037701965484733045735828416253596553872621952102284006099583790063921752863544322081179339182065131570713349723145171871983414555587818726584328759247657033465427035377258098129263161363657183181482353189718360726117282373506704215501138865345442649356113619466277162316807861213666566542528369148317013906691586282481172176372089935276506741555781018478287611/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3008742227464583791889103539498477379938824972437542911052037701965484733045735828416253596553872621952102284006099583790063921752863544322081179339182065131570713349723145171871983414555587818726584328759247657675571860329856445993757910973879363427119446565002933631512360332755849758058374932037530046847165101288285717613759399782531079919057648379867893509497615653082245714222831830128606326605168729174392806139/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"2399/256",
"9597/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "1/2",
"x": "critical-4"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 679,
"argument": "[12.52647633766919899749632841982585877587316380406295356256049682326406888958109933805037688918436820699917787038801217233548126517 +/- 2.47e-129]",
"root_certificate": {
"lower": "4021665521464229740680088816068490544121818504563748019592455185035866795223364558495157809339868173405313690438322118153587844686421381346138330119413349449247145363980530659640690407438790884617033517268570492173144201590189835490186921133433081843891059413169373106916558468371573062737703073893998346042228903328181437468679750040320686520821423967158741307549611537178251786572712737480279373277934641492111100111/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "4021665521464229740680088816068490544121818504563748019592455185035866795223364558495157809339868173405313690438322118153587844686421381346138330119413349449247145363980530659640690407438790884617033517268570492815250634884669023385815568945948788087829023624982588377702801518753916116580576867066182950240037890997000877920122341961638099873336543977878317803140535603978016328619172477673609193141547589648025618639/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"12827/1024",
"3207/256"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "1/2",
"x": "critical-5"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 675,
"argument": "[15.67607834519436765803116420880392239745736336325003764198375417132477472355647848088385813947614999571113592575148581377243154854 +/- 3.86e-129]",
"root_certificate": {
"lower": "5032855377138788464535021124588977694638073718090972218964648414513408278872257377900263336287626616830326431746667427003500365901150226998735715899707996555225788025718251036919616091639157861195081558672665937798811707012145465268885053677444481162985161901878110693351878010698510229350289015752905223057406823642814554104058008530337921244681415675508650580430723571727690075405658169230256079037698359143478287611/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "5032855377138788464535021124588977694638073718090972218964648414513408278872257377900263336287626616830326431746667427003500365901150226998735715899707996555225788025718251036919616091639157861195081558672665938440918140306624653164513701489960187406923126113691325964138121061080853283193162808925089827255215811311633994555500600451655334597196535686228227076021647638527454617452117909423585898901311307299392806139/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"4013/256",
"16053/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "1/2",
"x": "critical-6"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 671,
"argument": "[18.82299891800755401538464625346406409269306702306034606352691081288331017469042566358875508082334111191312233348918629894826315737 +/- 4.00e-129]",
"root_certificate": {
"lower": "1510796087393458926376077945474904000914671995858288706966553262813376330104220709502348496762212565066870011498882636980229593202647238935131005544275083888953287129356424636226352235170498561052863136284579452027086673034525580442390943489865735200819635136514014709522953154888492074859080928325310854640363497696486840273589601251349654589387097828634638572840550897088701220219405866696659117772482894572551700809/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1510796087393458926376077945474904000914671995858288706966553262813376330104220709502348496762212565066870011498882636980229593202647238935131005544275083888953287129356424636226352235170498561052863136284579452187613281358145377416298105442994661761804126189467318527219513917484077838319799376618357005689815744613691700386450249231679007927515877831314532696738281913788642355731020801744991572738386131611530330441/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"9637/512",
"19275/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "1",
"x": "critical-1"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 692,
"argument": "[3.683022856585177699898967242833996081455464500662397987123564408701748806150655026402709296476557508156934141639866036327486333869 +/- 2.35e-130]",
"root_certificate": {
"lower": "4729785340367905186723023645805463103709376150106424958961544858261087165099799257708382983839805737819135216732885164472717816757548617488629039977475055312583778731343592019573385863158662817560670950122423573679966009971932440679271718043821684048422516204089752645968106373307305922622710667354748939189417037385120009435298093522661053629380442647433830133452438982089941790697947847032959319811412695454528384819/1284212866588958375791257295625031412487875928423626430541572486100764686107685747586344369208395617975337638880902885183842634826705030240021439152991181848133599529084092919480386659639727225896311829037056000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "4729785340367905186723023645805463103709376150106424958961544858261087165099799257708382983839805737819135216732885164472717816757548617488629039977475055312583778731343592019573385863158662817560670950122423576248391743149849192261786309293884509024174373051342613729113078574836678137994205840043487355980652988060397771241068461207930707039440922690312136115816135249288999958883786807806278599265864488078186458931/1284212866588958375791257295625031412487875928423626430541572486100764686107685747586344369208395617975337638880902885183842634826705030240021439152991181848133599529084092919480386659639727225896311829037056000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"3771/1024",
"943/256"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "1",
"x": "critical-2"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 687,
"argument": "[6.941499953654175655751943717077043026911751384632681964399449055096754485005597344279578848449787351194801207427882010524739682165 +/- 1.76e-130]",
"root_certificate": {
"lower": "278573861059667207187496378533253458085591852081015990283224545478260633523059151097618515302322183148208528345283026754562897281271351208187115765445618137721041853745899618707423269540854549322361853356305463751100644460765854183239528853350063721011111327901819471756683373431598934075588891374379426728691441199413518364093243940116119684715548642713608630242610221379157897948745833039196320261460077123311983217/40131652080904949243476790488282231640246122763238325954424140190648896440865179612073261537762363061729301215028215161995082338334532195000669973530974432754174985283877903733762083113741475809259744657408000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "278573861059667207187496378533253458085591852081015990283224545478260633523059151097618515302322183148208528345283026754562897281271351208187115765445618137721041853745899618707423269540854549322361853356305463831363948622575752670193109829914527001503356854378471380604963754729391815805948115520902502253417564658015948420523567930280796353779938644053555692191475729729128465704553300563362547744411695642801298033/40131652080904949243476790488282231640246122763238325954424140190648896440865179612073261537762363061729301215028215161995082338334532195000669973530974432754174985283877903733762083113741475809259744657408000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"1777/256",
"7109/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "1",
"x": "critical-3"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 682,
"argument": "[10.12340465543661307978775272308125546768581817803118348545042985829656524379142568674396912972388303192115394453558943959942397701 +/- 2.84e-129]",
"root_certificate": {
"lower": "3250151628049564831967729235340412761042774437950798626967293167855586062151596428582480700480354902088266509425177660829471595785154911419861775652815130542744875020294936124478622119467979750527243783163706694958868624805129365468226682178116617126868905730067666926853063333298540063238251558590131206769514793134967105218575240922586949681673688326170353741408172843477888695384724619244471740250500292432052506361/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3250151628049564831967729235340412761042774437950798626967293167855586062151596428582480700480354902088266509425177660829471595785154911419861775652815130542744875020294936124478622119467979750527243783163706695600975058099608553363855329990632323370806869941880882197639306383680883117081125351762315810967323780803786545670017832843904363034188808336889930236999096910277653237431184359437801560114113240587967024889/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"5183/512",
"10367/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "1",
"x": "critical-4"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 677,
"argument": "[13.28575815678285443726207195650325163672497853878609635126630101069374137048420523979625250117780072519470229500751393450926573031 +/- 3.73e-129]",
"root_certificate": {
"lower": "1066358847958109086356963804190930060154127628345457521511749073785912074887947068081252935062633270738809681566390349294858551459703143901693661598883272148877784478351040605478346448483420900928583950771840524296453657623324758146754747779934064268030960015355329824875187797533580293152404320512956883273478632606097495502953668557770814491132157952239289225829720027198965303419328291379540800883673690470989200809/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1066358847958109086356963804190930060154127628345457521511749073785912074887947068081252935062633270738809681566390349294858551459703143901693661598883272148877784478351040605478346448483420900928583950771840524456980265946944555120661909733062990829015451068308633642571748560129166056613122768806003034322930879523302355615814316538100167829260937954919183349727451043898906438930943226427873255849576927509967830441/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"3401/256",
"13605/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "1",
"x": "critical-5"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 672,
"argument": "[16.44005800729328160696721307436945658339753305822696051923644924031333411025890810332812913805294867112803298349341514373966274834 +/- 1.14e-129]",
"root_certificate": {
"lower": "2639066752554357992114744424086874303258771010062911598990900789438860528153097708395904196988021549619753937579120363576637073191033427696649779495331857767393080216385500535010944730981308192906422342105366187673269302624017229070258628591906024738563429949529867278003501226747818731269124291303233797939959935506034025949185254541029290073779302010709239829770254904274591781038122458503944898626313731497398323493/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "2639066752554357992114744424086874303258771010062911598990900789438860528153097708395904196988021549619753937579120363576637073191033427696649779495331857767393080216385500535010944730981308192906422342105366187994322519271256823018072952498163877860532412055436474913396622751938990258190561187889326100038864429340443746174906550501687996750036862016069028077565716937674474052061352328600609808558120205575355582757/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"8417/512",
"16835/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "1",
"x": "critical-6"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 668,
"argument": "[19.59024175662949470914931472422189926101553087663054676411175398127877759352979948056193997739586397626448076557444823337468977433 +/- 1.04e-131]",
"root_certificate": {
"lower": "3144755065431484358363881534736487709899592406190892545012601956555142241458323595339756863247116202727290297693714818709202557743884220914048664158180675111070258578748214083723072403234373111502431721374530901550513638301323775263929421617224370305739279606932955294833736137064418140301596932939738555403914158743865315975487609102661076516785112080025106249957476785054680906522566881867983710622892901724449104743/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3144755065431484358363881534736487709899592406190892545012601956555142241458323595339756863247116202727290297693714818709202557743884220914048664158180675111070258578748214083723072403234373111502431721374530901871566854948563369211743745523482223427708261712839562930226857662255589667223033829525830857502818652578275036201208905063319783193042672085384894497752938818454563177545796751964648620554699375802406364007/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"5015/256",
"20061/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "3/2",
"x": "critical-1"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 691,
"argument": "[4.354435048325859298743872728677615737332184796220745421690983400945987829009649036740205447287193945057452058097429932538943516810 +/- 3.58e-130]",
"root_certificate": {
"lower": "699002689473247658187892757526790564461418805427143602634011305980473577121818218974548398267291406610851742881075031484921145173765151438222621454085260650331591160423212655276861028056507293431280272997301688123062354979596160357780663238353035025359255753885849013118402673936642994570895823192011894621436268600304155144169001549455934159143344301738492497040474645001739303723436587879855750730739161795249885993/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "699002689473247658187892757526790564461418805427143602634011305980473577121818218974548398267291406610851742881075031484921145173765151438222621454085260650331591160423212655276861028056507293431280272997301688444115571626835754305594987144610888147328237859792456648511524199127814521492332719778104196720340762434713875369890297510114640835400904307098280744835936678401621574746666457976520660662545635873207145257/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"2229/512",
"4459/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "3/2",
"x": "critical-2"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 687,
"argument": "[7.655545006452811526918833303507877811518410826564343302439876188111693642408621842171770876923266016208793221397216701397781811790 +/- 1.95e-130]",
"root_certificate": {
"lower": "1228918674754693867192448661936381217490008680857449772885659812798583051007903044160837725538608566548287290612445557155047820001610709420251295291390812417849126755052463726641624016711074858396920088362790037563924619671653450366308793983034169423982327046818101069959542818544833274010930836864193324788019123619518885793949403940345617288592328607211982700963482344586375935396798804923032975426421687430015510993/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1228918674754693867192448661936381217490008680857449772885659812798583051007903044160837725538608566548287290612445557155047820001610709420251295291390812417849126755052463726641624016711074858396920088362790037884977836318893044314123117889292022545951309152724708705352664343736004800932367733450285626886923617453928606019670699901004323964849888612571770948758944377986258206420028675019697885358228161507972770257/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"7839/1024",
"245/32"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "3/2",
"x": "critical-3"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 681,
"argument": "[10.85653060352759963851875774317299634152120395186943811844104994802264902401529748446400894684037034599633533172742915682518998196 +/- 4.84e-129]",
"root_certificate": {
"lower": "1742762035945866634108053909011264892331041648162128761157536271248118758654034360424598083896939857970280912416306406648055915633389032505613509858978911835388067413663148533512472000613869693926876280612308162682677230723629576597154998234665265807927978286363127027014496416432823298214052939425140617036377384744587296147697450196066832468833156486524536379941701417561220010904382145745781116789684817618003792243/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1742762035945866634108053909011264892331041648162128761157536271248118758654034360424598083896939857970280912416306406648055915633389032505613509858978911835388067413663148533512472000613869693926876280612308163003730447370869170544969322140923118929896960392269734662407617941623994825135489836011232919135281878578997016373418746156725539145090716491884324627737163450961102281927612015842446026721491291695961051507/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"11117/1024",
"5559/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "3/2",
"x": "critical-4"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 677,
"argument": "[14.02984495025212489019997413851294498748952432840329267920786979969729835888431052570102270029374274769658323161303071092692036107 +/- 2.71e-129]",
"root_certificate": {
"lower": "4504326850340475855584327147637454992252161932956817161732487474456655158822373417421410933911001758434773821455035435482774430237709734656506166162182003616710997374717292512391998355522764162141967525167209389859363273164563378337873879331548720413882305250267892444795884209784361931218549162149111956959410869177519904533535846549879864335165840683331506515903936592529910752280419009976859286700399965893966568861/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "4504326850340475855584327147637454992252161932956817161732487474456655158822373417421410933911001758434773821455035435482774430237709734656506166162182003616710997374717292512391998355522764162141967525167209390501469706459042566233502527144064426657820269462081107715582127260166704985061422955321296561157219856846339344984978438471197277687680960694051083011494860659329675294326878750170189106564012914049881087389/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"7183/512",
"14367/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "3/2",
"x": "critical-5"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 673,
"argument": "[17.19128477071101130210242231625198519522876335650880281071622586359190494293522118368947912196920144269562131341014077214529395210 +/- 4.78e-129]",
"root_certificate": {
"lower": "2759658636967736479794284736922722506129076144764467503382933238794197007832704249336929465043345156801505858011264161382148919038155879268954261471900878790342622381220387666842201707577794635569403740287311824993763410955613918026672938320641285440374061411646371818742044613928358551991622684645998595486572903485614611148335299444130301995953647522290811725268518240034864738391345436376009701421962306326499885993/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "2759658636967736479794284736922722506129076144764467503382933238794197007832704249336929465043345156801505858011264161382148919038155879268954261471900878790342622381220387666842201707577794635569403740287311825314816627602853511974487262226899138562343043517552979454135166139119530078913059581232090897585477397320024331374056595404789008672211207527650599973063980273434747009414575306472674611353768780404457145257/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"17603/1024",
"4401/256"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "3/2",
"x": "critical-6"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 669,
"argument": "[20.34649596740828622106693100235947182635601903829644512404821152804662272658000654773945018915006312358829143503929670180345189181 +/- 3.22e-129]",
"root_certificate": {
"lower": "1633076994459129816132051476829741772207058612789328492261663677325058119466337649899042901255546621801345090494246084061553337420254275533750482085840076363419750302067108140090035838936891498638990787934536556583160924773795583837840790611477873765659413130952117794077916559283376432789200094629854059172828113535297967504863684394867232698992922134869526237970916815031269838423519173243446616291307471904094669559/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1633076994459129816132051476829741772207058612789328492261663677325058119466337649899042901255546621801345090494246084061553337420254275533750482085840076363419750302067108140090035838936891498638990787934536556743687533097415380811747952564606800326643904183905421611774477321878962196249918542922900210222280360452502827617724332375196586037121702137549420361868647831731210973935134108291779071257210708943073299191/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"10417/512",
"20835/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "2",
"x": "critical-1"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 690,
"argument": "[5.002582931446063945200175746152009228334609977036730649648820748881575016103033479448095344055901194929302748834236519596970966665 +/- 1.43e-130]",
"root_certificate": {
"lower": "803047670842668052693790637682087408918966172479815879153885986973351371179706479606930180404397096337353750392268934496331099870044604594041911756957461570506817164633191149357765308592167183613589201943804974691678237864713304866045399235541174329067161024613279274164884780619994404247462412792305002615043236303856809108463075120972180002293102408109998234770900030810695688171446245597049227586494014090171760993/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "803047670842668052693790637682087408918966172479815879153885986973351371179706479606930180404397096337353750392268934496331099870044604594041911756957461570506817164633191149357765308592167183613589201943804975012731454511952898813859723141799027451036143130519886909558006305811165931168899309378397304713947730138266529334184371081630886678550662413469786482566362064210577959194676115693714137518300488168129020257/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"2561/512",
"5123/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "2",
"x": "critical-2"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 685,
"argument": "[8.350724701413079526349713733602333381416649214202504504302040102610459741893610230754527285466116291639275494544272616377000090628 +/- 4.81e-130]",
"root_certificate": {
"lower": "2681027026724228591310916939360742844338782040806063403429298560334026359229147496808856986834838087757784044000222397864524845484417914747112749038330891587610330176141039055619142762657184495460854893745784251222939222579661723038409774775082887660589517189332649595857128141260234218188685896483600147858583528390048151205241855366790233931163546621180416527231730985984646962649723681962305762146624178540450943861/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "2681027026724228591310916939360742844338782040806063403429298560334026359229147496808856986834838087757784044000222397864524845484417914747112749038330891587610330176141039055619142762657184495460854893745784251865045655874140910934038422587598593904527481401145864866643371191642577272031559689655784752056392516058867591656684447288107647283678666631899993022822655052784411504696183422155635582010237126696365462389/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"8551/1024",
"1069/128"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "2",
"x": "critical-3"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 680,
"argument": "[11.57419546521764654624264501799547713072422912641389483699683626114930583999313122869824111439073854098114830451893429160320527809 +/- 4.52e-130]",
"root_certificate": {
"lower": "232245792763251196050162334750369393110423163865352283737673943157318833369241290069025558746520307683124251433452661560338990736278723414221777270709814534782371072155643716646773197073365890814336495636760561895240994195797479922207576795030158684005355514610319274718253099516372988880648367687705732533081170418568903259855613611290067114806566897881470693360443344197208327140532300542246897430917387881113999421/20065826040452474621738395244141115820123061381619162977212070095324448220432589806036630768881181530864650607514107580997541169167266097500334986765487216377087492641938951866881041556870737904629872328704000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "232245792763251196050162334750369393110423163865352283737673943157318833369241290069025558746520307683124251433452661560338990736278723414221777270709814534782371072155643716646773197073365890814336495636760561935372646276702429165684367283312390324251478277848645229142393290165269429745827979760967270295444232147870118288070775606372405449338761898551444224334876098372193611018436034304330011172393197140858656829/20065826040452474621738395244141115820123061381619162977212070095324448220432589806036630768881181530864650607514107580997541169167266097500334986765487216377087492641938951866881041556870737904629872328704000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"11851/1024",
"2963/256"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "2",
"x": "critical-4"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 675,
"argument": "[14.76090930620767553660808951449355247481021721973774960198661093429766867816433066279001210240224532894446659034374060984148384669 +/- 2.43e-129]",
"root_certificate": {
"lower": "2369518706698073970281461216169563877638336249720810230249842744702018737202001853352760452989809286732814170917878873234313037231278645540059013751949478496014585355242868148767514425854762679655485652210739717832146999488447611510247802559699643364146570743909215430697079840743057234989991101569937867052943818322306889913235915062368625154986861193719483683684892550795422380510640432894884242346988246267906135993/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "2369518706698073970281461216169563877638336249720810230249842744702018737202001853352760452989809286732814170917878873234313037231278645540059013751949478496014585355242868148767514425854762679655485652210739718153200216135687205458062126465957496486115552849815823066090201365934228761911427998156030169151848312156716610138957211023027331831244421199079271931480354584195304651533870302991549152278794720345863395257/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"15115/1024",
"3779/256"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "2",
"x": "critical-5"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 670,
"argument": "[17.93128593946685547124074881113936864170295166046754184810710842805554555942725325698638628669135781331665879276290825822121487168 +/- 7.08e-130]",
"root_certificate": {
"lower": "359806064342953344054482359234107605674727535973513318375322391269359422951548140205453543691414500474978015681307152699468291367356058539653849650277154587523264872364129868111568254909058962164209637563667190986972432973680561384515821257970271594879026168776799925124321830693983360265079485596043327358973439871401117181617316254855905760847347186908223660684993055387971403758636621911420601146122580447031968171/20065826040452474621738395244141115820123061381619162977212070095324448220432589806036630768881181530864650607514107580997541169167266097500334986765487216377087492641938951866881041556870737904629872328704000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "359806064342953344054482359234107605674727535973513318375322391269359422951548140205453543691414500474978015681307152699468291367356058539653849650277154587523264872364129868111568254909058962164209637563667191027104085054585510627992611746252503235125148932015125879548462021342879801130259097669304865121336501600702332209832478249938244095379542187578197191659425809562956687636540355673503714887598389706776625579/20065826040452474621738395244141115820123061381619162977212070095324448220432589806036630768881181530864650607514107580997541169167266097500334986765487216377087492641938951866881041556870737904629872328704000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"18361/1024",
"9181/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "2",
"x": "critical-6"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 666,
"argument": "[21.09289450441273945818897500084238969128769292067048792714147270708252948821035416631993817787361088288915594125250044168785738975 +/- 3.03e-129]",
"root_certificate": {
"lower": "1692985407260648167160463423655826766995400315105676511596483254685202505679100526877086108695442896926108624761198667251879132518203734614478427225868628817543653232480128597087505441809414240423052606997672054013542366015532302733668339969933033910586488671472278822188326047454016802753813080657977275442176820829831208813512415999241884505046645692126696188931232636273566701570722285264535216449998878154094669559/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1692985407260648167160463423655826766995400315105676511596483254685202505679100526877086108695442896926108624761198667251879132518203734614478427225868628817543653232480128597087505441809414240423052606997672054174068974339152099707575501923061960471570979724425582639884886810049602566214531528951023426491629067747036068926373063979571237843175425694806590312828963652973507837082337220312867671415902115193073299191/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"21599/1024",
"675/32"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "5/2",
"x": "critical-1"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 690,
"argument": "[5.634296563929558627196554110287561922489832931609550111012878305608041347934974943266575074628358045030036970264750099517034406909 +/- 4.01e-130]",
"root_certificate": {
"lower": "3617818070788148429882663512380846382327804130303431859171253684882975689033727955608045811546223235331688102262739935958782393656644117451363958065884257493358990547986472264047101854254134934492597253435374772040072642653470346639899422625310771900558651314872977985698584359821934775573291048688012989062463835501654960087957253441976873123280703412264418395868915954279869043974369743038534467654351891779388215847/642106433294479187895628647812515706243937964211813215270786243050382343053842873793172184604197808987668819440451442591921317413352515120010719576495590924066799764542046459740193329819863612948155914518528000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3617818070788148429882663512380846382327804130303431859171253684882975689033727955608045811546223235331688102262739935958782393656644117451363958065884257493358990547986472264047101854254134934492597253435374773324285509242428722431156718250342184388434579738499408527271070460586620883259038635032382197458081810839293840990842437284611699828310943433703571387050764087879398128067289223425194107381577788091217252903/642106433294479187895628647812515706243937964211813215270786243050382343053842873793172184604197808987668819440451442591921317413352515120010719576495590924066799764542046459740193329819863612948155914518528000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"5769/1024",
"2885/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "5/2",
"x": "critical-2"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 685,
"argument": "[9.030901729624807826247317469529744373187921085775453522067752128298313051511903516170062482343721594688756080823614755883550790422 +/- 2.20e-130]",
"root_certificate": {
"lower": "1449700024760582097231822581128613401037532726000159675079787530369090748155300118047736206341174581169047874278226272813058993916223833895655923997297095934320454153397567958138202734073351843855157330827568063695766023598093377262595043778057117380136613654803252629489325628042661006974694495839772335402846333785527230488022803892864264432790107438630452483441980312041492223545862823776129034018621966665855354743/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1449700024760582097231822581128613401037532726000159675079787530369090748155300118047736206341174581169047874278226272813058993916223833895655923997297095934320454153397567958138202734073351843855157330827568064016819240245332971210409367684314970502105595760709860264882447153233832533896131392425864637501750827619936950713744099853522971109047667443990240731237442345441374494569092693872793943950428440743812614007/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"9247/1024",
"289/32"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "5/2",
"x": "critical-3"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 680,
"argument": "[12.27886255165681201266033413208763844384319507732225495116623428012470952166556095170726441668273751127015272033799283565208379895 +/- 1.81e-130]",
"root_certificate": {
"lower": "1971084159489375818523705639614780024049835482317209424127333717524773766983454829316616287568782364112908611591071553087855410655390523379663571751370548171426664026610750829943977562415748620439910488069705420348114491048887476226229736403771287674219357860540294385171840235381902741076369771500718380827338078041769542012965812539166195752032925908898695035460360147604541536198102387934791722005711123770347542243/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1971084159489375818523705639614780024049835482317209424127333717524773766983454829316616287568782364112908611591071553087855410655390523379663571751370548171426664026610750829943977562415748620439910488069705420669167707696127070174044060310029140796188339966446902020564961760573074267997806668086810682926242571876179262238687108499824902428290485914258483283255822181004423807221332258031456631937517597848304801507/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"12573/1024",
"6287/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "5/2",
"x": "critical-4"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 675,
"argument": "[15.48065496517280802940710894531380245713642519462520600937733943876487483070815869637903024239443334378869456710313031522197699977 +/- 1.91e-129]",
"root_certificate": {
"lower": "4970114072374790847296438863217272387184837782653597707364631590199536993120561626102256214996756542736570448582742520483057571916752926739489099032727195932173030943376406929776214138493257949885363585782623004344040488942924601141016647386409215765472492354180877612125916073580134424332289424930081989346454635189434726258846678170563862686686314219195044878037314207242496498140159892201146193121584505688888443861/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "4970114072374790847296438863217272387184837782653597707364631590199536993120561626102256214996756542736570448582742520483057571916752926739489099032727195932173030943376406929776214138493257949885363585782623004986146922237403789036645295198924922009410456565994092882912159123962477478175163218102266593544263622858254166710289270091881276039201434229914621373628238274042261040186619632394476012985197453844802962389/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"3963/256",
"15853/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "5/2",
"x": "critical-5"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 671,
"argument": "[18.66130899916646676183165197698405525631778011282981302199408189958414613428703029744072956649340611733806857440203866136073170718 +/- 6.18e-130]",
"root_certificate": {
"lower": "2995636640515236766199177588115082684530542096947891461281270647220210098166312540923711193346926347011081802750544470024827590715106232293979994768392341672698634439852107614081761972729517715389097215002807829132986002673168993012504199534433277110979982566415051988635294753202091971139287094681957297929005852128274425156071220014455604756136272898782694308446791424327423869294822618904159270829067752188316292243/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "2995636640515236766199177588115082684530542096947891461281270647220210098166312540923711193346926347011081802750544470024827590715106232293979994768392341672698634439852107614081761972729517715389097215002807829454039219320408586960318523440691130232948964672321659624028416278393263498060723991268049600027910345962684145381792515975114311432393832904142482556242253457727306140318052489000824180760874226266273551507/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"19109/1024",
"9555/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "5/2",
"x": "critical-6"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 667,
"argument": "[21.83038985874104266834430360820871579524882080789103962351408684216851586260440033063280403264247874212858826351291576798429461478 +/- 4.20e-129]",
"root_certificate": {
"lower": "3504358442406045063879598111161641245874601403956153364122188576508311811214175066152850148355645879128527942458026655250493467203563293730536306545909216448072776369836038724315126309613057632606512247667829942815248719078972553812948212592607290305303330372226025016809500675778111964379464926800607002510603861150344886263043203037755283949263953337825045749308283457003102650911746248275899660444365069693199104743/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3504358442406045063879598111161641245874601403956153364122188576508311811214175066152850148355645879128527942458026655250493467203563293730536306545909216448072776369836038724315126309613057632606512247667829943136301935726212147760762536498865143427272312478132632652202622200969283491300901823386699304609508354984754606488764498998413990625521513343184833997103745490402984921934976118372564570376171543771156364007/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"11177/512",
"22355/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "3",
"x": "critical-1"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 689,
"argument": "[6.253633208459813609636417532495818524244851963678262042083142850523735154576955563983873690105343816144481939423714708320126433850 +/- 1.15e-131]",
"root_certificate": {
"lower": "2007749057308020584676437488517563120306610305473592766098218453073355133299218490890641206676833647633688051080184185440572450200725368825234391967988013814980939242516864233555936917623229194342619377739440945508345626490666825402754151038601302321429298205017155638625729083782948920246975348802677081533109573178153936840461889364159401582532758394136204221086753349625386112409085874033727066864284128796798600111/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "2007749057308020584676437488517563120306610305473592766098218453073355133299218490890641206676833647633688051080184185440572450200725368825234391967988013814980939242516864233555936917623229194342619377739440946150452059785146013298382798851117008565367262416830370909411972134165291974089849141974861685730918560846973377291904481285476814935047878404855780716677677416425150654455545614227056886727897076952713118639/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"6403/1024",
"1601/256"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "3",
"x": "critical-2"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 684,
"argument": "[9.698787984148771075001507771777920786883624420373736394728287422026779721752159564394306110114844739014729116968452263310277263566 +/- 5.57e-131]",
"root_certificate": {
"lower": "3113827079890559572723402492918548835148467492179841179798411271356592902319891933580270925535443239628682628973818046731142868474727835008502358835873684087568322000098161891973142594070262817452249245713606967277051664829073113966208143406087585486108756552657597939543670030415026533938719137547648790367604372117638730887682222313659818161852338565448881371347638711979928600648147855436937732894929499280197037611/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3113827079890559572723402492918548835148467492179841179798411271356592902319891933580270925535443239628682628973818046731142868474727835008502358835873684087568322000098161891973142594070262817452249245713606967919158098123552301861836791218603291730046720764470813210329913080797369587781592930719833394565413359786458171339124814234977231514367458576168457866938562778779693142694607595630267552758542447436111556139/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"9931/1024",
"2483/256"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "3",
"x": "critical-3"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 678,
"argument": "[12.97240905229221626523651157223084737529180653310049403619909162461989847331146000206877700177558826274306517557875457411062261927 +/- 1.04e-129]",
"root_certificate": {
"lower": "4164833653902184971252255928799355778148150002560807117599029254066795316571731616212658306660112734391127649474160977459295771876358732112579379469520437718180193555736385794129150868856439525148722970319557043215862876766921912049433658814867503534911677882932175360411800067787452771382960127010085409682812089735443350659583669422329854521329627447557991898533475964074203766096392846221525304292353243481857193861/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "4164833653902184971252255928799355778148150002560807117599029254066795316571731616212658306660112734391127649474160977459295771876358732112579379469520437718180193555736385794129150868856439525148722970319557043857969310061401099945062306627383209778849642094745390631198043118169795825225833920182270013880621077404262791111026261343647267873844747458277568394124400030873968308142852586414855124155966191637771712389/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"13283/1024",
"3321/256"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "3",
"x": "critical-4"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 673,
"argument": "[16.19044719506921028507359067130645308657134408037790395026085328402524257676964889347458827274259049301689353819734294444513390553 +/- 3.24e-129]",
"root_certificate": {
"lower": "649749393866780971621659764420934110840191414419461623715012525951824400310804830677977672479680656668058854107207235061170516962062375777665903823965999965942880740983152961171948423144608501734714317239502714583577944902660104454176559928120457719896949881698538060500086353719112409286891782802733412565330089436909448677596722723180222944135193362185803134158169614914654502481321137386315847199064027623800264467/40131652080904949243476790488282231640246122763238325954424140190648896440865179612073261537762363061729301215028215161995082338334532195000669973530974432754174985283877903733762083113741475809259744657408000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "649749393866780971621659764420934110840191414419461623715012525951824400310804830677977672479680656668058854107207235061170516962062375777665903823965999965942880740983152961171948423144608501734714317239502714663841249064470002941130140904684921000389195408175189969348366735016905291017251006949256488090056212895511878734027046713344899613199583363525750196107035123264625070237128604910482074682015646143289579283/40131652080904949243476790488282231640246122763238325954424140190648896440865179612073261537762363061729301215028215161995082338334532195000669973530974432754174985283877903733762083113741475809259744657408000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"16579/1024",
"4145/256"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "3",
"x": "critical-5"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 668,
"argument": "[19.38238844973612964351172520893375869864033419125667006672860971215023240314535721159467350239457138767119278112099179293711316828 +/- 1.08e-129]",
"root_certificate": {
"lower": "3111389079047044001694195912036665133831895346103832496250333926797207847343180043928300337018296793287464839633692017969894007269969601859950911663895927577867163371802475405581658348769407154036645247609363050553288920526837814079368004911928820908682327752448728424460654376253950519933209815929615263287967666708353771023998044960253660642869618456000111217665008952081297882535853712361581955707178637808433479743/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3111389079047044001694195912036665133831895346103832496250333926797207847343180043928300337018296793287464839633692017969894007269969601859950911663895927577867163371802475405581658348769407154036645247609363050874342137174077408027182328818186674030651309858355336059853775901445122046854646712515707565386872160542763491249719340920912367319127178461359899465460470985481180153559083582458246865638985111886390739007/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"19847/1024",
"2481/128"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "3",
"x": "critical-6"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 664,
"argument": "[22.55979185776426097758612857841211322766884947527086383111922359594799807767490906416242420291819931945069453332853325974545623074 +/- 2.93e-129]",
"root_certificate": {
"lower": "3621446871413710539141939264650039478299189537316034015601182688849577532657935014993225855664885096520960938073878131004570210030566634937852054120798684997932421874749936984835208919738544286651652241434813702611377217150176738929237304985555392236213931359072114510937381828935468191122327493433229846202082253700611445640320617780258066552578145973430386382059715493596998039754691485959934170028672740286460823493/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3621446871413710539141939264650039478299189537316034015601182688849577532657935014993225855664885096520960938073878131004570210030566634937852054120798684997932421874749936984835208919738544286651652241434813702932430433797416332877051628891813245358182913464978722146330503354126639718043764390019322148300986747535021165866041913740916773228835705978790174629855177526996880310777921356056599079960479214364418082757/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"23101/1024",
"11551/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "7/2",
"x": "critical-1"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 689,
"argument": "[6.863232023466264874199857909312959367319422650559341336190092007357779274430477871840355038469970846973079078084923549879034742122 +/- 1.15e-130]",
"root_certificate": {
"lower": "4406925435460374626815282310137460126759358818893719421796790690701981889047747031316870342193170806744584226350747151227427948851211163251263070742532676093081611493938595517041523614790732088045250210395752784435617471716478352405221815382635919792785818255987373878183435508530544941023538539149620879781940446942453293695966450933221588473786166330159905796264755278528377208757381152365252889307264985346282747097/642106433294479187895628647812515706243937964211813215270786243050382343053842873793172184604197808987668819440451442591921317413352515120010719576495590924066799764542046459740193329819863612948155914518528000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "4406925435460374626815282310137460126759358818893719421796790690701981889047747031316870342193170806744584226350747151227427948851211163251263070742532676093081611493938595517041523614790732088045250210395752785719830338305436728196479111007667332280661746679613804419755921609295231048709286125493990088177558422280092174598851634775856415178816406351599058787446603412127906292850300632751912529034490881658111784153/642106433294479187895628647812515706243937964211813215270786243050382343053842873793172184604197808987668819440451442591921317413352515120010719576495590924066799764542046459740193329819863612948155914518528000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"7027/1024",
"1757/256"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "7/2",
"x": "critical-2"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 684,
"argument": "[10.35637345659090159927435138246188760019984846757682567702580455912213574754683994926374539696120132923482681080320435596654434577 +/- 3.35e-129]",
"root_certificate": {
"lower": "207809188189912519100149450134389709860847201245449887571128348596889045739636416608511624487919792068007460928374636609931749182999279113272685794849119881923746669151504266504980378633519003188096474285666635837477717135410549484564067604567468435053335566972082212621103881604478059272559892625863095249291779954603258191412921587950421191052653509827725015040919187019654283133514947418290770338675146975352280671/20065826040452474621738395244141115820123061381619162977212070095324448220432589806036630768881181530864650607514107580997541169167266097500334986765487216377087492641938951866881041556870737904629872328704000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "207809188189912519100149450134389709860847201245449887571128348596889045739636416608511624487919792068007460928374636609931749182999279113272685794849119881923746669151504266504980378633519003188096474285666635877609369216315498728040858092849700075299458330210408167045244072253374500137739504699124633011654841683904473219628083583032759525584848510497698546015351941194639567011418681180373884080150956235096938079/20065826040452474621738395244141115820123061381619162977212070095324448220432589806036630768881181530864650607514107580997541169167266097500334986765487216377087492641938951866881041556870737904629872328704000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"2651/256",
"10605/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "7/2",
"x": "critical-3"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 678,
"argument": "[13.65630424191650206879262666089969197514459700859023960895638391256580734936498428723704763644813239488015057775190816550136482077 +/- 4.79e-129]",
"root_certificate": {
"lower": "2192200202190317902511188568834217919075850373145708869176226460406658666712888658459804841673906829292674455352026986629401259381608433991656500641276013077403175943580611045308307708014095917731482385016807736160865486869611040583103306910562185236325933206413192963856649051520394912453547128914480593540907416865508343591133962084197814301269240608800691610793386593980934831476997256195768813273416087454429573493/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "2192200202190317902511188568834217919075850373145708869176226460406658666712888658459804841673906829292674455352026986629401259381608433991656500641276013077403175943580611045308307708014095917731482385016807736481918703516850634530917630816820038358294915312319800599249770576711566439374984025500572895639811910699918063816855258044856520977526800614160479858588848627380817102500227126292433723205222561532386832757/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"437/32",
"13985/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "7/2",
"x": "critical-4"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 674,
"argument": "[16.89139992976102584285082447217135283521197169688279259787881424471828331161700383567472768380635350734871984693523006556347563746 +/- 3.94e-129]",
"root_certificate": {
"lower": "2711519140562367145027516781544011509747555658293175885730137530048514093427481840401640567196453199378898620745302236332907395606704540777313972851290194923490448218815928849218601199105541115859530463938552793378972104763511956150042654222341849691060434776033940385558083287042617488930338822649600208362366762885958307936970876044505722874320267512729060171597403553599644640364968036429213924935565516775718635993/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "2711519140562367145027516781544011509747555658293175885730137530048514093427481840401640567196453199378898620745302236332907395606704540777313972851290194923490448218815928849218601199105541115859530463938552793700025321410751550097856978128599702813029416881940548020951204812233789015851775719235692510461271256720368028162692172005164429550577827518088848419392865586999526911388197906525878834867371990853675895257/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"1081/64",
"17297/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "7/2",
"x": "critical-5"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 669,
"argument": "[20.09539340703326363584803711496466525556830192880906192436364841411374029804068774836543565545467458209679568957594282444745270946 +/- 3.26e-129]",
"root_certificate": {
"lower": "3225845346559880289127329905946127778496725250688869086851707748180719912382389459280399624406785505274261406580386391630791851027444036575888756118132033224384993218426876148066697201873691414919972587852696083501591397487832622132806655031804852808758869106516360040925978738009438077932750941652551968201081702141465199234266868014895321053718481892744486738147954513518885940975760714045914454987750575369468635993/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3225845346559880289127329905946127778496725250688869086851707748180719912382389459280399624406785505274261406580386391630791851027444036575888756118132033224384993218426876148066697201873691414919972587852696083822644614135072216080620978938062705930727851212422967676319100263200609604854187838238644270299986195975874919459988163975554027729976041898104274985943416546918768211998990584142579364919557049447425895257/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"20577/1024",
"10289/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "7/2",
"x": "critical-6"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 665,
"argument": "[23.28179585235706518347068794918467671468973971116228394003535392741449747636326418421593019540744221897371189787274742140932863333 +/- 3.84e-130]",
"root_certificate": {
"lower": "3737347723861798525665194481483776724975483464143682839834589734565613457372914523974275322891380375166265745260689856099427753768461077566058252259818944463748652393154206579383817276145171449856934931068245857329623007421231571154679212641214916398034893200969120908321346618371940328183893697861715043450823789417784378198534774994780374274498051664141154358739043809393821870917723056627888098961220309561363167243/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3737347723861798525665194481483776724975483464143682839834589734565613457372914523974275322891380375166265745260689856099427753768461077566058252259818944463748652393154206579383817276145171449856934931068245857650676224068471165102493536547472769520003875306875728543714468143563111855105330594447807345549728283252194098424256070955439080950755611669500942606534505842793704141940952926724553008893026783639320426507/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"745/32",
"23841/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "4",
"x": "critical-1"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 688,
"argument": "[7.464921736757132886707953099279417679362546548449115853171722865717794143118661072312396065621214572421895651463496864102381169886 +/- 4.21e-130]",
"root_certificate": {
"lower": "4793274271211551675935703147356370143440949789964692941380350832082706414937208267569244640224624137145210931874431147851989923803586606995908808506961481464696796772224344913890895764565828417669351458532293615435055678943360515935146795934719713339233337656564679160492302052979720299906523999409313604581391768497956813347335679995685967947372626973405476898687437114687501580434212951869978384660606087946380403347/642106433294479187895628647812515706243937964211813215270786243050382343053842873793172184604197808987668819440451442591921317413352515120010719576495590924066799764542046459740193329819863612948155914518528000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "4793274271211551675935703147356370143440949789964692941380350832082706414937208267569244640224624137145210931874431147851989923803586606995908808506961481464696796772224344913890895764565828417669351458532293616719268545532318891726404091559751125827109266080191109702064788153744406407592271585753682812977009743835595694250220863838320794652402866994844629889869285248287030664527132432256638024387831984258209440403/642106433294479187895628647812515706243937964211813215270786243050382343053842873793172184604197808987668819440451442591921317413352515120010719576495590924066799764542046459740193329819863612948155914518528000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"1911/256",
"7645/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "4",
"x": "critical-2"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 681,
"argument": "[11.00516914980918855142306083142632538212554132052577468292332862870780714296465345000463785378303227518148092194758040151652962162 +/- 4.40e-129]",
"root_certificate": {
"lower": "3533244955293206982634267239376779687337049350424746885232652722511269924030614435421775602294844299628187788776568187931153177660286749583524209995469088834879055850219578738008452796014197801437987804502098468056383337207013206566883955457570335620608364870319195344803967388488375834619302577917858275000130864269641142414032836540824909377439925972812356166901331691430395308039923711176917039130838961255294693861/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3533244955293206982634267239376779687337049350424746885232652722511269924030614435421775602294844299628187788776568187931153177660286749583524209995469088834879055850219578738008452796014197801437987804502098468698489770501492394462512603270086041864546329082132410615590210438870718888462176371090042879197939851938460582865475428462142322729955045983531932662492255758230159850086383451370246858994451909411209212389/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"11269/1024",
"5635/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "4",
"x": "critical-3"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 676,
"argument": "[14.33172351923309980888470586795660779323292456522073084811026771660411052943682277544518424952139732880619195688255177366513714325 +/- 3.08e-129]",
"root_certificate": {
"lower": "1150311483987170864613048055586447513249086471148087483921059883235048571146417050152077309353342776224286041177073473071941159369506395890744439690512652407056039159126908941959947269848687000514281129892084176733808173593606405847053990013700534682157508671408960753032987682194801518510022154464597923677637829269300226965192044139908159428846779638760812099645709541393755777952087397220791658221982978495891544559/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1150311483987170864613048055586447513249086471148087483921059883235048571146417050152077309353342776224286041177073473071941159369506395890744439690512652407056039159126908941959947269848687000514281129892084176894334781917226202820961151966829461243141999724362264570729548444790387281970740602757644074727090076186505087078052692120237512766975559641440706223543440558093696913463702332269124113187886215534870174191/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"14675/1024",
"3669/256"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "4",
"x": "critical-4"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 671,
"argument": "[17.58443601710271999461955301975322727735384427882700447182539908248537307087668414759700197392568489523317855494124336041285015558 +/- 8.73e-130]",
"root_certificate": {
"lower": "705692468277300310516374507100983879562426101473521313089819155228854975928419808806353757815170006926561062253982254005943068400360031338649264139888745322871988484835684611524124391927802814536387666300121925850368396545007210903762676187603614417674698645788673511268774948264272465606854764493865882676352860729234751520726854400360366305906873986408590510742162868400956449467502259087836016352873575048116670717/40131652080904949243476790488282231640246122763238325954424140190648896440865179612073261537762363061729301215028215161995082338334532195000669973530974432754174985283877903733762083113741475809259744657408000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "705692468277300310516374507100983879562426101473521313089819155228854975928419808806353757815170006926561062253982254005943068400360031338649264139888745322871988484835684611524124391927802814536387666300121925930631700706817109390716257164168077698166944172265325420117055329562065347337213988640388958201078984187837181577157178390525042974971263987748537572691028376750927017223309726612002243835825193567605985533/40131652080904949243476790488282231640246122763238325954424140190648896440865179612073261537762363061729301215028215161995082338334532195000669973530974432754174985283877903733762083113741475809259744657408000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"9003/512",
"18007/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "4",
"x": "critical-5"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 667,
"argument": "[20.80106233841112811220231813727334440933100986780034756064876244251918596099464323758692579615790670898329960343312050164994588978 +/- 4.65e-129]",
"root_certificate": {
"lower": "834780996678330519025869342931561225414334961318693916769085771147649470107144717590719812256771031949397204640661281588611533646610913634623607686052932727721072224317246988389718206480498935478631633975342870779948295523041864724849560797556342299494072309937578579025173460428861935924762585343934903252612707802041844261600474046327938530460990615307939458167696149013642587267940050244418550666075479344991670717/40131652080904949243476790488282231640246122763238325954424140190648896440865179612073261537762363061729301215028215161995082338334532195000669973530974432754174985283877903733762083113741475809259744657408000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "834780996678330519025869342931561225414334961318693916769085771147649470107144717590719812256771031949397204640661281588611533646610913634623607686052932727721072224317246988389718206480498935478631633975342870860211599684851763211803141774120805579986317836414230487873453841726654817655121809490457978777338831260644274318030798036492615199525380616647886520116561657363613155023747517768584778149027097864480985533/40131652080904949243476790488282231640246122763238325954424140190648896440865179612073261537762363061729301215028215161995082338334532195000669973530974432754174985283877903733762083113741475809259744657408000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"5325/256",
"21301/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "4",
"x": "critical-6"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 662,
"argument": "[23.99700412290264389642805105934119268115773058147077336035738785740346770555835113906899536783147232397497025564975351162676983248 +/- 6.92e-130]",
"root_certificate": {
"lower": "3852157681777482141161265078943187165188194045305437529023330650182970498995596634556620378373553412293294302034491788247175236578340700254046776104285035994520292017239696042547635910321730043336805517792895018298620252852180656017070283016193220595272072705621354853449874450287105836133104724409028274863745884092647888927021112320825948730062107138762382683924622489453151338672992206248177780440555140799156135993/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3852157681777482141161265078943187165188194045305437529023330650182970498995596634556620378373553412293294302034491788247175236578340700254046776104285035994520292017239696042547635910321730043336805517792895018619673469499420249964884606922451073717241054811527962488842995975478277363054541620995120576962650377927057609152742408281484655406319667144122170931720084522853033609696222076344842690372361614877113395257/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"6143/256",
"24573/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "9/2",
"x": "critical-1"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 687,
"argument": "[8.060030062676982471603869405038288327220781862056524984117824482244647281997239680358987762195938945713431973822352392920999201699 +/- 2.31e-130]",
"root_certificate": {
"lower": "1293849288947948688329138760220434405618942839606798887595675155635749213576883184569762424422820981886384480326146760548167974166230734440016715042521755634019406842982275366788004983512868950707761212820213651823929416801042724326678310987773075119273683345147940175887793316867249537636660094149860547202798559703297705289018944715846516982645639083024087391349177991954814925618027639721272379762039706534019417243/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1293849288947948688329138760220434405618942839606798887595675155635749213576883184569762424422820981886384480326146760548167974166230734440016715042521755634019406842982275366788004983512868950707761212820213652144982633448282318274492634894030928241242665451054547811280914842058421064558096990735952849301703053537707425514740240676505223658903199088383875639144640025354697196641257509817937289693846180611976676507/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"8253/1024",
"4127/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "9/2",
"x": "critical-2"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 681,
"argument": "[11.64635404084290228000981787167842783788949889462782323331356103131439928689335863012881389780217386824693412782659869911635153395 +/- 2.68e-129]",
"root_certificate": {
"lower": "3739099427025190588138531169123390714082940970999490394654310848644789501138159965317930354757902130839754963803745362052481291564796616887882975183637773920289167431777216819034661778086315112096374971645811396719058354230869449837054530364886475540278121338956680713237442085063328982818650157663963331090152327263817796949803905954942697144791416142652959335328280839706137099098658686371882994000824541699630631361/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3739099427025190588138531169123390714082940970999490394654310848644789501138159965317930354757902130839754963803745362052481291564796616887882975183637773920289167431777216819034661778086315112096374971645811397361164787525348637732683178177402181784216085550769895984023685135445672036661523950836147935287961314932637237401246497876260110497306536153372535830919204906505901641145118426565212813864437489855545149889/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"11925/1024",
"5963/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "9/2",
"x": "critical-3"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 677,
"argument": "[14.99962446085050019891255358731659125035317080941276969739302983610416830857079579160174005444548084983357842660620990610844345652 +/- 2.73e-129]",
"root_certificate": {
"lower": "4815677681656670029480096131779692969298640213452293941075077478529688711909202807359566186973235466055510587140593318185579559465291854229355003327664930054657643359148477916684703046203543924773986944829735181484838145674652195406179195153710740837774487140365704545326010750713001406885260589185953939351853227166773837212292731538207556606362903915503702552093792836693823212668018888663019368697913736951095475111/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "4815677681656670029480096131779692969298640213452293941075077478529688711909202807359566186973235466055510587140593318185579559465291854229355003327664930054657643359148477916684703046203543924773986944829735182126944578969131383301807842966226447081712451352178919816112253801095344460728134382358138543549662214835593277663735323459524969958878023926223279047684716903493587754714478628856349188561526685107009993639/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"15359/1024",
"15"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "9/2",
"x": "critical-4"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 672,
"argument": "[18.27033007947677975822605409580740634387579407453372768070710767633144284973812339183907256728022362888167934487205197311972690409 +/- 3.29e-129]",
"root_certificate": {
"lower": "91652316269106824384926035280269685823531012092721428535818485278689989950289389602402210943755936249595568586221566718360226964820973834650228557530102028137089656549282294235609078273194939537746677809325492339225853738395300169949973412306999930071021329130510700997703557146154376781677752397191051685049759812572214364691322674506398912993284938944732345085433994711812161068802636924900055794467718819338558449/5016456510113118655434598811035278955030765345404790744303017523831112055108147451509157692220295382716162651878526895249385292291816524375083746691371804094271873160484737966720260389217684476157468082176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "91652316269106824384926035280269685823531012092721428535818485278689989950289389602402210943755936249595568586221566718360226964820973834650228557530102028137089656549282294235609078273194939537746677809325492349258766758621537480819171034377557840132552019940092189603738604808378486997972655415506436125640525244897518121745113173276983496626333689112225727829042183255558482038278570365420834229836671134274722801/5016456510113118655434598811035278955030765345404790744303017523831112055108147451509157692220295382716162651878526895249385292291816524375083746691371804094271873160484737966720260389217684476157468082176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"4677/256",
"18709/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "9/2",
"x": "critical-5"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 668,
"argument": "[21.50002894598492373043246734657442155024097406157962700026407032488634959941475429382322797646608862570336004988388026847612194979 +/- 4.33e-129]",
"root_certificate": {
"lower": "431415840694826253502224820703595664365134936077746750393342459499860096599101629697558550840829015311762312406601361511455718406754831758313488941333840525559736913547098790973856738631033597348424511000688908563051053424902564652681489574516861870596183004315571005988588840674991197560843153375230094372281509150714490443760991442733540593834629295958428286176466553202777357856741811498351975070139532961680405671/20065826040452474621738395244141115820123061381619162977212070095324448220432589806036630768881181530864650607514107580997541169167266097500334986765487216377087492641938951866881041556870737904629872328704000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "431415840694826253502224820703595664365134936077746750393342459499860096599101629697558550840829015311762312406601361511455718406754831758313488941333840525559736913547098790973856738631033597348424511000688908603182705505807513896158280062799093510842305767553896960412729031323887638426022765448491632134644570880015705471976153437815878928366824296628401817150899307377762641734645545260435088811615342221425063079/20065826040452474621738395244141115820123061381619162977212070095324448220432589806036630768881181530864650607514107580997541169167266097500334986765487216377087492641938951866881041556870737904629872328704000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"43/2",
"22017/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "9/2",
"x": "critical-6"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 664,
"argument": "[24.70594239862055231769793207158654451017151431835604133304758164789605247097578203003122210625522935582280987526227618348571655084 +/- 2.70e-129]",
"root_certificate": {
"lower": "991490284672318301434303867836238479335858534113356218938052721897241268900025952855339499914502746292132371163246178071113869777001930098151534609772297033734623944607264807690214820404086399172990732089120021827257104853999564766271518334260370192573254725316402961794943399076969281401123881636888982845806074417517534209004754157711128783821778220930997029419017750110893827687734321718948074068527948217061983217/40131652080904949243476790488282231640246122763238325954424140190648896440865179612073261537762363061729301215028215161995082338334532195000669973530974432754174985283877903733762083113741475809259744657408000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "991490284672318301434303867836238479335858534113356218938052721897241268900025952855339499914502746292132371163246178071113869777001930098151534609772297033734623944607264807690214820404086399172990732089120021907520409015809463253225099310824833473065500251793054870643223780374762163131483105783412058370532197876119964265435078147875805452886168222270944091367883258460864395443541789243114301551479566736551298033/40131652080904949243476790488282231640246122763238325954424140190648896440865179612073261537762363061729301215028215161995082338334532195000669973530974432754174985283877903733762083113741475809259744657408000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"12649/512",
"25299/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "5",
"x": "critical-1"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 686,
"argument": "[8.649556243697198250773866680113377247263131755163053069983414064367086646068579985131387607283194248739581508043184918231726411967 +/- 1.15e-130]",
"root_certificate": {
"lower": "2776967854610200499599881100685843663852661044678007124720627332554969982794077651134563894449159875751056783851019046527476918721518179410385228646294453738639201738478630628947306500258972646565341818418058309239467370185831816292540848157950568035454263513888172173920398247541429731917204836190550885120458413978465746439896763845584351809827558104786517061032333778886164747290298541584880639140518755566818131361/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "2776967854610200499599881100685843663852661044678007124720627332554969982794077651134563894449159875751056783851019046527476918721518179410385228646294453738639201738478630628947306500258972646565341818418058309881573803480311004188169495970466274279392227725701387444706641297923772785760078629362735489318267401647285186891339355766901765162342678115506093556623257845685929289336758281778210459004131703722732649889/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"8857/1024",
"4429/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "5",
"x": "critical-2"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 680,
"argument": "[12.28086872580784822502668409874082189205329841389426426568317494813501101745541010847845176650795793854078616681822923019172197469 +/- 4.62e-129]",
"root_certificate": {
"lower": "1971406203821548179051496092710958934274633599947502900232508953274543129639411024990356130816724312706743335720477829419599429127697957847992948943167058938113008638431851203216267714440557689164250264270391955040949302360316843667900885275272184658366455647973947601956456029142084255011370832703546598516601865282646829290386098110321339546043340657494319732590064585561380080908005648289413756361709163015953010993/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1971406203821548179051496092710958934274633599947502900232508953274543129639411024990356130816724312706743335720477829419599429127697957847992948943167058938113008638431851203216267714440557689164250264270391955362002519007556437615715209181530037780335437753880555237349577554333255781932807729289638900615506359117056549516107394070980046222300900662854107980385526618961262351931235518386078666293515637093910270257/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"12575/1024",
"393/32"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "5",
"x": "critical-3"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 674,
"argument": "[15.66079930454037724236540456642521289099438660866477206832389714575997014772804050462483376070698738016598508907109651518184005038 +/- 4.48e-129]",
"root_certificate": {
"lower": "1256987497997385224570887826567869467258940386131988119980673446526743455824896715699060877191783499477175249584585950882727716485715217613578744282353907587261432567034078648501017203219037824258224406807008678760590182384443921691714589774326800676388684875198062470097815844425657055854334070800312601029103892986159776804261504883366452125965191510980536072722262624460405166285056692099940605296992324504192325809/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1256987497997385224570887826567869467258940386131988119980673446526743455824896715699060877191783499477175249584585950882727716485715217613578744282353907587261432567034078648501017203219037824258224406807008678921116790708063718665621751727455727237373175928151366287794376607021242819315052519093358752078556139903364636917122152863695805464093971513660430196619993641160346301796671627148273060262895561543170955441/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"4009/256",
"16037/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "5",
"x": "critical-4"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 670,
"argument": "[18.94973975601650295139050639808185512600338748898440651847788879923731590596876369858747647078204941836280300797235243037283905369 +/- 4.79e-129]",
"root_certificate": {
"lower": "3041937451648587743359144598781181677407551834752807061330000072335059715251943509857071086441022788007555054012903857433879565464528151944352080354817936453715073688667465874109215380434507118972679343620035436858998059157605095254384101176172575990613905330469393657775199676738942041797177805173359385100067878812420493934660676867382819225822427968781635132412722933462781393737433684655566566294537112539878792243/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3041937451648587743359144598781181677407551834752807061330000072335059715251943509857071086441022788007555054012903857433879565464528151944352080354817936453715073688667465874109215380434507118972679343620035437180051275804844689202198425082430429112582887436376001293168321201930113568718614701759451687198972372646830214160381972828041525902079987974141423380208184966862663664760663554752231476226343586617836051507/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"4851/256",
"19405/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "5",
"x": "critical-5"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 665,
"argument": "[22.19284180942824127392617424419779216346778656643733625856458755798179130368631852256849077249929251156396720297682583514174490692 +/- 3.11e-129]",
"root_certificate": {
"lower": "1781270812365070475875086746919902434264374503547459975694118735301912874108140828862779116042996345273379030083714834153692877387135756343046580743172746402538136698636521825962009009251137160567405043329169423927098607056303293571083191216587648972325689012101529748255752050153533557448321712243238920518932925633675111744463249284354615402123394693556818484691059411719609122717841513217761289163731597575481388309/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1781270812365070475875086746919902434264374503547459975694118735301912874108140828862779116042996345273379030083714834153692877387135756343046580743172746402538136698636521825962009009251137160567405043329169424087625215379923090544990353169716575533310180065054833565952312812749119320909040160536285071568385172550879971857323897264683968740252174696236712608588790428419550258229456448266093744129634834614460017941/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"22725/1024",
"11363/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "5",
"x": "critical-6"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 660,
"argument": "[25.40907278886767389150016533237832638282916747180471596718532826766941554485898867152271575585759851105589782687520414852031042530 +/- 2.58e-129]",
"root_certificate": {
"lower": "1019708068861226706970316808918571475572784116336676741421951187055425571734090227042375795169005513836558775905559920675489314365875495470003964930241550000398544594343864000043505078966847341893344778946573753105976185558730382902053217967061923929114628334347866168558572692801903592128913335943053135008200316529472756124449877375105104842013589844199802885369583656518479989085117117431422109167676698522237764467/40131652080904949243476790488282231640246122763238325954424140190648896440865179612073261537762363061729301215028215161995082338334532195000669973530974432754174985283877903733762083113741475809259744657408000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1019708068861226706970316808918571475572784116336676741421951187055425571734090227042375795169005513836558775905559920675489314365875495470003964930241550000398544594343864000043505078966847341893344778946573753186239489720540281389006798943626387209606873860824518077406853074099696473859272560089576210532926439988075186180880201365269781511077979845539749947318449164868450556840924584955588336650628317041727079283/40131652080904949243476790488282231640246122763238325954424140190648896440865179612073261537762363061729301215028215161995082338334532195000669973530974432754174985283877903733762083113741475809259744657408000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"13009/512",
"26019/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": false
}
},
{
"params": {
"nu": "11/2",
"x": "critical-1"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 686,
"argument": "[9.234274105050692725657690394593336560761641566396485728922643031343351737303448019245081369679669794210672611424106663883271312630 +/- 5.97e-131]",
"root_certificate": {
"lower": "741173351207208641189008522020732633838201450080640322247983695409270457018675718687771008953810704738002881986634875525128851310480628829059391820842519837733188837253684014453586941039373221950252843674980504981906110548541712935163698620666509858364723976583813793743512279924396131293970713120788157551398348508969643970340897953292279037420418631794500379930022278510353435967935934836757710038923286113079044559/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "741173351207208641189008522020732633838201450080640322247983695409270457018675718687771008953810704738002881986634875525128851310480628829059391820842519837733188837253684014453586941039373221950252843674980505142432718872161509909070860573795436419349215029537117611440073042519981894754689161413834308600850595426174504083201545933621632375549198634474394503827753295210294571479550869885090165004826523152057674191/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"9455/1024",
"591/64"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "11/2",
"x": "critical-2"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 680,
"argument": "[12.90947764343532399731411126218922156758030699964435257771566231419313321515785296014598607760257331529787259787144044334418996809 +/- 2.50e-129]",
"root_certificate": {
"lower": "4144629322660537125355136833347989754169967259063211359979973841774799162231258050351228764373144146614828070518711359297108225557112531251326545475260758674788622660688742852691140092468017405579573642373937336820642058022755624955542295041846261747210626644682421271973407799508899774584239680063610623751227069737889535695646239079581833196683483705746865418876378935210419860912655358034490689908178896558029068861/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "4144629322660537125355136833347989754169967259063211359979973841774799162231258050351228764373144146614828070518711359297108225557112531251326545475260758674788622660688742852691140092468017405579573642373937337462748491317234812851170942854361967991148590856495636542759650849891242828427113473235795227949036057406708976147088831000899246549198603716466441914467303002010184402959115098227820509771791844713943587389/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"13219/1024",
"3305/256"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "11/2",
"x": "critical-3"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 675,
"argument": "[16.31591222199098532065516886497229343642129743225487782890548380886515361721001903675408434375157565798594889804206653875539098249 +/- 1.92e-129]",
"root_certificate": {
"lower": "2619138050702108080827379745666242796998724986842643299004098807243540176819869973760703644091723472960341459925778549077300085894105631573733641650540194431807447628223526870781420589396845733687138753636969341433742222568817627577441138136391370013639017476223267523109468735718712501127744497617171081051833774015935772871528502796936150066300307617850046236813468198999382438402133284817405610016093776053062385993/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "2619138050702108080827379745666242796998724986842643299004098807243540176819869973760703644091723472960341459925778549077300085894105631573733641650540194431807447628223526870781420589396845733687138753636969341754795439216057221525255462042649223135607999582129875158502590260909884028049181394203263383150738267850345493097249798757594856742557867623209834484608930232399264709425363154914070519947900250131019645257/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"16707/1024",
"4177/256"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "11/2",
"x": "critical-4"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 671,
"argument": "[19.62322895991434804253614501974453904328812177969443318447315728612895792915109561476320952891961709431404485936046144541116965017 +/- 1.93e-129]",
"root_certificate": {
"lower": "1575025194646441816889871896560431556277311001008851852071643758196362559589058775486884708111822849829603258565092271511015230922105327454217850856251178311228363842128294187274867581780920389065982776576107543258627972124281644492817444562624007405619628913022356642385819428054642036811071819733645357449928126960323391828160705744085367106816014041342251757467579753187743892608971078384681945502065681132610294559/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "1575025194646441816889871896560431556277311001008851852071643758196362559589058775486884708111822849829603258565092271511015230922105327454217850856251178311228363842128294187274867581780920389065982776576107543419154580447901441466724606515752933966604119965975660460082380190650227800271790268026691508499380373877528251941021353724414720444944794044022145881365310769887685028120586013433014400467968918171588924191/80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"10047/512",
"20095/1024"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "11/2",
"x": "critical-5"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 667,
"argument": "[22.87997953494212182188244272323197854647024272332667051497587007086135259488487250665867108813952918297569836473362470740596225105 +/- 1.75e-129]",
"root_certificate": {
"lower": "3672845513258090624254688975340609260010010982488823697917687433514750870547109569324640368863153150919886284558244161594380992708963666605838252884737458280530170599944087171177153524864807889828681742469264308589110249338112599087730339568080122176757205267259510303517983921223608829203975622714411445953734879918684370011817560674951053878865020035133288076216981995752669476290524637952781148856983706778160042243/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "3672845513258090624254688975340609260010010982488823697917687433514750870547109569324640368863153150919886284558244161594380992708963666605838252884737458280530170599944087171177153524864807889828681742469264308910163465985352193035544663474337975298726187373166117938911105446414780356125412519300503748052639373753094090237538856635609760555122580040493076324012444029152551747313754508049446058788790180856117301507/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
1,
-1
],
"second_derivative_sign": -1,
"defining_interval": [
"23429/1024",
"11715/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
},
{
"params": {
"nu": "11/2",
"x": "critical-6"
},
"stored_interval_contains_ball": true,
"accuracy_bits": 663,
"argument": "[26.10680403564430154512980211216315681604061878863003935233745195224203849642598343766855036640169845127281614698647368061456704380 +/- 1.76e-130]",
"root_certificate": {
"lower": "4190836706011369443221635073395013089386600428116362090647682925106722316121183538707698720457175072735785616234057494413960181838918484743257349424135746989327833697889715966371917725110310659422634733017679210052712866323216307362038004535203211619580355577946610599395942246654533392023016865406970922599451215579784608763606823402504221157160236701607803702569347991387547308444954804108870547866926715201011604743/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"upper": "4190836706011369443221635073395013089386600428116362090647682925106722316121183538707698720457175072735785616234057494413960181838918484743257349424135746989327833697889715966371917725110310659422634733017679210373766082970455901309852328441461064741549337683853218234789063771845704918944453761993063224698355709414194328989328119363162927833417796706967591950364810024787429579468184674205535457798733189278968864007/160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
"endpoint_signs": [
-1,
1
],
"second_derivative_sign": 1,
"defining_interval": [
"26733/1024",
"13367/512"
]
},
"independent_argument_policy": "Evaluate at the certified bracket midpoint; the rigorous Arb value separately propagates the entire argument ball.",
"mpmath_160_digits": true,
"mpmath_210_digits": true,
"bessel_identities": {
"wronskian": true,
"stationary_residual_contains_zero": true,
"elementary_half_order_check": true
}
}
],
"retained_identifiers_and_text": []
}