The Dimension of Space from the Granularity of Hilbert Space

{"Why":[0],"do":[1],"we":[2],"live":[3],"in":[4,133,206],"a":[5,30,36,100,123,150,156,167,203,218,311,339,366,369,376,427],"three-dimensional":[6],"world?":[7],"We":[8],"now":[9,273],"know:":[10],"it":[11],"follows":[12],"from":[13,103,197,275,300,349,355,418],"two":[14,127,239,380],"postulates":[15,420],"and":[16,92,107,155,279,292,341,391,399,412,434],"some":[17],"counting.":[18],"The":[19,50,225,361,382,403],"first":[20,96],"is":[21,25,29,52,75,88,126,211,227,231,237,269,272,364,379,385,389,393,406],"that":[22,53,84,236,316],"quantum":[23],"mechanics":[24],"granular:":[26],"every":[27,165,267,336],"state":[28],"record":[31],"of":[32,38,68,169,260,286],"L":[33,39,42,185],"bits":[34],"on":[35,152,440],"ring":[37,154],"Planck":[40,195],"cells,":[41,175],"=":[43,193,414],"6.4×10⁶¹":[44],"universal,":[45],"each":[46],"record's":[47],"phase":[48],"hidden.":[49],"second":[51],"the":[54,85,89,95,104,172,179,198,209,264,276,280,301,308,324,334,356,387,394,409,419,422,441],"momenta":[55,136],"an":[56,108,147,242,270,331],"elementary":[57,109],"interaction":[58],"can":[59],"carry":[60],"have":[61],"one":[62,80,115,118,121,153,188,254,281,291,315,342,373],"address":[63,86,271,282,332,345],"space,":[64,70,262],"addressed":[65],"by":[66,178,221,253,372],"directions":[67,173,259],"n-dimensional":[69,261],"n":[71,143,192,208,352,413],"unknown.":[72],"All":[73],"else":[74],"derived:":[76],"interactions,":[77],"their":[78],"legs,":[79,114],"momentum":[81,98,189,343],"per":[82,344],"address,":[83],"space":[87,230],"cosmological":[90],"horizon,":[91],"n.":[93],"From":[94],"follow":[97],"conservation,":[99,408],"gauge":[101,180,277,357,428],"field":[102],"hidden":[105,423],"phase,":[106,424],"event":[110,125,148,235,378],"with":[111,120,160,183],"exactly":[112],"three":[113],"mark":[116],"crossing":[117,367],"link":[119],"quantum;":[122],"four-leg":[124,234,377],"crossings,":[128,240],"coincident":[129],"at":[130,222],"most":[131],"once":[132],"L.":[134],"Three":[135],"summing":[137],"to":[138,202,307,431],"zero":[139],"are":[140,258,359,416],"coplanar":[141],"for":[142],"≥":[144,347],"2,":[145],"so":[146,191,229,375],"needs":[149],"direction":[151,268],"magnitude,":[157],"L²":[158],"labels":[159],"no":[161],"n;":[162],"Palmer's":[163],"rule,":[164],"probability":[166],"multiple":[168],"1/L,":[170],"gives":[171],"L^(n−1)":[174],"all":[176],"addresses":[177,257],"clause,":[181],"which":[182,425],"finite":[184,350],"fills":[186],"them":[187],"each,":[190],"3.":[194],"pixels":[196],"horizon":[199,226],"entropy":[200],"agree":[201],"factor":[204],"π;":[205],"real":[207],"root":[210,388],"3.008;":[212],"2":[213,251,288,328],"or":[214,241],"4":[215],"would":[216,246],"need":[217],"count":[219],"wrong":[220],"least":[223],"3×10³⁰.":[224],"one,":[228],"one.":[232],"A":[233],"not":[238,263],"energy-dependent":[243],"light":[244],"speed,":[245],"falsify":[247],"it.":[248],"v12:":[249],"Postulate":[250,287,327],"weakened":[252],"word:":[255],"its":[256],"directions.":[265],"That":[266],"derived,":[274],"clause":[278],"space.":[283],"Two":[284],"words":[285],"remain":[289],"postulated,":[290],"directions,":[293],"correcting":[294],"v11's":[295],"\\"only":[296],"one.\\"":[297],"Citation":[298],"removed":[299],"abstract.":[302],"Wolfram's":[303],"hypergraph-rewriting":[304],"models":[305],"added":[306],"introduction":[309],"as":[310,330],"third":[312],"prior":[313],"approach,":[314],"leaves":[317],"dimension":[318],"open.":[319],"v5":[320],"(9":[321],"Sep)":[322],"remains":[323],"priority":[325],"record.v11:":[326],"restated":[329],"space;":[333],"sphere,":[335],"great":[337],"circle":[338],"ring,":[340],"(n":[346],"3":[348,354],"L,":[351],"≤":[353],"clause)":[358],"derived.":[360],"three-leg":[362,410],"vertex":[363],"exact:":[365],"shifts":[368],"link's":[370],"flux":[371],"unit,":[374],"crossings.":[381],"L²/2":[383],"accounting":[384],"withdrawn;":[386],"3.008":[390],"π":[392],"whole":[395],"residual.":[396],"Minor":[397],"corrections":[398],"unused":[400],"material":[401],"removed.v8:":[402],"two-body":[404],"premise":[405],"removed;":[407],"vertex,":[411],"k":[415],"derived":[417],"through":[421],"forces":[426],"coupling.":[429],"References":[430],"Wilson,":[432],"Peierls,":[433],"'t":[435],"Hooft":[436],"added;":[437],"concept":[438],"DOI":[439],"title":[442],"page.":[443]}