LANA Project: Computational Verification of IUT Theory for abc Conjecture — E8 Intelligence Research

{"FINDING:":[0],"LANA":[1],"project":[2],"is":[3,27,87,122,151,162],"a":[4,62,123,129,152],"computational":[5],"verification":[6],"effort":[7],"for":[8,44,54,99],"the":[9,20,88,91,118,126,136,163,174],"IUT":[10,106],"theory":[11,107],"(Inter-universal":[12],"Teichmüller":[13],"theory)":[14],"underpinning":[15],"Mochizuki's":[16],"claimed":[17],"proof":[18],"of":[19,128,173],"abc":[21,41,137],"conjecture;":[22],"no":[23],"new":[24],"mathematical":[25],"result":[26],"presented":[28],"in":[29],"these":[30],"sources,":[31],"only":[32],"process":[33],"updates":[34],"and":[35,114],"expository":[36],"summaries.":[37],"|":[38,143],"MATH:":[39],"The":[40,79,105,145],"conjecture":[42,92],"itself:":[43],"any":[45],"ε":[46,98],">":[47],"0,":[48],"there":[49],"exists":[50],"C(ε)":[51,71],"such":[52],"that":[53],"coprime":[55],"positive":[56],"integers":[57],"a,":[58],"b,":[59],"c":[60,69],"with":[61,139],"+":[63,97],"b":[64],"=":[65,76,83,149,160],"c,":[66],"we":[67],"have":[68],"<":[70,95],"·":[72],"rad(abc)^(1+ε),":[73],"where":[74],"rad(n)":[75],"∏_{p|n}":[77],"p.":[78],"Szpiro":[80,146],"ratio":[81,147,154],"σ":[82,94,148,159],"log(c)":[84],"/":[85],"log(rad(abc))":[86],"operative":[89],"constant;":[90],"implies":[93],"1":[96,161],"all":[100],"but":[101],"finitely":[102],"many":[103],"triples.":[104],"involves":[108],"Hodge–Arakelov-theoretic":[109],"evaluation,":[110],"étale":[111],"theta":[112],"functions,":[113],"log-volume":[115],"estimates":[116],"—":[117,155],"key":[119],"numerical":[120],"output":[121],"bound":[124],"on":[125],"\\"log-volume\\"":[127],"certain":[130],"arithmetic":[131],"line":[132],"bundle,":[133],"which":[134],"yields":[135],"inequality":[138],"an":[140],"explicit":[141],"constant.":[142],"CONNECTION:":[144],"log(c)/log(rad(abc))":[150],"logarithmic":[153],"its":[156],"critical":[157],"threshold":[158],"boun":[164],"Author:":[165],"Andrew":[166],"Stewart":[167],"Caldin,":[168],"Independent":[169],"Researcher,":[170],"UK.":[171],"Part":[172],"E8":[175],"Intelligence":[176],"Research":[177],"series.":[178],"Platform:":[179],"e8intelligence.com":[180]}