{"id":"https://openalex.org/W7225638172","doi":"https://doi.org/10.33774/coe-2026-x83l6","title":"Flytrons within the Law of the Unity of Being of the Triune Substance","display_name":"Flytrons within the Law of the Unity of Being of the Triune Substance","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225638172","doi":"https://doi.org/10.33774/coe-2026-x83l6"},"language":"en","primary_location":{"id":"doi:10.33774/coe-2026-x83l6","doi":"https://doi.org/10.33774/coe-2026-x83l6","is_oa":true,"landing_page_url":"https://doi.org/10.33774/coe-2026-x83l6","pdf_url":"https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/6acfd9a353721e95054f1a83/original/flytrons-within-the-law-of-the-unity-of-being-of-the-triune-substance.pdf","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/6acfd9a353721e95054f1a83/original/flytrons-within-the-law-of-the-unity-of-being-of-the-triune-substance.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147190751","display_name":"Anatolii Mukha","orcid":"https://orcid.org/0009-0005-4614-6667","observed_orcids":["https://orcid.org/0009-0005-4614-6667"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Anatolii Mukha","raw_affiliation_strings":["Independent Researcher , retired person Kharkiv , Ukraine"],"raw_orcid":"https://orcid.org/0009-0005-4614-6667","affiliations":[{"raw_affiliation_string":"Independent Researcher , retired person Kharkiv , Ukraine","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5147190751"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10224","display_name":"Quantum Chromodynamics and Particle Interactions","score":0.9208999872207642,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10224","display_name":"Quantum Chromodynamics and Particle Interactions","score":0.9208999872207642,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.01899999938905239,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.014299999922513962,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mass-gap","display_name":"mass gap","score":0.9359999895095825},{"id":"https://openalex.org/keywords/quantum-yang-mills-theory","display_name":"quantum Yang-Mills theory","score":0.9150000214576721},{"id":"https://openalex.org/keywords/clay-millennium-prize","display_name":"Clay Millennium Prize","score":0.6610000133514404},{"id":"https://openalex.org/keywords/arithmetic-invariants","display_name":"arithmetic invariants","score":0.7009999752044678},{"id":"https://openalex.org/keywords/osterwalder-schrader-axioms","display_name":"Osterwalder-Schrader axioms","score":0.8840000033378601},{"id":"https://openalex.org/keywords/euclidean-quantum-field-theory","display_name":"Euclidean quantum field theory","score":0.7020000219345093},{"id":"https://openalex.org/keywords/su-n-yang-mills-theory","display_name":"SU(N) Yang-Mills theory","score":0.7990000247955322},{"id":"https://openalex.org/keywords/non-perturbative-quantum-field-theory","display_name":"non-perturbative quantum field theory","score":0.8090000152587891},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"spectral gap","score":0.4230000078678131}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6985999941825867},{"id":"https://openalex.org/C32518243","wikidata":"https://www.wikidata.org/wiki/Q907926","display_name":"Holonomy","level":2,"score":0.5489000082015991},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5440000295639038},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5116000175476074},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4909000098705292},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4726000130176544},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4490000009536743},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.43459999561309814},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4262999892234802},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4180999994277954},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4138000011444092},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.3896999955177307},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.382999986410141},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3815000057220459},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3693000078201294},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.32420000433921814},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3192000091075897},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.3084000051021576},{"id":"https://openalex.org/C2780297109","wikidata":"https://www.wikidata.org/wiki/Q917390","display_name":"Essential spectrum","level":3,"score":0.29330000281333923},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C146710177","wikidata":"https://www.wikidata.org/wiki/Q1154996","display_name":"Fiber bundle","level":3,"score":0.28439998626708984},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.2833000123500824},{"id":"https://openalex.org/C125773388","wikidata":"https://www.wikidata.org/wiki/Q792542","display_name":"Axiomatic system","level":3,"score":0.27869999408721924},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.2680000066757202},{"id":"https://openalex.org/C40976572","wikidata":"https://www.wikidata.org/wiki/Q2330873","display_name":"Gauge (firearms)","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.33774/coe-2026-x83l6","doi":"https://doi.org/10.33774/coe-2026-x83l6","is_oa":true,"landing_page_url":"https://doi.org/10.33774/coe-2026-x83l6","pdf_url":"https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/6acfd9a353721e95054f1a83/original/flytrons-within-the-law-of-the-unity-of-being-of-the-triune-substance.pdf","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.33774/coe-2026-x83l6","doi":"https://doi.org/10.33774/coe-2026-x83l6","is_oa":true,"landing_page_url":"https://doi.org/10.33774/coe-2026-x83l6","pdf_url":"https://www.cambridge.org/engage/api-gateway/coe/assets/orp/resource/item/6acfd9a353721e95054f1a83/original/flytrons-within-the-law-of-the-unity-of-being-of-the-triune-substance.pdf","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225638172.pdf","grobid_xml":"https://content.openalex.org/works/W7225638172.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1970564715","https://openalex.org/W7212002760","https://openalex.org/W7212313511","https://openalex.org/W7212593891","https://openalex.org/W7213579769","https://openalex.org/W7213581296","https://openalex.org/W7214026557","https://openalex.org/W7214114170","https://openalex.org/W7214425027","https://openalex.org/W7214490711","https://openalex.org/W7214519530","https://openalex.org/W7214538542","https://openalex.org/W7214935461","https://openalex.org/W7215785229","https://openalex.org/W7219707879","https://openalex.org/W7220393511","https://openalex.org/W7220677037","https://openalex.org/W7221811798","https://openalex.org/W7221830871"],"related_works":["https://openalex.org/W7154710888","https://openalex.org/W6911818656","https://openalex.org/W7171314596","https://openalex.org/W6893325725","https://openalex.org/W6930803520","https://openalex.org/W7222916299","https://openalex.org/W6911996753","https://openalex.org/W6968317485","https://openalex.org/W4412911966","https://openalex.org/W6968447705"],"abstract_inverted_index":{"We":[0,104],"prove":[1,105],"the":[2,13,18,27,41,91,163],"existence":[3],"of":[4],"a":[5,31,67,95,140,156,173],"mass":[6,143],"gap":[7],"in":[8,132],"quantum":[9,70],"Yang\u2013Mills":[10,137],"theory":[11,89],"within":[12],"ZEBTS":[14],"axiomatic":[15],"framework,":[16],"addressing":[17],"Clay":[19],"Millennium":[20],"Prize":[21],"problem.":[22],"Our":[23,145],"approach":[24],"relies":[25],"on":[26],"flytron":[28],"model,":[29],"introducing":[30],"discrete\u2011arithmetic":[32],"structure":[33,158],"that":[34,166],"encodes":[35],"gauge":[36],"bundle":[37],"topology":[38],"and":[39,54,101,153],"controls":[40],"spectrum.":[42],"Each":[43],"state":[44],"is":[45,127,130],"assigned":[46],"an":[47,113],"integer":[48],"weight":[49],"derived":[50],"from":[51,172],"holonomy":[52],"traces":[53],"arithmetic":[55,154],"invariants,":[56],"determining":[57],"energy":[58],"via":[59],"$E_\\pi":[60,117],"=":[61],"\\Lambda":[62,119,124],"\\cdot":[63],"\\log":[64,120,125],"\\Psi(\\pi)$":[65],"as":[66],"discrete":[68],"topological":[69,80],"number.":[71],"Discreteness":[72],"ensures":[73],"no":[74],"continuous":[75],"spectrum":[76],"near":[77],"zero,":[78],"while":[79],"dependence":[81],"guarantees":[82],"persistence":[83],"across":[84],"all":[85],"sectors.":[86],"The":[87],"Euclidean":[88],"satisfies":[90],"Osterwalder\u2013Schrader":[92],"axioms,":[93],"yielding":[94],"valid":[96],"Hilbert":[97],"space,":[98],"self\u2011adjoint":[99],"Hamiltonian,":[100],"local":[102],"observables.":[103],"$\\Psi(\\pi)":[106],"\\ge":[107,118],"2$":[108,121],"for":[109,135,159],"nontrivial":[110],"loops,":[111],"establishing":[112],"explicit":[114],"lower":[115],"bound":[116],"so":[122],"$(0,":[123],"2)$":[126],"empty.":[128],"This":[129],"formalized":[131],"Theorem":[133],"MG":[134],"$\\mathrm{SU}(N)$":[136],"theory,":[138,150],"confirming":[139],"gauge\u2011invariant,":[141],"stable":[142],"gap.":[144],"method":[146],"unites":[147],"topology,":[148],"spectral":[149],"operator":[151],"algebras,":[152],"into":[155],"coherent":[157],"nonperturbative":[160],"QFT,":[161],"validating":[162],"foundational":[164],"principle":[165],"key":[167],"physical":[168],"properties":[169],"emerge":[170],"rigorously":[171],"unified":[174],"mathematical":[175],"framework.":[176]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
