back to table · edit · history · where entries came from · files · download
14590 bytes, as of the version from 2026-10-30 19:31 (current). Recorded here, not run.
{
"controls_passed": true,
"entries": [
{
"all_displayed_identities_checked": true,
"beta": "0.3589038426086023489212077095394976938733198790188782811837733386976592448431413347536499791124832650",
"beta_radius": "7.9556876e-128",
"coarse_beta_and_e_match": true,
"exact_certificate_passed": true,
"independent_beta": "[0.35890384260860234892120770953949769387331987901887828118377333869765924484314133475364997911248326504502999178045361948752161 +/- 5.71e-126]",
"independent_beta_radius": "2.6599446e-126",
"independent_enclosure_inside_written_interval": true,
"independent_root_endpoint_residuals": [
"[1.346706861223057295200344984046152473677808855648234e-127 +/- 5.82e-179]",
"[-7.1067726157420078297729347911404725471144662117672e-129 +/- 1.83e-179]"
],
"k": 1,
"root_derivative_certificate_degree": 8,
"same_bracket_at_700_bits": true,
"xi_lower": "1882708952023858206341587593883096949153464055886105887326937945769058709576123808418891995026547417413588662575064589089887249/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304",
"xi_upper": "941354476011929103170793796941548474576732027943052943663468972884529354788061904209445997513273708706794331287532294544943625/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152"
},
{
"all_displayed_identities_checked": true,
"beta": "0.4034546560514278875104263937991677914926072257320901229910846733194936819231593658758351340069518789",
"beta_radius": "6.6625986e-128",
"coarse_beta_and_e_match": true,
"exact_certificate_passed": true,
"independent_beta": "[0.40345465605142788751042639379916779149260722573209012299108467331949368192315936587583513400695187889295202143589422015718691 +/- 6.48e-126]",
"independent_beta_radius": "4.2665378e-126",
"independent_enclosure_inside_written_interval": true,
"independent_root_endpoint_residuals": [
"[6.503599506761089660244073746e-128 +/- 8.76e-156]",
"[-1.056255614616489674128714561e-127 +/- 1.01e-155]"
],
"k": 2,
"root_derivative_certificate_degree": 12,
"same_bracket_at_700_bits": true,
"xi_lower": "1216344401195627905580256872460441422532272270135473834317029796056925633383429730872616944469979311959843539141209515191146437/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304",
"xi_upper": "608172200597813952790128436230220711266136135067736917158514898028462816691714865436308472234989655979921769570604757595573219/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152"
},
{
"all_displayed_identities_checked": true,
"beta": "0.4266350788289110340115277434309860626782686583947364785409904099343559390387146239911605383518065690",
"beta_radius": "6.0618653e-128",
"coarse_beta_and_e_match": true,
"exact_certificate_passed": true,
"independent_beta": "[0.4266350788289110340115277434309860626782686583947364785409904099343559390387146239911605383518065690404071116842984255716488 +/- 3.06e-125]",
"independent_beta_radius": "5.8951027e-126",
"independent_enclosure_inside_written_interval": true,
"independent_root_endpoint_residuals": [
"[1.664254828326679190637499739e-127 +/- 1.22e-155]",
"[-1.96409763221807760412197030e-128 +/- 5.07e-155]"
],
"k": 3,
"root_derivative_certificate_degree": 16,
"same_bracket_at_700_bits": true,
"xi_lower": "899327463970502622252257590066599446377642729747394137193950783727302994529732370497303554138554178917908638018194999582988213/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304",
"xi_upper": "449663731985251311126128795033299723188821364873697068596975391863651497264866185248651777069277089458954319009097499791494107/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152"
},
{
"all_displayed_identities_checked": true,
"beta": "0.4408438858453380818788005671156565580641702779828970724093421009921843092520957824079281359528278095",
"beta_radius": "5.7142720e-128",
"coarse_beta_and_e_match": true,
"exact_certificate_passed": true,
"independent_beta": "[0.4408438858453380818788005671156565580641702779828970724093421009921843092520957824079281359528278095203819052529923937852669 +/- 1.23e-125]",
"independent_beta_radius": "7.5349376e-126",
"independent_enclosure_inside_written_interval": true,
"independent_root_endpoint_residuals": [
"[1.347986958560844120669926636e-127 +/- 2.33e-155]",
"[-6.08173505034558406786829011e-128 +/- 5.37e-155]"
],
"k": 4,
"root_derivative_certificate_degree": 20,
"same_bracket_at_700_bits": true,
"xi_lower": "356801524992437507330870894768238405655840068778063486415173146395946656657924827813862149942802876706495629885371069195300249/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152",
"xi_upper": "713603049984875014661741789536476811311680137556126972830346292791893313315849655627724299885605753412991259770742138390600499/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304"
},
{
"all_displayed_identities_checked": true,
"beta": "0.4504437511469904155870450255636579921249617349316140669755082541085733629982880546262065081368000199",
"beta_radius": "5.4875430e-128",
"coarse_beta_and_e_match": true,
"exact_certificate_passed": true,
"independent_beta": "[0.4504437511469904155870450255636579921249617349316140669755082541085733629982880546262065081368000199178585756042443371593474 +/- 5.46e-125]",
"independent_beta_radius": "9.1811262e-126",
"independent_enclosure_inside_written_interval": true,
"independent_root_endpoint_residuals": [
"[1.943583661792794853290494238e-127 +/- 1.35e-155]",
"[-7.7511450024848301216985705e-129 +/- 1.70e-155]"
],
"k": 5,
"root_derivative_certificate_degree": 24,
"same_bracket_at_700_bits": true,
"xi_lower": "73940511394289432659024533940673170389695788380269441003572548078092772839156516101245863897591825594878043094489916347647101/1353842624082429130653522550851115089568572790710847937094960732721983060451965636249987502980536903367866802227247837807116288",
"xi_upper": "591524091154315461272196271525385363117566307042155528028580384624742182713252128809966911180734604759024344755919330781176809/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304"
},
{
"all_displayed_identities_checked": true,
"beta": "0.4573637367354507890597402325162575738162407756461796798543286680230306504592551110014315400078797924",
"beta_radius": "5.3279415e-128",
"coarse_beta_and_e_match": true,
"exact_certificate_passed": true,
"independent_beta": "[0.4573637367354507890597402325162575738162407756461796798543286680230306504592551110014315400078797924070643739289654950065937 +/- 5.88e-125]",
"independent_beta_radius": "1.0831214e-125",
"independent_enclosure_inside_written_interval": true,
"independent_root_endpoint_residuals": [
"[4.21272278237828889013569191e-128 +/- 7.30e-155]",
"[-1.64682414432633365222370533e-127 +/- 3.30e-154]"
],
"k": 6,
"root_derivative_certificate_degree": 28,
"same_bracket_at_700_bits": true,
"xi_lower": "505138467001078672083963909671700035531086848953287800599524777333822662055050024069677844692577967175084525496700009244108113/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304",
"xi_upper": "252569233500539336041981954835850017765543424476643900299762388666911331027525012034838922346288983587542262748350004622054057/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152"
},
{
"all_displayed_identities_checked": true,
"beta": "0.4625883433024108650841521266487169934337558054636693002729858392788013772044512546831952890458037012",
"beta_radius": "5.2094880e-128",
"coarse_beta_and_e_match": true,
"exact_certificate_passed": true,
"independent_beta": "[0.4625883433024108650841521266487169934337558054636693002729858392788013772044512546831952890458037011823217716247906603136918 +/- 2.48e-125]",
"independent_beta_radius": "1.2483857e-125",
"independent_enclosure_inside_written_interval": true,
"independent_root_endpoint_residuals": [
"[5.57594347894809009331812180e-128 +/- 7.92e-155]",
"[-1.546090441177126292123035828e-127 +/- 8.07e-155]"
],
"k": 7,
"root_derivative_certificate_degree": 32,
"same_bracket_at_700_bits": true,
"xi_lower": "220390442249167024695105290860799111242356694753191277022927606766752385573129378949323494020079492295560555616304597548738459/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152",
"xi_upper": "440780884498334049390210581721598222484713389506382554045855213533504771146258757898646988040158984591121111232609195097476919/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304"
},
{
"all_displayed_identities_checked": true,
"beta": "0.4666725198614399817480380279421531070060618084985290769908372082567362898420959009952668600578514947",
"beta_radius": "5.1180815e-128",
"coarse_beta_and_e_match": true,
"exact_certificate_passed": true,
"independent_beta": "[0.4666725198614399817480380279421531070060618084985290769908372082567362898420959009952668600578514946663774806894227644325708 +/- 2.95e-125]",
"independent_beta_radius": "1.4138262e-125",
"independent_enclosure_inside_written_interval": true,
"independent_root_endpoint_residuals": [
"[6.794808133575308406172224e-129 +/- 5.53e-154]",
"[-2.06361580864978063413522624e-127 +/- 1.52e-154]"
],
"k": 8,
"root_derivative_certificate_degree": 36,
"same_bracket_at_700_bits": true,
"xi_lower": "390975205895615053184810523422187848291334823517130321988990846319698669254406102630138569095988942361777958860536723836290867/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304",
"xi_upper": "97743801473903763296202630855546962072833705879282580497247711579924667313601525657534642273997235590444489715134180959072717/2707685248164858261307045101702230179137145581421695874189921465443966120903931272499975005961073806735733604454495675614232576"
},
{
"all_displayed_identities_checked": true,
"beta": "0.4699528712415190837142322925587485213335326473795846505542923667411204968634900109609866127428395359",
"beta_radius": "5.0454053e-128",
"coarse_beta_and_e_match": true,
"exact_certificate_passed": true,
"independent_beta": "[0.4699528712415190837142322925587485213335326473795846505542923667411204968634900109609866127428395358623497441543667020543457 +/- 6.00e-125]",
"independent_beta_radius": "1.5793932e-125",
"independent_enclosure_inside_written_interval": true,
"independent_root_endpoint_residuals": [
"[3.4885485106288485450235592e-128 +/- 6.00e-154]",
"[-1.80513750003272172969836230e-127 +/- 1.96e-154]"
],
"k": 9,
"root_derivative_certificate_degree": 40,
"same_bracket_at_700_bits": true,
"xi_lower": "351285694378615142303945437755437286680372070686391275754209958039331976136378896700473555290022866300760879205973814030712897/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304",
"xi_upper": "175642847189307571151972718877718643340186035343195637877104979019665988068189448350236777645011433150380439602986907015356449/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152"
},
{
"all_displayed_identities_checked": true,
"beta": "0.4726454147635197162171961338556955822870470885280978441091384585974743660295423655066730947687918184",
"beta_radius": "4.9862360e-128",
"coarse_beta_and_e_match": true,
"exact_certificate_passed": true,
"independent_beta": "[0.4726454147635197162171961338556955822870470885280978441091384585974743660295423655066730947687918184202501610550645761644788 +/- 4.04e-125]",
"independent_beta_radius": "1.7450541e-125",
"independent_enclosure_inside_written_interval": true,
"independent_root_endpoint_residuals": [
"[4.5985880990716342576070100e-128 +/- 1.62e-154]",
"[-1.71256666654483818579352442e-127 +/- 2.26e-154]"
],
"k": 10,
"root_derivative_certificate_degree": 44,
"same_bracket_at_700_bits": true,
"xi_lower": "318913625786271090201881969127024754983515325550916990094150972927484732915310185348025375738127061787094832782065295785601865/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304",
"xi_upper": "159456812893135545100940984563512377491757662775458495047075486463742366457655092674012687869063530893547416391032647892800933/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152"
}
],
"python_version": "3.12.3",
"quadrature_bits": 600,
"root_working_bits": [
500,
700
],
"sage_version": "10.9",
"skill_manifest": "agents/runs/20261030T190951Z-build-skills/manifest.json",
"skill_sha256": "dedecbdca15a728b6e594bfa79f0d149896fca336080ac27b53f513e0b16cd2e",
"stored_readback": true,
"table": "T628"
}