{"id":"https://openalex.org/W7225328742","doi":"https://doi.org/10.5281/zenodo.23981640","title":"The Prime Field Architecture of the Arithmetic Modulation Field: Yang-Mills Existence and Mass Gap on R\u2074 \u2014 Volume 5: The Hilbert Space and the Vacuum Sector","display_name":"The Prime Field Architecture of the Arithmetic Modulation Field: Yang-Mills Existence and Mass Gap on R\u2074 \u2014 Volume 5: The Hilbert Space and the Vacuum Sector","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225328742","doi":"https://doi.org/10.5281/zenodo.23981640"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23981640","doi":"https://doi.org/10.5281/zenodo.23981640","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23981640","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23981640","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5143506205","display_name":"David-Michael Skerl","orcid":"https://orcid.org/0009-0001-7647-382X","observed_orcids":["https://orcid.org/0009-0001-7647-382X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Skerl, David-Michael","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0001-7647-382X","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5143506205"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.38769999146461487,"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":0.38769999146461487,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.17970000207424164,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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":0.07090000063180923,"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/yang-mills-existence-and-mass-gap","display_name":"Yang-Mills mass gap","score":0.8809999823570251},{"id":"https://openalex.org/keywords/hilbert-spaces","display_name":"Hilbert spaces","score":0.8539999723434448},{"id":"https://openalex.org/keywords/vacuum-sector","display_name":"vacuum sector","score":0.9779999852180481},{"id":"https://openalex.org/keywords/wightman-axioms","display_name":"Wightman axioms","score":0.7940000295639038},{"id":"https://openalex.org/keywords/separable-hilbert-space","display_name":"separable Hilbert space","score":0.7110000252723694},{"id":"https://openalex.org/keywords/prime-numbers","display_name":"prime numbers","score":0.6140000224113464},{"id":"https://openalex.org/keywords/su-3-symmetry","display_name":"SU(3) symmetry","score":0.8569999933242798},{"id":"https://openalex.org/keywords/light-cone","display_name":"light cone","score":0.7110000252723694},{"id":"https://openalex.org/keywords/resolution-of-identity","display_name":"resolution of the identity","score":0.7260000109672546}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7530999779701233},{"id":"https://openalex.org/C171636804","wikidata":"https://www.wikidata.org/wiki/Q1149458","display_name":"Compactness theorem","level":4,"score":0.49570000171661377},{"id":"https://openalex.org/C17566778","wikidata":"https://www.wikidata.org/wiki/Q467602","display_name":"Proofs of Fermat's little theorem","level":5,"score":0.48100000619888306},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.48069998621940613},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.47620001435279846},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4284000098705292},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.4221000075340271},{"id":"https://openalex.org/C115047598","wikidata":"https://www.wikidata.org/wiki/Q54505","display_name":"Quantum field theory","level":2,"score":0.3935999870300293},{"id":"https://openalex.org/C68227491","wikidata":"https://www.wikidata.org/wiki/Q2914432","display_name":"No-go theorem","level":4,"score":0.39100000262260437},{"id":"https://openalex.org/C194886279","wikidata":"https://www.wikidata.org/wiki/Q430271","display_name":"Fundamental theorem","level":3,"score":0.38670000433921814},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3822000026702881},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.375900000333786},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3702999949455261},{"id":"https://openalex.org/C116335209","wikidata":"https://www.wikidata.org/wiki/Q240651","display_name":"Prime element","level":3,"score":0.3580999970436096},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3458999991416931},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34299999475479126},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.33799999952316284},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.32510000467300415},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3215000033378601},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.3077000081539154},{"id":"https://openalex.org/C6947382","wikidata":"https://www.wikidata.org/wiki/Q1143773","display_name":"Vacuum energy","level":2,"score":0.2971999943256378},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C198470675","wikidata":"https://www.wikidata.org/wiki/Q3983971","display_name":"Kelvin\u2013Stokes theorem","level":5,"score":0.2939000129699707},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C190565394","wikidata":"https://www.wikidata.org/wiki/Q6935001","display_name":"Multiplicative number theory","level":4,"score":0.265500009059906},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C130498168","wikidata":"https://www.wikidata.org/wiki/Q170008","display_name":"Arithmetic progression","level":2,"score":0.25839999318122864}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23981640","doi":"https://doi.org/10.5281/zenodo.23981640","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23981640","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23981641","doi":"https://doi.org/10.5281/zenodo.23981641","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23981641","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23981640","doi":"https://doi.org/10.5281/zenodo.23981640","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23981640","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7221456947","https://openalex.org/W7225331086","https://openalex.org/W7225244811","https://openalex.org/W7225249160","https://openalex.org/W7225269568","https://openalex.org/W7225246593","https://openalex.org/W7225299600","https://openalex.org/W7221436141","https://openalex.org/W7221436347","https://openalex.org/W7170030730"],"abstract_inverted_index":{"Volume":[0],"5":[1],"of":[2,8,57,62,100,164],"14.":[3],"Establishes":[4,134],"the":[5,9,13,17,22,58,69,114,129,135,144,148,157,175,178],"quantum":[6],"structure":[7],"Prime":[10],"Field":[11],"Architecture:":[12],"Hilbert":[14],"space":[15],"H_PFA,":[16],"vacuum":[18,140],"sector":[19,141],"V,":[20],"and":[21,156],"arithmetic":[23,145,179],"mass":[24],"gap":[25,150],"\u0394":[26,85,181],"=":[27,29,41,64,86,88,109,111,124,152,162,182],"|V|":[28,87],"13":[30,55,89],">":[31,90,154],"0.":[32],"Proves":[33,53,78,103,118],"Theorem":[34,54,79,104,119],"12":[35],"(H_PFA":[36],"separable,":[37],"complete,":[38],"positive-definite):":[39],"H_PFA":[40],"L\u00b2(\u2124_{\u22650}":[42],"\u00d7":[43],"P1)":[44],"\u2245":[45],"l\u00b2(\u2115)":[46],"\u2297":[47],"\u2102\u2078,":[48],"satisfying":[49],"Wightman":[50],"Axiom":[51],"W1.":[52],"(Purity":[56],"Vacuum):":[59],"every":[60],"element":[61],"V":[63,142],"{1,7,11,13,17,19,23,29,31,37,41,43,47}":[65],"is":[66,113,128,174],"prime":[67],"(or":[68],"Cornerstone":[70],"n=1);":[71],"zero":[72],"P1":[73,116],"composites":[74],"exist":[75],"in":[76],"[1,48].":[77],"14":[80],"(The":[81],"Arithmetic":[82],"Mass":[83],"Gap):":[84],"0":[91],"\u2014":[92],"an":[93],"exact":[94],"theorem":[95,180],"about":[96],"counting":[97],"integers,":[98],"independent":[99],"any":[101],"parameter.":[102],"15":[105],"(First":[106],"Excitation):":[107],"n\u2080":[108],"49":[110],"7\u00b2":[112],"first":[115],"composite.":[117],"16":[120],"(Vacuum":[121],"Uniqueness):":[122],"|\u03a9\u2080\u27e9":[123],"(1/\u221a8)":[125],"\u03a3_{r\u2208P1}":[126],"|0,r\u27e9":[127],"unique":[130],"SU(3)-invariant":[131],"minimum-energy":[132],"state.":[133],"PFA":[136],"Light":[137],"Cone":[138],"(the":[139],"as":[143],"light":[146],"cone),":[147],"energy":[149],"\u0394_E":[151],"1":[153],"0,":[155],"completeness":[158],"relation":[159],"(PFAT":[160],"Decomposition":[161],"resolution":[163],"identity":[165],"on":[166],"H_PFA).":[167],"Answers":[168],"Wolfgang":[169],"Pauli's":[170],"1954":[171],"question":[172],"\"What":[173],"mass?\"":[176],"with":[177],"13.":[183]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-11-06T00:00:00"}
