Why φ? The Golden Ratio as Universal Efficiency Limit in Computational Finitism

{"The":[0,76,117,149,214],"golden":[1,198],"ratio":[2,199],"φ":[3,36,155,167,194,217],"appears":[4],"throughout":[5],"Computational":[6],"Finitism:":[7],"in":[8,16,24,81,122,159,168],"the":[9,13,17,25,41,56,73,86,94,100,107,123,126,142,174,178,185,207,211],"Fibonacci":[10],"weights":[11],"of":[12,20,40,55,125,188],"Golden-Fano":[14],"Automaton,":[15],"φ-fractal":[18],"scaling":[19],"information":[21,58],"dynamics,":[22],"and":[23,67,106,144,177,183],"antifragile":[26],"entropy":[27],"≈":[28],"0.988.":[29],"Its":[30],"status,":[31],"however,":[32],"remains":[33],"ambiguous.":[34],"Is":[35],"a":[37,44,114,130,152,202],"geometric":[38],"property":[39],"measurement":[42],"interface,":[43],"convenient":[45],"coordinate":[46],"imposed":[47],"by":[48,92],"observers,":[49],"or":[50],"an":[51],"intrinsic":[52],"efficiency":[53,71],"limit":[54],"universe's":[57],"processing?":[59],"We":[60,128,170],"argue":[61],"that":[62,68,135,162],"both":[63],"readings":[64],"are":[65,99,147],"correct,":[66],"for":[69,133],"universal":[70],"limits":[72],"distinction":[74],"dissolves.":[75],"ontic":[77,143],"reading":[78,119],"is":[79,85,120,200,206],"grounded":[80,121],"Hurwitz's":[82],"theorem":[83,96],"(φ":[84],"\\"most":[87],"irrational\\"":[88],"number,":[89],"least":[90],"approximable":[91],"rationals),":[93],"KAM":[95],"(golden":[97],"tori":[98],"last":[101],"to":[102,173,210],"break":[103],"under":[104],"perturbation),":[105],"Pell":[108],"equation":[109],"(optimal":[110],"discrete":[111,138,160],"rotation":[112],"on":[113],"pixelated":[115],"lattice).":[116],"epistemic":[118,145],"base-independence":[124],"substrate.":[127],"propose":[129],"formal":[131],"duality:":[132],"constraints":[134],"any":[136],"long-lived":[137],"system":[139],"must":[140],"satisfy,":[141],"descriptions":[146],"equivalent.":[148],"duality":[150],"makes":[151],"falsifiable":[153],"prediction:":[154],"should":[156],"emerge":[157],"spontaneously":[158],"systems":[161],"were":[163],"not":[164,201],"designed":[165],"with":[166],"mind.":[169],"connect":[171],"this":[172],"Fano":[175,190],"geometry":[176,191],"percolation":[179],"threshold":[180],"=":[181],"0.325,":[182],"identify":[184],"precise":[186],"division":[187],"labor:":[189],"governs":[192,195],"structure,":[193],"dynamics.":[196],"\\"The":[197],"magic":[203],"number.":[204],"It":[205],"unique":[208],"solution":[209],"anti-resonance":[212],"problem.":[213],"universe":[215],"uses":[216],"because":[218],"it":[219],"has":[220],"no":[221],"choice.\\"":[222]}