A Geometric Proof of the Yang-Mills Mass Gap, Quark Confinement, and Strong CP Conservation

{"Abstract:":[0],"We":[1,84],"present":[2],"a":[3,35,67,117,124,140],"rigorous":[4],"non-perturbative":[5],"proof":[6],"of":[7,21,59],"the":[8,29,60,76,80,97,102,107,110,146,150,158,163,173,177],"Yang-Mills":[9],"mass":[10,127],"gap":[11,128],"by":[12],"reconstructing":[13],"spacetime":[14],"as":[15,34,42,91,139],"an":[16,43],"emergent":[17],"holographic":[18],"Haar-Random":[19,136],"Superposition":[20],"Sierpinski":[22],"tensor":[23],"networks.":[24],"To":[25],"enforce":[26],"Gauss's":[27],"Law,":[28],"Hilbert":[30],"space":[31],"is":[32],"formulated":[33],"topological":[36],"String-Net":[37],"Condensate.":[38],"Fractal":[39],"lacunarity":[40],"acts":[41,138],"effective":[44],"non-trivial":[45],"Polyakov":[46],"loop":[47],"at":[48],"T=0,":[49],"forcing":[50],"BPST":[51],"instantons":[52],"into":[53],"KVLL":[54],"Constituent":[55],"Monopoles.":[56],"The":[57,71],"super-renormalizability":[58],"UV":[61],"limit":[62],"(d_s":[63],"<":[64],"4)":[65],"guarantees":[66],"Second-Order":[68],"Phase":[69],"Transition.":[70],"fractional":[72,87],"topology":[73],"perfectly":[74],"cancels":[75],"dimension":[77],"divergence":[78],"via":[79],"dual":[81],"Coxeter":[82],"number.":[83],"prove":[85],"that":[86],"non-local":[88],"terms":[89],"behave":[90],"irrelevant":[92],"operators,":[93],"strictly":[94,125],"decaying":[95],"in":[96,176],"deep":[98],"IR":[99],"to":[100],"restore":[101],"Wightman":[103],"Microcausality":[104],"Axiom.":[105],"In":[106],"macroscopic":[108],"limit,":[109],"Haar-ensemble":[111],"restores":[112],"Osterwalder-Schrader":[113],"Reflection":[114],"Positivity,":[115],"yielding":[116],"unitary,":[118],"local":[119],"R^4":[120],"zero-temperature":[121],"theory":[122],"with":[123],"positive":[126],"and":[129,148,182],"Area":[130],"Law":[131],"Quark":[132],"Confinement.":[133],"Finally,":[134],"this":[135],"ensemble":[137],"geometric":[141],"Peccei-Quinn":[142],"mechanism,":[143],"washing":[144],"out":[145],"theta-vacuum":[147],"solving":[149,162],"Strong":[151],"CP":[152],"Problem.":[153],"Note:":[154],"This":[155],"preprint":[156],"provides":[157],"explicit":[159],"mathematical":[160],"derivation":[161],"Clay":[164],"Mathematics":[165],"Institute":[166],"Millennium":[167],"Prize":[168],"problem,":[169],"stemming":[170],"directly":[171],"from":[172],"framework":[174],"introduced":[175],"foundational":[178],"treatise":[179],"\\"Geometry,":[180],"Tensors,":[181],"Quantum":[183],"Gravity\\"":[184],"(Unified":[185],"Grand":[186],"Synthesis).":[187]}

Authors

Institutions

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-04
DOI
https://doi.org/10.5281/zenodo.22301094
Primary Topic
Noncommutative and Quantum Gravity Theories
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
preprint

A Geometric Proof of the Yang-Mills Mass Gap, Quark Confinement, and Strong CP Conservation

Reinaldo M. Silva-Filho
Zenodo (CERN European Organization for Nuclear Research)
Noncommutative and Quantum Gravity Theories
preprint

A Geometric Proof of the Yang-Mills Mass Gap, Quark Confinement, and Strong CP Conservation

Reinaldo M. Silva-Filho
preprint en

Abstract

Abstract: We present a rigorous non-perturbative proof of the Yang-Mills mass gap by reconstructing spacetime as an emergent holographic Haar-Random Superposition of Sierpinski tensor networks. To enforce Gauss's Law, the Hilbert space is formulated as a topological String-Net Condensate. Fractal lacunarity acts as an effective non-trivial Polyakov loop at T=0, forcing BPST instantons into KVLL Constituent Monopoles. The super-renormalizability of the UV limit (d_s < 4) guarantees a Second-Order Phase Transition. The fractional topology perfectly cancels the dimension divergence via the dual Coxeter number. We prove that fractional non-local terms behave as irrelevant operators, strictly decaying in the deep IR to restore the Wightman Microcausality Axiom. In the macroscopic limit, the Haar-ensemble restores Osterwalder-Schrader Reflection Positivity, yielding a unitary, local R^4 zero-temperature theory with a strictly positive mass gap and Area Law Quark Confinement. Finally, this Haar-Random ensemble acts as a geometric Peccei-Quinn mechanism, washing out the theta-vacuum and solving the Strong CP Problem. Note: This preprint provides the explicit mathematical derivation solving the Clay Mathematics Institute Millennium Prize problem, stemming directly from the framework introduced in the foundational treatise "Geometry, Tensors, and Quantum Gravity" (Unified Grand Synthesis).

Zenodo (CERN European Organization for Nuclear Research)
Universidade Federal de Lavras (BR)
Life in Land
Noncommutative and Quantum Gravity Theories
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.