{"id":"https://openalex.org/W7213187155","doi":"https://doi.org/10.48550/arxiv.2609.11965","title":"Gauge Rigidity and Holonomy Classification of Time-Scaled Intertwining Cocycles on Hilbert Bundles","display_name":"Gauge Rigidity and Holonomy Classification of Time-Scaled Intertwining Cocycles on Hilbert Bundles","publication_year":2026,"publication_date":"2026-08-21","ids":{"openalex":"https://openalex.org/W7213187155","doi":"https://doi.org/10.48550/arxiv.2609.11965"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.11965","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11965","pdf_url":"https://arxiv.org/pdf/2609.11965","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.11965","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5117458691","display_name":"Anton Alexa","orcid":"https://orcid.org/0009-0007-0014-2446","observed_orcids":["https://orcid.org/0009-0007-0014-2446"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alexa, Anton","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5117458691"],"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.7860999703407288,"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"}},"topics":[{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.7860999703407288,"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"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.16699999570846558,"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"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.01140000019222498,"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/hilbert-bundles","display_name":"Hilbert bundles","score":0.7720000147819519},{"id":"https://openalex.org/keywords/operator-networks","display_name":"operator networks","score":0.800000011920929},{"id":"https://openalex.org/keywords/transport-companies","display_name":"transport companies","score":0.6349999904632568},{"id":"https://openalex.org/keywords/scaling-fields","display_name":"scaling fields","score":0.5759999752044678},{"id":"https://openalex.org/keywords/berry-connection","display_name":"Berry connection","score":0.8930000066757202},{"id":"https://openalex.org/keywords/centralizers","display_name":"centralizers","score":0.7730000019073486},{"id":"https://openalex.org/keywords/representations-of-fundamental-groups","display_name":"fundamental group representations","score":0.8799999952316284},{"id":"https://openalex.org/keywords/parity-operator","display_name":"parity operator","score":0.6700000166893005},{"id":"https://openalex.org/keywords/monodromy","display_name":"monodromy","score":0.5460000038146973}],"concepts":[{"id":"https://openalex.org/C32518243","wikidata":"https://www.wikidata.org/wiki/Q907926","display_name":"Holonomy","level":2,"score":0.9556000232696533},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6901999711990356},{"id":"https://openalex.org/C106953101","wikidata":"https://www.wikidata.org/wiki/Q1814838","display_name":"Parallel transport","level":2,"score":0.6291000247001648},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5576000213623047},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5468000173568726},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5065000057220459},{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.4309000074863434},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.40209999680519104},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.38019999861717224},{"id":"https://openalex.org/C188313703","wikidata":"https://www.wikidata.org/wiki/Q1972470","display_name":"Unitary operator","level":3,"score":0.37689998745918274},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.36239999532699585},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.35510000586509705},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.3183000087738037},{"id":"https://openalex.org/C146710177","wikidata":"https://www.wikidata.org/wiki/Q1154996","display_name":"Fiber bundle","level":3,"score":0.29809999465942383},{"id":"https://openalex.org/C56907000","wikidata":"https://www.wikidata.org/wiki/Q1365548","display_name":"Principal bundle","level":3,"score":0.2833999991416931},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28279998898506165},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C75174853","wikidata":"https://www.wikidata.org/wiki/Q190629","display_name":"Centralizer and normalizer","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.26159998774528503},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.260699987411499},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C2992500303","wikidata":"https://www.wikidata.org/wiki/Q5680845","display_name":"Operator matrix","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.2556999921798706}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.11965","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11965","pdf_url":"https://arxiv.org/pdf/2609.11965","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.11965","doi":"https://doi.org/10.48550/arxiv.2609.11965","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.11965","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.11965","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11965","pdf_url":"https://arxiv.org/pdf/2609.11965","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213187155.pdf","grobid_xml":"https://content.openalex.org/works/W7213187155.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7171636286","https://openalex.org/W3133288230","https://openalex.org/W7017953183","https://openalex.org/W7130564931","https://openalex.org/W2888504937","https://openalex.org/W3087657202","https://openalex.org/W2130014121","https://openalex.org/W7134926643","https://openalex.org/W2950679020","https://openalex.org/W2513348884"],"abstract_inverted_index":{"We":[0],"extend":[1],"the":[2,20,23,42,65,74,87,96,99,126,136,148,152,161],"discrete":[3],"gauge":[4],"rigidity":[5],"of":[6,89,98,108,133,156,169],"time-scaled":[7],"intertwining":[8,66],"cocycles":[9,73,125],"to":[10,57,95,147],"operator":[11,79,150],"networks":[12],"over":[13,85,142],"a":[14,50,58,77,82,90],"connected":[15],"manifold":[16],"M":[17],"and":[18,101],"classify":[19],"holonomy":[21,88,127,145],"that":[22,41],"continuous":[24,51],"setting":[25],"admits.":[26],"For":[27,71],"dissipative":[28],"semigroups":[29],"$S_x(t)=e^{-tA_x}$":[30],"linked":[31],"by":[32,64,116,130,165],"transport":[33,75,114],"operators":[34],"$K_\u03b3S_{\u03b3(0)}(t)=S_{\u03b3(1)}(\u03bb(\u03b3)t)K_\u03b3$":[35],"along":[36],"paths":[37],"$\u03b3$,":[38],"we":[39],"prove":[40],"scaling":[43],"field":[44],"carries":[45],"no":[46],"monodromy:":[47],"$\u03bb(x,y)=\u03c4(x)/\u03c4(y)$":[48],"for":[49,122],"positive":[52],"function":[53],"$\u03c4$,":[54],"unique":[55],"up":[56],"multiplicative":[59],"constant,":[60],"with":[61],"multiplicativity":[62],"forced":[63],"relation":[67],"rather":[68],"than":[69],"assumed.":[70],"regular":[72],"defines":[76],"bounded":[78],"connection":[80,154],"on":[81,106],"Hilbert":[83],"bundle":[84],"M;":[86],"closed":[91],"loop":[92],"is":[93,111,128,163],"confined":[94],"commutant":[97],"generator":[100],"decomposes":[102],"into":[103],"spectral":[104],"sectors,":[105],"each":[107],"which":[109],"it":[110],"adiabatic":[112],"(Berry-Wilczek-Zee)":[113],"twisted":[115],"an":[117],"independent":[118],"commutant-valued":[119],"sector":[120],"potential;":[121],"flat":[123],"unitary":[124,131],"classified":[129],"representations":[132],"$\u03c0_1(M)$":[134],"in":[135],"commutant.":[137],"An":[138],"explicit":[139],"rotating":[140],"network":[141],"$S^1$":[143],"exhibits":[144],"equal":[146],"parity":[149],"while":[151],"Berry":[153],"one-form":[155],"every":[157],"level":[158],"vanishes":[159],"identically:":[160],"monodromy":[162],"carried":[164],"$\\mathbb{Z}_2$":[166],"orientation":[167],"classes":[168],"Moebius":[170],"eigenline":[171],"bundles.":[172]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-15T00:00:00"}