Hidden Fixed Points in Olympiad Extremes — E8 Intelligence Research
{"FINDING:":[0],"The":[1,150],"\\"hardest\\"":[2],"competition":[3],"problems":[4],"cluster":[5],"around":[6],"structural":[7],"invariants":[8],"—":[9,27,54,89,124],"the":[10,134,137,162],"1988":[11,38,118],"IMO":[12,18,39,64],"Problem":[13],"6":[14],"(Vieta":[15],"jumping),":[16],"2011":[17,63],"Q2":[19],"(windmill":[20],"combinatorics),":[21],"and":[22,146],"Putnam's":[23],"hardest":[24,100],"(group-theoretic":[25],"symmetry)":[26],"each":[28,83],"revealing":[29],"hidden":[30],"algebraic":[31],"or":[32],"combinatorial":[33],"fixed":[34],"points.":[35],"|":[36,116],"MATH:":[37],"P6:":[40],"if":[41],"a²+b²":[42],"=":[43],"k(ab+1)":[44],"for":[45,66],"positive":[46],"integers,":[47],"then":[48],"k":[49],"is":[50],"a":[51,78,92,107,113],"perfect":[52,122],"square":[53],"proof":[55],"via":[56],"Vieta":[57],"jumping":[58],"(descent":[59],"on":[60,106],"quadratic":[61],"roots).":[62],"Q2:":[65],"odd":[67],"n,":[68],"any":[69],"arrangement":[70],"of":[71,126,161],"n":[72],"points":[73],"in":[74],"general":[75],"position":[76],"admits":[77],"\\"windmill\\"":[79],"rotation":[80],"that":[81],"visits":[82],"point":[84],"exactly":[85],"once":[86],"per":[87],"half-turn":[88],"equivalent":[90],"to":[91],"cyclic":[93],"order":[94],"invariant":[95],"under":[96],"180°":[97],"rotation.":[98],"Putnam":[99],"(2014":[101],"B6?):":[102],"involves":[103],"group":[104],"action":[105],"set":[108],"with":[109],"orbit-stabilizer":[110],"counting,":[111],"yielding":[112],"binomial":[114],"identity.":[115],"CONNECTION:":[117],"P6's":[119],"k=1,4,9,...":[120],"are":[121],"squares":[123,128],"ratios":[125,142],"consecutive":[127],"approach":[129],"1,":[130],"not":[131],"golden;":[132],"but":[133],"descent":[135],"mirrors":[136],"Euclidean":[138],"algorithm,":[139],"whose":[140],"worst-case":[141],"involve":[143],"φ":[144],"(1.618)":[145],"its":[147],"reciprocal":[148],"(0.618).":[149],"windmill":[151],"pro":[152],"Author:":[153],"Andrew":[154],"Stewart":[155],"Caldin,":[156],"Independent":[157],"Researcher,":[158],"UK.":[159],"Part":[160],"E8":[163],"Intelligence":[164],"Research":[165],"series.":[166],"Platform:":[167],"e8intelligence.com":[168]}
Authors
- Andrew Stewart Caldin
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-09-01
- DOI
- https://doi.org/10.5281/zenodo.22235729
- Primary Topic
- Computability, Logic, AI Algorithms
- Type
- preprint