Reflection as a Resource: Stratified Representability, Fixed Points Under Restricted Internalization, and a Selector-Strength Hierarchy Paper 28 of the NEMS Suite

{"Paper":[0,19],"26":[1],"(General":[2],"Self-Reference":[3],"Calculus)":[4],"showed":[5],"that":[6,50,202],"any":[7],"system":[8,74],"with":[9,140],"full":[10],"representability":[11,64,235],"(repr-spec)":[12],"satisfies":[13],"the":[14,35,91,102,149,177,227,241,246],"Master":[15],"Fixed-Point":[16],"Theorem":[17],"(\\\\MFP-1).":[18],"27":[20],"(Closure":[21],"Audits)":[22],"formalized":[23],"when":[24],"determinacy":[25],"is":[26,42,84,88,108,127,176,209,256],"genuine":[27],"vs.":[28],"silently":[29],"outsourced.":[30],"The":[31,81,207],"present":[32],"paper":[33],"fills":[34],"graded":[36],"middle":[37],"ground:":[38],"how":[39,49],"much":[40],"internalization":[41,168],"enough":[43],"for":[44],"which":[45],"fixed":[46,119,155],"points,":[47],"and":[48,187,197,236],"maps":[51],"to":[52,170,193,198],"selector":[53],"strength":[54],"(NEMS":[55],"IIa/IIb)":[56],"in":[57,79,211,230],"an":[58],"abstract,":[59],"non-physics":[60],"way.":[61],"We":[62,100,191],"parameterize":[63],"by":[65],"a":[66,73,117,133,154,161,182],"class":[67],"\\\\RepClass":[68,87,107,115,126,143,248],"\\\\subseteq":[69],"(\\\\SRICod":[70],"\\\\to":[71],"\\\\SRIObj):":[72],"may":[75],"only":[76,222],"internalize":[77],"transformers":[78],"\\\\RepClass.":[80],"key":[82],"notion":[83],"diagonal":[85,150],"closure:":[86],"closed":[89],"under":[90],"diagonalization":[92],"template":[93],"F":[94,113,141],"\\\\mapsto":[95,97],"(c":[96],"F(\\\\ulcorner":[98,123],"\\\\run(c,c)\\\\urcorner)).":[99],"prove":[101,132],"Diagonal":[103],"Closure":[104],"Theorem:":[105],"if":[106],"diagonally":[109,129],"closed,":[110,130],"then":[111],"every":[112,251],"\\\\in":[114,142],"has":[116],"mixed":[118],"point":[120,156],"p":[121],"\\\\simeq":[122],"p\\\\urcorner).":[124],"When":[125],"not":[128,250],"we":[131,180],"formal":[134,247],"method-level":[135],"separation:":[136],"identity-only":[137],"on":[138],"\\\\mathbbN":[139],"but":[144],"G_F":[145],"\\\\notin":[146],"\\\\RepClass,":[147],"so":[148],"construction":[151],"cannot":[152],"produce":[153],"via":[157],"\\\\repr(G_F).":[158],"This":[159],"yields":[160],"resource":[162],"theory":[163],"of":[164,167],"reflection:":[165],"levels":[166],"correspond":[169],"achievable":[171],"fixed-point":[172],"guarantees.":[173],"Full":[174],"\\\\SRIz":[175],"top":[178],"level;":[179],"deliver":[181],"Lean-proved":[183],"strict":[184,242],"separation":[185],"(identity-only)":[186],"roadmap":[188],"further":[189],"hierarchies.":[190],"bridge":[192],"Closure's":[194],"internality":[195],"predicate":[196],"SelfReference's":[199],"MFP-1,":[200],"showing":[201],"Reflection":[203,228],"extends":[204],"both":[205],"conservatively.":[206],"development":[208],"mechanized":[210],"Lean":[212],"4":[213],"(without":[214],"custom":[215],"axioms":[216],"beyond":[217],"Lean/mathlib;":[218],"classical":[219],"choice":[220],"used":[221],"where":[223],"explicitly":[224],"stated),":[225],"as":[226],"library":[229],"nems-lean.":[231],"Trust":[232],"boundary.":[233],"Stratified":[234],"diagonal-closure":[237],"hypotheses":[238],"are":[239,244],"explicit;":[240],"separations":[243],"about":[245],"constraints,":[249],"physical":[252],"\\"reflection\\"":[253],"metaphor.":[254],"Mechanization":[255],"nems-lean":[257],".":[258,260],"See":[259]}