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erdos_699_off_diagonal_explicit_pairs.json
json
{
"scope": "Twenty fully numerical off-diagonal pair thresholds for the index-twelve ramp proof.",
"index": 12,
"height_variable": "h=n-11",
"ramp_file": "erdos_699_index_12_ramp.json",
"source_file": "erdos_699_off_diagonal_pairs.json",
"gcd_file": "erdos_699_off_diagonal_gcd_numeric.json",
"bootstrap_file": "erdos_699_off_diagonal_gcd_bootstrap.json",
"records": [
{
"edge": [
2,
3,
5000,
500
],
"seed": {
"P": 9,
"Q": 8,
"a": 1,
"b": 1,
"difference": 1
},
"directions": [
49,
16,
20
],
"gcd_log_rate": "23227916254221845996448859093560240610629198561209494601845597876663/2985599114320808476684797847005180308845772749302032639251774500000",
"gcd_m0": 14192,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "2409317997/362408529274",
"factorial_prefactor_F": "5504/245",
"left_block": 65,
"right_block": 36,
"threshold_power_of_ten": 927178,
"intervals": {
"first_decay_rate": "[0.0865919744035376668562355510940363568265, 0.0865919744035376668562355510940363568265]",
"second_decay_rate": "[150.5027738378844111575261623921058558929, 150.5027738378844111575261623921058558929]",
"log_Q_integrand_maximum": "[-39.80111092821416732451020880159696091632, -39.80111092821416732451020880159696091632]",
"log_E_integrand_maximum": "[-42.84898623912570776603288088823901459355, -42.84898623912570776603288088823901459355]",
"log_Q_prefactor": "[82.71419402549678725360242014663445774594, 82.71419402549678725360242014663445774594]",
"log_E_prefactor": "[88.80994464731986813664776431991856510039, 88.80994464731986813664776431991856510039]",
"log_first_prefactor": "[87.30931387563137718045485419844463845505, 87.30931387563137718045485419844463845505]",
"log_second_prefactor": "[86.61272006998364875385727384607351369109, 86.61272006998364875385727384607351369109]",
"available_block_per_log_height": "[0.006651748194580734799488678134225397312169, 0.006651748194580734799488678134225397312169]",
"first_gain": "[0.0005756696806892012983372076466160649842256, 0.0005756696806892012983372076466160649842256]",
"second_gain": "[0.0005532770777700827462214124027432652767336, 0.0005532770777700827462214124027432652767336]",
"log_coefficient": "[233.4883598782287976485739229065718386142, 233.4883598782287976485739229065718386142]",
"threshold_log_upper_bound": "[-933.1323933615121979232445168224367260676, -933.1323933615121979232445168224367260676]",
"threshold_block_lower_bound": "[14193.01041148563742412694177454974769977, 14193.01041148563742412694177454974769977]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
2,
3,
5000,
500
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 6532638126
},
{
"edge": [
2,
5,
1500,
3000
],
"seed": {
"P": 128,
"Q": 125,
"a": 1,
"b": 1,
"difference": 3
},
"directions": [
34,
8,
27
],
"gcd_log_rate": "1721536782169550567363726076544318691302006658358171245209/529651191437069435386950954920822030025930509893509750000",
"gcd_m0": 17247,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "2853904933/694820622238",
"factorial_prefactor_F": "8",
"left_block": 42,
"right_block": 35,
"threshold_power_of_ten": 1823712,
"intervals": {
"first_decay_rate": "[0.08198753592271088854913981969579577789333, 0.08198753592271088854913981969579577789333]",
"second_decay_rate": "[245.5455949609146478410423443167781885544, 245.5455949609146478410423443167781885544]",
"log_Q_integrand_maximum": "[-24.64938694922489760682608732217702866916, -24.64938694922489760682608732217702866916]",
"log_E_integrand_maximum": "[-41.98457631548094008741327517739565188922, -41.98457631548094008741327517739565188922]",
"log_Q_prefactor": "[51.37821544012963114190387100872858704255, 51.37821544012963114190387100872858704255]",
"log_E_prefactor": "[86.04859417264171610307824671916583348266, 86.04859417264171610307824671916583348266]",
"log_first_prefactor": "[58.6281409768476188518864394369009523189, 58.6281409768476188518864394369009523189]",
"log_second_prefactor": "[84.49240077472642801134335757972617462007, 84.49240077472642801134335757972617462007]",
"available_block_per_log_height": "[0.004142232897064078738047995921203817227489, 0.004142232897064078738047995921203817227489]",
"first_gain": "[0.0003367554527392704729066849310997725630092, 0.0003367554527392704729066849310997725630092]",
"second_gain": "[0.00855352058813608120792384740136845175649, 0.00855352058813608120792384740136845175649]",
"log_coefficient": "[325.9293245904170976477066777581512040998, 325.9293245904170976477066777581512040998]",
"threshold_log_upper_bound": "[-1072.941288775823858733640196774580927737, -1072.941288775823858733640196774580927737]",
"threshold_block_lower_bound": "[17248.00013122707336895744878450316410929, 17248.00013122707336895744878450316410929]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
2,
5,
1500,
3000
],
"uniform_gcd_m0": 1000000000,
"uniform_threshold_power_of_ten": 105734693179
},
{
"edge": [
2,
7,
1000,
3500
],
"seed": {
"P": 8,
"Q": 7,
"a": 1,
"b": 1,
"difference": 1
},
"directions": [
46,
21,
30
],
"gcd_log_rate": "228021751892016246681052826171237846550537700919573315132659921063/24805080341980638099444158940850137364403639496644730157062000000",
"gcd_m0": 6201,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "5635464820/873085911401",
"factorial_prefactor_F": "7203/230",
"left_block": 67,
"right_block": 51,
"threshold_power_of_ten": 417296,
"intervals": {
"first_decay_rate": "[0.239098670044666906107302164869886242625, 0.239098670044666906107302164869886242625]",
"second_decay_rate": "[155.0514189185306805595630944561353167762, 155.0514189185306805595630944561353167762]",
"log_Q_integrand_maximum": "[-49.03685196480204132965931892637630472789, -49.03685196480204132965931892637630472789]",
"log_E_integrand_maximum": "[-52.62171606947117821644971219267632644432, -52.62171606947117821644971219267632644432]",
"log_Q_prefactor": "[101.5178775055702501963105497769532937529, 101.5178775055702501963105497769532937529]",
"log_E_prefactor": "[108.6876057149085239698913363095533371858, 108.6876057149085239698913363095533371858]",
"log_first_prefactor": "[105.995214320048456668624189719292952757, 105.995214320048456668624189719292952757]",
"log_second_prefactor": "[106.6081641732286880416396399451788074816, 106.6081641732286880416396399451788074816]",
"available_block_per_log_height": "[0.006459828541293866003104140362695039421313, 0.006459828541293866003104140362695039421313]",
"first_gain": "[0.001543298461182756956722508554588687970851, 0.001543298461182756956722508554588687970851]",
"second_gain": "[0.0008027906490180178085813919824511664430064, 0.0008027906490180178085813919824511664430064]",
"log_coefficient": "[258.0029231245985855980205828992370509621, 258.0029231245985855980205828992370509621]",
"threshold_log_upper_bound": "[-499.5905542786596547085025459974219529372, -499.5905542786596547085025459974219529372]",
"threshold_block_lower_bound": "[6202.01301435523577473092106058981955226, 6202.01301435523577473092106058981955226]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
2,
7,
1000,
3500
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 6728396139
},
{
"edge": [
2,
7,
2500,
1500
],
"seed": {
"P": 8,
"Q": 7,
"a": 1,
"b": 1,
"difference": 1
},
"directions": [
34,
23,
49
],
"gcd_log_rate": "127180207709376478233784167418566103014689221451023111036607087/11874483370831331455690085207573916019350011139392897913000000",
"gcd_m0": 8976,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "357043823/59283607169",
"factorial_prefactor_F": "56603/1666",
"left_block": 57,
"right_block": 72,
"threshold_power_of_ten": 647335,
"intervals": {
"first_decay_rate": "[1.173582537141681901225417136355410474292, 1.173582537141681901225417136355410474292]",
"second_decay_rate": "[167.2681478849320755873164794010263085783, 167.2681478849320755873164794010263085783]",
"log_Q_integrand_maximum": "[-54.24877345390442133612668787833713964865, -54.24877345390442133612668787833713964865]",
"log_E_integrand_maximum": "[-57.36395111123406184386369260697927047234, -57.36395111123406184386369260697927047234]",
"log_Q_prefactor": "[112.0231833514022602272938080111002859728, 112.0231833514022602272938080111002859728]",
"log_E_prefactor": "[118.2535386660615412427678174683845476202, 118.2535386660615412427678174683845476202]",
"log_first_prefactor": "[116.5005201658804666996074479534399449769, 116.5005201658804666996074479534399449769]",
"log_second_prefactor": "[116.174097124381705314516121104010017916, 116.174097124381705314516121104010017916]",
"available_block_per_log_height": "[0.006066855430754001237332666402286958036856, 0.006066855430754001237332666402286958036856]",
"first_gain": "[0.00706806511406437523928920019482237660658, 0.00706806511406437523928920019482237660658]",
"second_gain": "[0.007395835693931648436067622041751865964122, 0.007395835693931648436067622041751865964122]",
"log_coefficient": "[279.7163097903829275837161860230105757877, 279.7163097903829275837161860230105757877]",
"threshold_log_upper_bound": "[-10241.33052877626761817898657600277891405, -10241.33052877626761817898657600277891405]",
"threshold_block_lower_bound": "[8977.009419281982734860972231729662196603, 8977.009419281982734860972231729662196603]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
2,
7,
2500,
1500
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 7211031829
},
{
"edge": [
2,
7,
4500,
500
],
"seed": {
"P": 8,
"Q": 7,
"a": 1,
"b": 1,
"difference": 1
},
"directions": [
19,
16,
49
],
"gcd_log_rate": "1074771214903675330642979478309903050791456979612551087105982843342389/135961756965645190090896278432752700382664035432768497063092423500000",
"gcd_m0": 14366,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "6442503317/859110765733",
"factorial_prefactor_F": "21760/931",
"left_block": 35,
"right_block": 65,
"threshold_power_of_ten": 832042,
"intervals": {
"first_decay_rate": "[0.3305088215767801606663277976734049297605, 0.3305088215767801606663277976734049297605]",
"second_decay_rate": "[133.5603532590599902168562235384654053187, 133.5603532590599902168562235384654053187]",
"log_Q_integrand_maximum": "[-40.33814810578521690267970129760352999899, -40.33814810578521690267970129760352999899]",
"log_E_integrand_maximum": "[-40.84550822963355434226657962146525884882, -40.84550822963355434226657962146525884882]",
"log_Q_prefactor": "[83.82786563526324566532782059919757372119, 83.82786563526324566532782059919757372119]",
"log_E_prefactor": "[84.84258588295992054450157724692103142085, 84.84258588295992054450157724692103142085]",
"log_first_prefactor": "[88.30520244974145213764146054153723272523, 88.30520244974145213764146054153723272523]",
"log_second_prefactor": "[82.76314434128008461624988088254650171662, 82.76314434128008461624988088254650171662]",
"available_block_per_log_height": "[0.007510821926942510129114106460025844881827, 0.007510821926942510129114106460025844881827]",
"first_gain": "[0.002478497842463222349154323290070864344302, 0.002478497842463222349154323290070864344302]",
"second_gain": "[0.001574014914167667706967761054012030687069, 0.001574014914167667706967761054012030687069]",
"log_coefficient": "[212.8168112788925148176481674709169710058, 212.8168112788925148176481674709169710058]",
"threshold_log_upper_bound": "[-2788.290065704844554053591919341872597634, -2788.290065704844554053591919341872597634]",
"threshold_block_lower_bound": "[14367.01110523915945432480744076081405358, 14367.01110523915945432480744076081405358]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
2,
7,
4500,
500
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 5791336850
},
{
"edge": [
2,
11,
3000,
500
],
"seed": {
"P": 512,
"Q": 1331,
"a": 13,
"b": 5,
"difference": 1
},
"directions": [
27,
35,
39
],
"gcd_log_rate": "3908983867088465627582789553873751233132156216782103516977911921/263323022584957291499396786527229472237554815848609000579000000",
"gcd_m0": 9130,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "790494643/443079622412",
"factorial_prefactor_F": "41650/351",
"left_block": 62,
"right_block": 74,
"threshold_power_of_ten": 2222724,
"intervals": {
"first_decay_rate": "[0.1812829060895741956114727726203121647205, 0.1812829060895741956114727726203121647205]",
"second_decay_rate": "[560.6684858141401412144107071557698002053, 560.6684858141401412144107071557698002053]",
"log_Q_integrand_maximum": "[-65.17062589048369769650724096468468844249, -65.17062589048369769650724096468468844249]",
"log_E_integrand_maximum": "[-44.65286457718093237956742265834884833769, -44.65286457718093237956742265834884833769]",
"log_Q_prefactor": "[135.1175222050965183318542496697065190082, 135.1175222050965183318542496697065190082]",
"log_E_prefactor": "[94.08199957849098769797461305703483879861, 94.08199957849098769797461305703483879861]",
"log_first_prefactor": "[146.3186914603959333967247697823605560255, 146.3186914603959333967247697823605560255]",
"log_second_prefactor": "[85.27872559598994317716603652234593108113, 85.27872559598994317716603652234593108113]",
"available_block_per_log_height": "[0.00178459807141006312725893391040574784258, 0.00178459807141006312725893391040574784258]",
"first_gain": "[0.0003234253142836464058756487268014022178548, 0.0003234253142836464058756487268014022178548]",
"second_gain": "[0.000283949242157402114706888364228485320512, 0.000283949242157402114706888364228485320512]",
"log_coefficient": "[641.0046598837116618411927221564791910457, 641.0046598837116618411927221564791910457]",
"threshold_log_upper_bound": "[-796.8024505382583312531939626933947968911, -796.8024505382583312531939626933947968911]",
"threshold_block_lower_bound": "[9131.000819839336632380517907681617186531, 9131.000819839336632380517907681617186531]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
2,
11,
3000,
500
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 24342611135
},
{
"edge": [
3,
5,
4000,
1000
],
"seed": {
"P": 625,
"Q": 2187,
"a": 7,
"b": 2,
"difference": 1
},
"directions": [
48,
23,
15
],
"gcd_log_rate": "8202296189520363869347408602217082905015766729717103710205759239/1047525899707201598794093889697036379474381807088171860011000000",
"gcd_m0": 13835,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "1840351063/940609623839",
"factorial_prefactor_F": "15341/240",
"left_block": 71,
"right_block": 38,
"threshold_power_of_ten": 3071169,
"intervals": {
"first_decay_rate": "[1.572076709061314020862703297497229930699, 1.572076709061314020862703297497229930699]",
"second_decay_rate": "[514.3811683020091635292474312355907616548, 514.3811683020091635292474312355907616548]",
"log_Q_integrand_maximum": "[-49.93600699757971340164288691221847831238, -49.93600699757971340164288691221847831238]",
"log_E_integrand_maximum": "[-34.58309197373959315332780930481120581986, -34.58309197373959315332780930481120581986]",
"log_Q_prefactor": "[104.0296593336622089084176184644378408507, 104.0296593336622089084176184644378408507]",
"log_E_prefactor": "[73.32382928598196841178746324962329586561, 73.32382928598196841178746324962329586561]",
"log_first_prefactor": "[114.8112164052522942559879521187509004382, 114.8112164052522942559879521187509004382]",
"log_second_prefactor": "[64.94016748719025360827907317327536557787, 64.94016748719025360827907317327536557787]",
"available_block_per_log_height": "[0.001969019158815671231114364258318715935602, 0.001969019158815671231114364258318715935602]",
"first_gain": "[0.003075848863666041606992650640079405668052, 0.003075848863666041606992650640079405668052]",
"second_gain": "[0.006413187660322081023171836809921399837522, 0.006413187660322081023171836809921399837522]",
"log_coefficient": "[574.4710582977954306264846326507456704012, 574.4710582977954306264846326507456704012]",
"threshold_log_upper_bound": "[-21161.01615766716781759214670126372123519, -21161.01615766716781759214670126372123519]",
"threshold_block_lower_bound": "[13836.00347989807510092261407205164368345, 13836.00347989807510092261407205164368345]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
3,
5,
4000,
1000
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 22196937398
},
{
"edge": [
3,
11,
1500,
6000
],
"seed": {
"P": 243,
"Q": 121,
"a": 1,
"b": 2,
"difference": 1
},
"directions": [
46,
10,
19
],
"gcd_log_rate": "413055596956498203808645816493239763692538081493386664218520377/84701847422496476910579857801099754245947679536467279310500000",
"gcd_m0": 16349,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "721981655/263187920452",
"factorial_prefactor_F": "10",
"left_block": 56,
"right_block": 29,
"threshold_power_of_ten": 2588463,
"intervals": {
"first_decay_rate": "[0.4034386685159786402463201600295467290969, 0.4034386685159786402463201600295467290969]",
"second_decay_rate": "[367.2139131849321711281288741179133962489, 367.2139131849321711281288741179133962489]",
"log_Q_integrand_maximum": "[-29.42142212250477247302829844124748404734, -29.42142212250477247302829844124748404734]",
"log_E_integrand_maximum": "[-39.30249062011731498107425070881208686672, -39.30249062011731498107425070881208686672]",
"log_Q_prefactor": "[61.14542933800359063007458833717933230228, 61.14542933800359063007458833717933230228]",
"log_E_prefactor": "[80.90756633322867564616649287230853794104, 80.90756633322867564616649287230853794104]",
"log_first_prefactor": "[69.03638605414250963111275809975709012534, 69.03638605414250963111275809975709012534]",
"log_second_prefactor": "[75.4145048898881271891902666876959094178, 75.4145048898881271891902666876959094178]",
"available_block_per_log_height": "[0.002763226223688613516328943360270324823288, 0.002763226223688613516328943360270324823288]",
"first_gain": "[0.001106719932609084957586128709741187283863, 0.001106719932609084957586128709741187283863]",
"second_gain": "[0.007347557307959096567320376788224051704776, 0.007347557307959096567320376788224051704776]",
"log_coefficient": "[438.1160885834820694120487720448087237945, 438.1160885834820694120487720448087237945]",
"threshold_log_upper_bound": "[-6142.507102267011650010816199006776625953, -6142.507102267011650010816199006776625953]",
"threshold_block_lower_bound": "[16350.00388629262025800405511804402333046, 16350.00388629262025800405511804402333046]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
3,
11,
1500,
6000
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 15831574377
},
{
"edge": [
3,
11,
2000,
5500
],
"seed": {
"P": 243,
"Q": 121,
"a": 1,
"b": 2,
"difference": 1
},
"directions": [
45,
12,
25
],
"gcd_log_rate": "3397360352360203166196050256461324460085762881569497169425087001021/536395240993491236918322389622155415980619168666013499105229000000",
"gcd_m0": 10921,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "2251912673/890825645651",
"factorial_prefactor_F": "12",
"left_block": 57,
"right_block": 37,
"threshold_power_of_ten": 1876410,
"intervals": {
"first_decay_rate": "[0.9492367486088101617694369024728019772304, 0.9492367486088101617694369024728019772304]",
"second_decay_rate": "[396.8600561480276680457473143749838628307, 396.8600561480276680457473143749838628307]",
"log_Q_integrand_maximum": "[-34.1056474577299908295729543470669985926, -34.1056474577299908295729543470669985926]",
"log_E_integrand_maximum": "[-45.65474335911335292431395446398921697367, -45.65474335911335292431395446398921697367]",
"log_Q_prefactor": "[70.696201565247981969375618173972876026, 70.696201565247981969375618173972876026]",
"log_E_prefactor": "[93.79439336801470615885761840781731278813, 93.79439336801470615885761840781731278813]",
"log_first_prefactor": "[78.58715828138690097041378793655063384906, 78.58715828138690097041378793655063384906]",
"log_second_prefactor": "[88.30133192467415770188139222320468426489, 88.30133192467415770188139222320468426489]",
"available_block_per_log_height": "[0.002536007785687984443999537662155536407877, 0.002536007785687984443999537662155536407877]",
"first_gain": "[0.002399569741065744488424528239516499243148, 0.002399569741065744488424528239516499243148]",
"second_gain": "[0.003220096109984336002423592395752679784361, 0.003220096109984336002423592395752679784361]",
"log_coefficient": "[480.5673136413873690071981181016148122226, 480.5673136413873690071981181016148122226]",
"threshold_log_upper_bound": "[-9871.719675368205837683167840848573418323, -9871.719675368205837683167840848573418323]",
"threshold_block_lower_bound": "[10922.00223767589698778544014252985676312, 10922.00223767589698778544014252985676312]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
3,
11,
2000,
5500
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 17180091873
},
{
"edge": [
3,
11,
3000,
4500
],
"seed": {
"P": 243,
"Q": 121,
"a": 1,
"b": 2,
"difference": 1
},
"directions": [
29,
10,
25
],
"gcd_log_rate": "657530336568619344274525321153615889516488737574010070867131/98255120365749454190157262547052319721298634733170869000000",
"gcd_m0": 18795,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "86947509/26613332572",
"factorial_prefactor_F": "10",
"left_block": 39,
"right_block": 35,
"threshold_power_of_ten": 2498572,
"intervals": {
"first_decay_rate": "[0.05875042650171502342743520754112704086019, 0.05875042650171502342743520754112704086019]",
"second_decay_rate": "[306.1281158593812211639730314978571172893, 306.1281158593812211639730314978571172893]",
"log_Q_integrand_maximum": "[-27.71540705992035745681312020960526204632, -27.71540705992035745681312020960526204632]",
"log_E_integrand_maximum": "[-37.30378465384541900087124428368607948304, -37.30378465384541900087124428368607948304]",
"log_Q_prefactor": "[57.73339921283476059764423187389488830024, 57.73339921283476059764423187389488830024]",
"log_E_prefactor": "[76.91015440068488368576048002205652317368, 76.91015440068488368576048002205652317368]",
"log_first_prefactor": "[65.6243559289736795986824016364726461233, 65.6243559289736795986824016364726461233]",
"log_second_prefactor": "[71.41709295734433522878425383744389465044, 71.41709295734433522878425383744389465044]",
"available_block_per_log_height": "[0.003267525428916852182204964697514230258609, 0.003267525428916852182204964697514230258609]",
"first_gain": "[0.0001919415098876443528063139087351954072794, 0.0001919415098876443528063139087351954072794]",
"second_gain": "[0.0001407015384661410146953027719904445126554, 0.0001407015384661410146953027719904445126554]",
"log_coefficient": "[373.2076401758766889705532635546455958266, 373.2076401758766889705532635546455958266]",
"threshold_log_upper_bound": "[-420.7076205014275175672467943572897457632, -420.7076205014275175672467943572897457632]",
"threshold_block_lower_bound": "[18796.00018228459126297951960721793018101, 18796.00018228459126297951960721793018101]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
3,
11,
3000,
4500
],
"uniform_gcd_m0": 1000000000,
"uniform_threshold_power_of_ten": 132931048004
},
{
"edge": [
3,
11,
3500,
3500
],
"seed": {
"P": 243,
"Q": 121,
"a": 1,
"b": 2,
"difference": 1
},
"directions": [
39,
18,
49
],
"gcd_log_rate": "21454966823040356353951478116341977347727475114162626807227123/2162375430468632144377208424231105005553984177109387470750000",
"gcd_m0": 8140,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "1594646528/790575472185",
"factorial_prefactor_F": "11556/637",
"left_block": 57,
"right_block": 67,
"threshold_power_of_ten": 1752835,
"intervals": {
"first_decay_rate": "[1.895796969677062959459375589995824165728, 1.895796969677062959459375589995824165728]",
"second_decay_rate": "[497.2099442088621835669307181398061252704, 497.2099442088621835669307181398061252704]",
"log_Q_integrand_maximum": "[-48.25936212536781190563029124490562441443, -48.25936212536781190563029124490562441443]",
"log_E_integrand_maximum": "[-60.46039140190342628134589233282557029397, -60.46039140190342628134589233282557029397]",
"log_Q_prefactor": "[99.41691465674958633132098833206677801644, 99.41691465674958633132098833206677801644]",
"log_E_prefactor": "[123.8189732098208150827521905079066697755, 123.8189732098208150827521905079066697755]",
"log_first_prefactor": "[107.3078713728885053323591580946445358395, 107.3078713728885053323591580946445358395]",
"log_second_prefactor": "[118.3259117664802666257759643232940412523, 118.3259117664802666257759643232940412523]",
"available_block_per_log_height": "[0.002022918316610150112046065697341315111424, 0.002022918316610150112046065697341315111424]",
"first_gain": "[0.003823956297471644572483073185611586999803, 0.003823956297471644572483073185611586999803]",
"second_gain": "[0.002907551670408882602519044528012416021328, 0.002907551670408882602519044528012416021328]",
"log_coefficient": "[610.7160413095232808097470957176242975573, 610.7160413095232808097470957176242975573]",
"threshold_log_upper_bound": "[-11109.10216400178615820656447712189092033, -11109.10216400178615820656447712189092033]",
"threshold_block_lower_bound": "[8141.001236211523646593482215031646866729, 8141.001236211523646593482215031646866729]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
3,
11,
3500,
3500
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 21530951375
},
{
"edge": [
3,
11,
4000,
2500
],
"seed": {
"P": 243,
"Q": 121,
"a": 1,
"b": 2,
"difference": 1
},
"directions": [
29,
16,
46
],
"gcd_log_rate": "3212833920586958895332335496076400957867473561195956563/608042034063354868054894152674972340829720660062000000",
"gcd_m0": 9636,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "2170130740/902276532479",
"factorial_prefactor_F": "512/29",
"left_block": 45,
"right_block": 62,
"threshold_power_of_ten": 1740123,
"intervals": {
"first_decay_rate": "[0.1297607703725603559411564468685241295411, 0.1297607703725603559411564468685241295411]",
"second_decay_rate": "[419.6319826119485063192172026254374076726, 419.6319826119485063192172026254374076726]",
"log_Q_integrand_maximum": "[-42.28971408632823888454884684654386779794, -42.28971408632823888454884684654386779794]",
"log_E_integrand_maximum": "[-50.06799814276249825958455742706560014032, -50.06799814276249825958455742706560014032]",
"log_Q_prefactor": "[87.45045696770951152666951075384941310306, 87.45045696770951152666951075384941310306]",
"log_E_prefactor": "[103.0070250805780302767409319148928777878, 103.0070250805780302767409319148928777878]",
"log_first_prefactor": "[95.34141368384843052770768051642717092612, 95.34141368384843052770768051642717092612]",
"log_second_prefactor": "[97.51396363723748181976470573028024926459, 97.51396363723748181976470573028024926459]",
"available_block_per_log_height": "[0.002427304604338233049637973775296285334967, 0.002427304604338233049637973775296285334967]",
"first_gain": "[0.0003120970417549106751372793358963304501137, 0.0003120970417549106751372793358963304501137]",
"second_gain": "[0.009287321760781779634054620085761314376189, 0.009287321760781779634054620085761314376189]",
"log_coefficient": "[512.5021069747860785876473812486369229878, 512.5021069747860785876473812486369229878]",
"threshold_log_upper_bound": "[-722.798978598687449210805214010197365361, -722.798978598687449210805214010197365361]",
"threshold_block_lower_bound": "[9637.000310546128124390931340274495429411, 9637.000310546128124390931340274495429411]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
3,
11,
4000,
2500
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 18056687365
},
{
"edge": [
3,
11,
5000,
2000
],
"seed": {
"P": 243,
"Q": 121,
"a": 1,
"b": 2,
"difference": 1
},
"directions": [
19,
14,
47
],
"gcd_log_rate": "7462540059652154322979306617982215451009744344109245860442625077727/1164621186965279066365442025924575036973218375771387256589773000000",
"gcd_m0": 14996,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "785938485/287620541324",
"factorial_prefactor_F": "15876/893",
"left_block": 33,
"right_block": 61,
"threshold_power_of_ten": 2383527,
"intervals": {
"first_decay_rate": "[1.396054149054866470184632519129153987867, 1.396054149054866470184632519129153987867]",
"second_decay_rate": "[366.2375631155885312998293330108823487964, 366.2375631155885312998293330108823487964]",
"log_Q_integrand_maximum": "[-37.08152491024436688137367054146781814556, -37.08152491024436688137367054146781814556]",
"log_E_integrand_maximum": "[-39.63252536451741917612896418946332510705, -39.63252536451741917612896418946332510705]",
"log_Q_prefactor": "[77.041027053515190710543513658768424459, 77.041027053515190710543513658768424459]",
"log_E_prefactor": "[82.14302796206129530005410095475943838198, 82.14302796206129530005410095475943838198]",
"log_first_prefactor": "[84.93198376965410971158168342134618228206, 84.93198376965410971158168342134618228206]",
"log_second_prefactor": "[76.64996651872074684307787477014680985874, 76.64996651872074684307787477014680985874]",
"available_block_per_log_height": "[0.002734638632290139874039574309646771499933, 0.002734638632290139874039574309646771499933]",
"first_gain": "[0.003814792496514194257716832584866902976375, 0.003814792496514194257716832584866902976375]",
"second_gain": "[0.0007636943458433075025393096465618058927105, 0.0007636943458433075025393096465618058927105]",
"log_coefficient": "[438.3713051959177377858648342249863351096, 438.3713051959177377858648342249863351096]",
"threshold_log_upper_bound": "[-3737.474193352913806004033934829051384505, -3737.474193352913806004033934829051384505]",
"threshold_block_lower_bound": "[14997.00100625181619724243049768779414226, 14997.00100625181619724243049768779414226]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
3,
11,
5000,
2000
],
"uniform_gcd_m0": 1000000000,
"uniform_threshold_power_of_ten": 158933576213
},
{
"edge": [
3,
11,
5500,
1500
],
"seed": {
"P": 243,
"Q": 121,
"a": 1,
"b": 2,
"difference": 1
},
"directions": [
15,
13,
48
],
"gcd_log_rate": "79023539048900100141346290323136705153196520119191162456131500001/13156323629877276922039482006088356380799796159243326873249000000",
"gcd_m0": 11952,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "2876309485/992825951813",
"factorial_prefactor_F": "13013/720",
"left_block": 28,
"right_block": 61,
"threshold_power_of_ten": 1791838,
"intervals": {
"first_decay_rate": "[0.5425009738158111102538464114430204454932, 0.5425009738158111102538464114430204454932]",
"second_decay_rate": "[346.1844863710265323958952704460926533774, 346.1844863710265323958952704460926533774]",
"log_Q_integrand_maximum": "[-34.76116472983875735835446377777944980217, -34.76116472983875735835446377777944980217]",
"log_E_integrand_maximum": "[-34.5918259448105114800351595225092804567, -34.5918259448105114800351595225092804567]",
"log_Q_prefactor": "[72.41678238444417104292302046719390052229, 72.41678238444417104292302046719390052229]",
"log_E_prefactor": "[72.07810481438767928628441195665356183135, 72.07810481438767928628441195665356183135]",
"log_first_prefactor": "[80.30773910058309004396119022977165834535, 80.30773910058309004396119022977165834535]",
"log_second_prefactor": "[66.58504337104713082930818577204093330812, 66.58504337104713082930818577204093330812]",
"available_block_per_log_height": "[0.002905553546808273616167047703999694718679, 0.002905553546808273616167047703999694718679]",
"first_gain": "[0.001571675975792842235115929653834684500358, 0.001571675975792842235115929653834684500358]",
"second_gain": "[0.002928781112668302193053787096046355449276, 0.002928781112668302193053787096046355449276]",
"log_coefficient": "[408.3117767732200799186799299205245234418, 408.3117767732200799186799299205245234418]",
"threshold_log_upper_bound": "[-6060.969643448305686736531999451800260817, -6060.969643448305686736531999451800260817]",
"threshold_block_lower_bound": "[11953.00012002379991031821295112413865497, 11953.00012002379991031821295112413865497]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
3,
11,
5500,
1500
],
"uniform_gcd_m0": 1000000000,
"uniform_threshold_power_of_ten": 149906967607
},
{
"edge": [
3,
11,
6000,
1000
],
"seed": {
"P": 243,
"Q": 121,
"a": 1,
"b": 2,
"difference": 1
},
"directions": [
11,
12,
49
],
"gcd_log_rate": "454852137924160985167858754278149240351371361340375135443312060868501/89340439349024432984531319163388615119478124663706652429773374000000",
"gcd_m0": 16697,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "1872213307/609100523257",
"factorial_prefactor_F": "10512/539",
"left_block": 23,
"right_block": 61,
"threshold_power_of_ten": 2359296,
"intervals": {
"first_decay_rate": "[0.1322977405856632345156512765870141944909, 0.1322977405856632345156512765870141944909]",
"second_decay_rate": "[325.6267694169478323424603490741817035678, 325.6267694169478323424603490741817035678]",
"log_Q_integrand_maximum": "[-32.43135316967617573618117115859124280788, -32.43135316967617573618117115859124280788]",
"log_E_integrand_maximum": "[-28.59368499382102305109381922010401547362, -28.59368499382102305109381922010401547362]",
"log_Q_prefactor": "[67.83326350916774606764122106944729710916, 67.83326350916774606764122106944729710916]",
"log_E_prefactor": "[60.15792715745744069746651719247284244064, 60.15792715745744069746651719247284244064]",
"log_first_prefactor": "[75.72422022530666506867939083202505493222, 75.72422022530666506867939083202505493222]",
"log_second_prefactor": "[54.6648657141168922404902910078602139174, 54.6648657141168922404902910078602139174]",
"available_block_per_log_height": "[0.003076468461326407358294521098352617937425, 0.003076468461326407358294521098352617937425]",
"first_gain": "[0.0004066481327023981408998850877467971748448, 0.0004066481327023981408998850877467971748448]",
"second_gain": "[0.0008902431374230991261872716880231388864329, 0.0008902431374230991261872716880231388864329]",
"log_coefficient": "[375.8930674928877615637081776651587086086, 375.8930674928877615637081776651587086086]",
"threshold_log_upper_bound": "[-1817.706792669216374884066567770956588238, -1817.706792669216374884066567770956588238]",
"threshold_block_lower_bound": "[16698.00071154172566011864652972024702842, 16698.00071154172566011864652972024702842]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
3,
11,
6000,
1000
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 14129212619
},
{
"edge": [
5,
7,
1500,
4000
],
"seed": {
"P": 25,
"Q": 49,
"a": 2,
"b": 1,
"difference": 1
},
"directions": [
43,
18,
18
],
"gcd_log_rate": "674129221271180075022130423313734345482117516563423881261445503209071/68963168083447590073261140378332140896841210591317310353339991500000",
"gcd_m0": 4571,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "4137240448/966426009183",
"factorial_prefactor_F": "1440/43",
"left_block": 61,
"right_block": 36,
"threshold_power_of_ten": 463819,
"intervals": {
"first_decay_rate": "[0.6492850033392501632308059097046482540332, 0.6492850033392501632308059097046482540332]",
"second_decay_rate": "[233.674714304126364711645887297643271724, 233.674714304126364711645887297643271724]",
"log_Q_integrand_maximum": "[-42.14103432635433989774577105498897318972, -42.14103432635433989774577105498897318972]",
"log_E_integrand_maximum": "[-37.26035775945524501310668521725485994761, -37.26035775945524501310668521725485994761]",
"log_Q_prefactor": "[87.79326692958516367649611001099422123308, 87.79326692958516367649611001099422123308]",
"log_E_prefactor": "[78.03191379578697390721793833552599474886, 78.03191379578697390721793833552599474886]",
"log_first_prefactor": "[94.10318520781168027917680437686990238003, 94.10318520781168027917680437686990238003]",
"log_second_prefactor": "[74.11989079035882784859918754761544290173, 74.11989079035882784859918754761544290173]",
"available_block_per_log_height": "[0.004282486186414589108705411578084911555428, 0.004282486186414589108705411578084911555428]",
"first_gain": "[0.002779569416147925338124899567340441754787, 0.002779569416147925338124899567340441754787]",
"second_gain": "[0.0003543680608982037786576688553968806223201, 0.0003543680608982037786576688553968806223201]",
"log_coefficient": "[303.727323722445170987498406386814502058, 303.727323722445170987498406386814502058]",
"threshold_log_upper_bound": "[-60.85035803843033151123556052614579919045, -60.85035803843033151123556052614579919045]",
"threshold_block_lower_bound": "[4572.00162795883024847287325730162563918, 4572.00162795883024847287325730162563918]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
5,
7,
1500,
4000
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 10144769018
},
{
"edge": [
5,
7,
2500,
3000
],
"seed": {
"P": 25,
"Q": 49,
"a": 2,
"b": 1,
"difference": 1
},
"directions": [
50,
25,
34
],
"gcd_log_rate": "109599157805375248922248848308351156905205230545441838033/8170129796837144003267289672217079412972259897842000000",
"gcd_m0": 5683,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "2799729293/918695509133",
"factorial_prefactor_F": "1375/34",
"left_block": 75,
"right_block": 59,
"threshold_power_of_ten": 810017,
"intervals": {
"first_decay_rate": "[2.238912788018191412604691258902527885321, 2.238912788018191412604691258902527885321]",
"second_decay_rate": "[328.2497506480165876741403004663103872527, 328.2497506480165876741403004663103872527]",
"log_Q_integrand_maximum": "[-58.3973751485735398189233511566764225082, -58.3973751485735398189233511566764225082]",
"log_E_integrand_maximum": "[-56.9902402843413146125585669400252776002, -56.9902402843413146125585669400252776002]",
"log_Q_prefactor": "[120.4945987826315899160441571516652341311, 120.4945987826315899160441571516652341311]",
"log_E_prefactor": "[117.6803290541671395033145887183629443151, 117.6803290541671395033145887183629443151]",
"log_first_prefactor": "[126.8045170608581065187248515175409152781, 126.8045170608581065187248515175409152781]",
"log_second_prefactor": "[113.768306048738993444695837930452392468, 113.768306048738993444695837930452392468]",
"available_block_per_log_height": "[0.003048549488634114280773343835246886191999, 0.003048549488634114280773343835246886191999]",
"first_gain": "[0.006823098246123414812530654677124232333898, 0.006823098246123414812530654677124232333898]",
"second_gain": "[0.0003428047411432157448603464472626748673486, 0.0003428047411432157448603464472626748673486]",
"log_coefficient": "[437.6109190503303447933237553520105514266, 437.6109190503303447933237553520105514266]",
"threshold_log_upper_bound": "[-187.32669699969544292717626254184080365, -187.32669699969544292717626254184080365]",
"threshold_block_lower_bound": "[5684.002629240202836859426916260214762703, 5684.002629240202836859426916260214762703]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
5,
7,
2500,
3000
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 14250820434
},
{
"edge": [
5,
7,
4000,
2000
],
"seed": {
"P": 25,
"Q": 49,
"a": 2,
"b": 1,
"difference": 1
},
"directions": [
42,
25,
50
],
"gcd_log_rate": "205095627613404405019690872903182166551508058480479305347493/12702683154713058881442216091446921499575434837778882000000",
"gcd_m0": 7127,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "2280754911/832800832652",
"factorial_prefactor_F": "1475/42",
"left_block": 67,
"right_block": 75,
"threshold_power_of_ten": 1130355,
"intervals": {
"first_decay_rate": "[3.855323949242419954040618057732985412253, 3.855323949242419954040618057732985412253]",
"second_decay_rate": "[365.4275387677933585996308913171118252349, 365.4275387677933585996308913171118252349]",
"log_Q_integrand_maximum": "[-60.46893957117410775597622371057538712105, -60.46893957117410775597622371057538712105]",
"log_E_integrand_maximum": "[-63.65024093914956763924482205899788609694, -63.65024093914956763924482205899788609694]",
"log_Q_prefactor": "[124.4966227928387674058521863594989651429, 124.4966227928387674058521863594989651429]",
"log_E_prefactor": "[130.8592255287896871723893830563439630946, 130.8592255287896871723893830563439630946]",
"log_first_prefactor": "[130.8065410710652840085328807253746462898, 130.8065410710652840085328807253746462898]",
"log_second_prefactor": "[126.9472025233615411137706322684334112475, 126.9472025233615411137706322684334112475]",
"available_block_per_log_height": "[0.002740791159305337029571463409974343395474, 0.002740791159305337029571463409974343395474]",
"first_gain": "[0.01055840566673026996326823784032782634611, 0.01055840566673026996326823784032782634611]",
"second_gain": "[0.0007802838107381312206601837339898502238981, 0.0007802838107381312206601837339898502238981]",
"log_coefficient": "[487.8607476246324393103475350780115038012, 487.8607476246324393103475350780115038012]",
"threshold_log_upper_bound": "[-1528.241949562185154973161383488216119646, -1528.241949562185154973161383488216119646]",
"threshold_block_lower_bound": "[7128.005339571266951928578748982996565978, 7128.005339571266951928578748982996565978]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
5,
7,
4000,
2000
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 15857942825
},
{
"edge": [
5,
11,
500,
3000
],
"seed": {
"P": 125,
"Q": 121,
"a": 1,
"b": 1,
"difference": 4
},
"directions": [
46,
10,
31
],
"gcd_log_rate": "45413030754293421616806416249086745374049353462765668463564442412187/9819821549340032471221203268734901984817092265613800290323438000000",
"gcd_m0": 13737,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "1392795011/397212315384",
"factorial_prefactor_F": "10",
"left_block": 56,
"right_block": 41,
"threshold_power_of_ten": 1701545,
"intervals": {
"first_decay_rate": "[0.8130029618787083858878826892708353056826, 0.8130029618787083858878826892708353056826]",
"second_decay_rate": "[285.7675229205124628946739641677263623185, 285.7675229205124628946739641677263623185]",
"log_Q_integrand_maximum": "[-30.84228448147715797648261958414916798011, -30.84228448147715797648261958414916798011]",
"log_E_integrand_maximum": "[-52.09476333399326506556106638559501882246, -52.09476333399326506556106638559501882246]",
"log_Q_prefactor": "[63.98715405594836163698323062298270016783, 63.98715405594836163698323062298270016783]",
"log_E_prefactor": "[106.4921117609805758151401242258744018525, 106.4921117609805758151401242258744018525]",
"log_first_prefactor": "[71.21336306604903330484745220062639238622, 71.21336306604903330484745220062639238622]",
"log_second_prefactor": "[105.8226811070379465478412389549448983424, 105.8226811070379465478412389549448983424]",
"available_block_per_log_height": "[0.003513501118045423929594282254592523541174, 0.003513501118045423929594282254592523541174]",
"first_gain": "[0.002850733538153786969916709703528869983304, 0.002850733538153786969916709703528869983304]",
"second_gain": "[0.002022255641145873628879054998364004729012, 0.002022255641145873628879054998364004729012]",
"log_coefficient": "[387.3233399789537731133041951468619567908, 387.3233399789537731133041951468619567908]",
"threshold_log_upper_bound": "[-7520.596421595997873580805497854957984381, -7520.596421595997873580805497854957984381]",
"threshold_block_lower_bound": "[13738.00357989523378457634831491981807516, 13738.00357989523378457634831491981807516]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
5,
11,
500,
3000
],
"uniform_gcd_m0": 100000000,
"uniform_threshold_power_of_ten": 12385678947
},
{
"edge": [
5,
11,
1000,
2500
],
"seed": {
"P": 125,
"Q": 121,
"a": 1,
"b": 1,
"difference": 4
},
"directions": [
38,
9,
31
],
"gcd_log_rate": "254003768281753500718700215391724629456325629986292031582029/60372345522353657864857867512965818696086258239049471000000",
"gcd_m0": 15235,
"gap_bound": 11,
"maximum_shift": 11,
"block_parameter": "1727756013/442219779116",
"factorial_prefactor_F": "9",
"left_block": 47,
"right_block": 40,
"threshold_power_of_ten": 1693601,
"intervals": {
"first_decay_rate": "[0.03077016420315099165389337399089745116815, 0.03077016420315099165389337399089745116815]",
"second_decay_rate": "[256.1254699820129613792249346040564694323, 256.1254699820129613792249346040564694323]",
"log_Q_integrand_maximum": "[-27.73504967383705059825067863990833924331, -27.73504967383705059825067863990833924331]",
"log_E_integrand_maximum": "[-47.6313402032829375701782044033136089944, -47.6313402032829375701782044033136089944]",
"log_Q_prefactor": "[57.66732392501032057929184775366172989591, 57.66732392501032057929184775366172989591]",
"log_E_prefactor": "[97.4599049839020945231468992804722693981, 97.4599049839020945231468992804722693981]",
"log_first_prefactor": "[64.89353293511099224715606933130542211431, 64.89353293511099224715606933130542211431]",
"log_second_prefactor": "[96.79047432995946525584801400954276588798, 96.79047432995946525584801400954276588798]",
"available_block_per_log_height": "[0.003909678669602309351165953895823118628811, 0.003909678669602309351165953895823118628811]",
"first_gain": "[0.0001202192636640208822317300046291013997933, 0.0001202192636640208822317300046291013997933]",
"second_gain": "[0.0006841433652711748936069133941472511556344, 0.0006841433652711748936069133941472511556344]",
"log_coefficient": "[348.7572551410095634840453705894038002744, 348.7572551410095634840453705894038002744]",
"threshold_log_upper_bound": "[-104.8806485853255757626324118536974303462, -104.8806485853255757626324118536974303462]",
"threshold_block_lower_bound": "[15236.00266367234372790568087199506928501, 15236.00266367234372790568087199506928501]"
},
"conclusion": "For every h>=10^K, the two listed cofactor upper bounds cannot both hold.",
"gcd_certificate_edge": [
5,
11,
1000,
2500
],
"uniform_gcd_m0": 1000000000,
"uniform_threshold_power_of_ten": 111157830508
}
],
"maximum_pair_threshold_power_of_ten": 3071169,
"ramp_algebraic_power_of_ten": 845,
"complete_row_cap_power_of_ten": 3071170,
"uniform_only_complete_row_cap_power_of_ten": 158933576214,
"conclusion": "Every bad triple at index twelve has n below the displayed complete row cap."
}
Graph