Pre-Registered Confrontation of a K3 x T2 Dual-Scale Hypothesis with Data: Four Observables, Four Negative Verdicts, and a Common Cause
{"A":[0,351,373],"research":[1],"programme":[2,49,316],"built":[3],"around":[4],"a":[5,35,56,69,145,180,215,278,309,336],"\\"micro/macro":[6],"dual-scale\\"":[7],"reading":[8],"of":[9,23,99,155,188,205,230,314,427],"string":[10,17,173,217],"theory":[11],"on":[12,392],"$K3×":[13],"T^2$":[14],"identifies":[15],"the":[16,20,24,28,78,97,107,115,120,125,137,163,171,236,262,270,286,291,299,315,326,341,354,419,422,425,428],"scale":[18,174,218],"with":[19,73,85,140,179,404],"geometric":[21],"mean":[22],"Planck":[25],"length":[26,37,142],"and":[27,33,82,113,159,212,243,269,281,298,322,339,421],"Hubble":[29],"radius,":[30],"$\\\\alpha'=\\\\ell_P":[31,238],"c/H_0$,":[32],"hence":[34],"self-dual":[36],"$s=\\\\sqrt{\\\\ell_P":[38],"c/H_0}≈47":[39],"μ$m.":[40],"We":[41,284],"report":[42],"what":[43],"happens":[44],"when":[45],"every":[46,150,153,244],"observable":[47],"this":[48,393],"can":[50],"derive":[51],"—":[52,63,214,219],"without":[53],"passing":[54],"through":[55],"compactification":[57],"that":[58,128],"has":[59],"never":[60],"been":[61],"constructed":[62],"is":[64,80,104,160,235,247,320,323,328,379],"written":[65],"down,":[66],"frozen":[67],"by":[68,106,162,210,223,353],"git":[70],"tag":[71,384],"together":[72],"its":[74,156,303],"decision":[75],"rule":[76],"before":[77,302],"verdict":[79],"computed,":[81],"then":[83],"confronted":[84],"pinned":[86,276,307],"data.":[87],"There":[88],"are":[89,265,348,375],"exactly":[90],"four":[91,232],"such":[92],"observables.":[93],"(P1)":[94],"$s$":[95],"as":[96,267,273,296,308],"radius":[98],"one":[100,300],"large":[101],"extra":[102],"dimension":[103],"excluded":[105,161,222],"Eöt-Wash":[108],"torsion-balance":[109],"bound":[110,117,139],"($<30":[111],"μ$m)":[112],"fails":[114],"neutron-star":[116],"($<44":[118],"μ$m);":[119],"programme's":[121,172],"own":[122],"T-duality":[123],"fixes":[124],"order-one":[126],"factor":[127],"could":[129],"have":[130,201],"rescued":[131],"it.":[132],"(C-A)":[133],"Vacuum":[134],"energy":[135],"saturating":[136],"Cohen–Kaplan–Nelson":[138],"infrared":[141],"$c/H$":[143],"forces":[144],"deceleration":[146],"parameter":[147],"$q=+1/2$":[148],"at":[149,170,176],"epoch,":[151],"for":[152],"value":[154],"only":[157],"parameter,":[158],"observed":[164],"acceleration.":[165],"(C-B)":[166],"Pre-big-bang":[167],"relic":[168],"gravitons":[169],"end":[175],"$≈6×10^{-5}$":[177],"Hz":[178],"peak":[181],"$\\\\Omega_{\\\\rm":[182],"GW}≈10^{-65}$,":[183],"more":[184],"than":[185],"fifty":[186],"orders":[187],"magnitude":[189],"below":[190],"LISA's":[191],"design":[192],"sensitivity:":[193],"not":[194],"falsifiable":[195],"in":[196,249,417],"practice.":[197],"(C-C)":[198],"Cosmic":[199],"F-strings":[200],"$Gμ\\\\sim10^{-62}$:":[202],"likewise":[203],"out":[204],"reach.":[206],"The":[207,227,312],"premise":[208],"shared":[209],"C-B":[211],"C-C":[213],"meV":[216],"was":[220,306,415],"already":[221],"LHC":[224],"resonance":[225],"searches.":[226],"common":[228],"cause":[229],"all":[231,395],"negative":[233],"verdicts":[234],"identification":[237],"c/H_0$":[239],"itself.":[240],"Every":[241],"derivation":[242],"numerical":[245],"comparison":[246,304],"kernel-checked":[248],"Lean":[250,355,381],"4":[251,356,387],"(DualScaleCosmology,":[252],"50":[253],"theorems;":[254],"repository":[255],"621":[256,399],"theorems,":[257],"0":[258],"failing,":[259],"release":[260],"v3.16.1);":[261],"physical":[263,377],"identifications":[264],"stated":[266],"conjectures":[268],"experimental":[271],"bounds":[272,293],"literature,":[274],"each":[275],"to":[277],"source":[279],"file":[280],"line":[282],"range.":[283],"record":[285],"two":[287],"freezes":[288],"made":[289,301],"after":[290],"relevant":[292],"were":[294],"known":[295],"retrodictions,":[297],"document":[305],"forward":[310],"prediction.":[311],"mathematics":[313],"(moonshine,":[317],"dyons,":[318],"lattices)":[319],"unaffected":[321],"reported":[324],"separately;":[325],"lesson":[327],"methodological:":[329],"pre-registration":[330],"turned":[331],"an":[332],"\\"order-one":[333],"tension\\"":[334],"into":[335],"recorded":[337],"exclusion":[338],"located":[340],"single":[342],"assumption":[343],"responsible.":[344],"Epistemic":[345],"tiers.":[346],"Claims":[347],"labelled":[349],"Tier":[350,363,368,372],"(checked":[352],"kernel;":[357],"axioms":[358,403,406],"propext,":[359],"Classical.choice,":[360],"Quot.sound":[361],"only),":[362],"L":[364],"(literature,":[365],"cited)":[366],"or":[367],"C":[369],"(conjecture).":[370],"Only":[371],"statements":[374],"machine-checked;":[376],"interpretation":[378],"not.":[380],"artifact:":[382],"SocrateAI-Scientific-Agora-LeanMaster,":[383],"v3.17.0":[385],"(Lean":[386],"v4.33.1,":[388],"Mathlib).":[389],"Release":[390],"gates":[391],"tag:":[394],"ten":[396],"libraries":[397],"build;":[398],"theorems":[400],"pass":[401],"#print":[402],"standard":[405],"only;":[407],"no":[408],"sorry/admit.":[409],"AI-assisted":[410],"tooling":[411],"(Anthropic":[412],"Claude":[413],"models)":[414],"used":[416],"preparing":[418],"formalization":[420],"manuscript,":[423],"under":[424],"direction":[426],"author.":[429]}
Authors
- Xavier Callens
- SocrateAI Scientific Agora Collaboration
Institutions
- Laboratoire de Mathématiques d'Orsay (FR)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-09-18
- DOI
- https://doi.org/10.5281/zenodo.22837836
- Primary Topic
- International Science and Diplomacy
- Type
- preprint