{"id":"https://openalex.org/W7206174331","doi":"https://doi.org/10.5281/zenodo.22262030","title":"Frame Duality on the Number Line","display_name":"Frame Duality on the Number Line","publication_year":2026,"publication_date":"2026-09-02","ids":{"openalex":"https://openalex.org/W7206174331","doi":"https://doi.org/10.5281/zenodo.22262030"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22262030","doi":"https://doi.org/10.5281/zenodo.22262030","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22262030","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.22262030","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139402108","display_name":"Eliza Sulea","orcid":"https://orcid.org/0009-0002-1417-1938","observed_orcids":["https://orcid.org/0009-0002-1417-1938"]},"institutions":[{"id":"https://openalex.org/I138659443","display_name":"Widener University","ror":"https://ror.org/00nsyd297","country_code":"US","type":"education","lineage":["https://openalex.org/I138659443"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sulea, Eliza","raw_affiliation_strings":["Widener University"],"raw_orcid":"https://orcid.org/0009-0002-1417-1938","affiliations":[{"raw_affiliation_string":"Widener University","institution_ids":["https://openalex.org/I138659443"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5139402108"],"corresponding_institution_ids":["https://openalex.org/I138659443"],"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/T11166","display_name":"Analytic Number Theory Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.0003000000142492354,"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/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.0,"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/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.968999981880188},{"id":"https://openalex.org/keywords/critical-line","display_name":"critical line","score":0.6489999890327454},{"id":"https://openalex.org/keywords/euler-product","display_name":"Euler product","score":0.8299999833106995},{"id":"https://openalex.org/keywords/functional-equations","display_name":"functional equations","score":0.6140000224113464},{"id":"https://openalex.org/keywords/prime-counting","display_name":"prime counting","score":0.5759999752044678},{"id":"https://openalex.org/keywords/yang-mills-existence-and-mass-gap","display_name":"Yang-Mills mass gap","score":0.9259999990463257},{"id":"https://openalex.org/keywords/casimir-energy","display_name":"Casimir energy","score":0.824999988079071},{"id":"https://openalex.org/keywords/godel-incompleteness","display_name":"G\u00f6del incompleteness","score":0.9649999737739563},{"id":"https://openalex.org/keywords/frame-duality","display_name":"frame duality","score":0.6299999952316284}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8233000040054321},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5227000117301941},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.49869999289512634},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.46779999136924744},{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.4390000104904175},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4050000011920929},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.4049000144004822},{"id":"https://openalex.org/C154483964","wikidata":"https://www.wikidata.org/wiki/Q825857","display_name":"Riemann sphere","level":3,"score":0.3912000060081482},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.3894999921321869},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3601999878883362},{"id":"https://openalex.org/C2780390204","wikidata":"https://www.wikidata.org/wiki/Q1036595","display_name":"Blowing up","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.3131999969482422},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.3125},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.3028999865055084},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.29919999837875366},{"id":"https://openalex.org/C18556879","wikidata":"https://www.wikidata.org/wiki/Q753035","display_name":"Riemann surface","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C84597430","wikidata":"https://www.wikidata.org/wiki/Q106227","display_name":"Locus (genetics)","level":3,"score":0.2808000147342682},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.2680000066757202},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C2776605787","wikidata":"https://www.wikidata.org/wiki/Q5186739","display_name":"Critical line","level":2,"score":0.25949999690055847},{"id":"https://openalex.org/C189903471","wikidata":"https://www.wikidata.org/wiki/Q1156903","display_name":"Riemann sum","level":4,"score":0.25699999928474426},{"id":"https://openalex.org/C1911482","wikidata":"https://www.wikidata.org/wiki/Q854531","display_name":"Real analysis","level":2,"score":0.2547000050544739},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":10,"locations":[{"id":"doi:10.5281/zenodo.22262030","doi":"https://doi.org/10.5281/zenodo.22262030","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22262030","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.22262031","doi":"https://doi.org/10.5281/zenodo.22262031","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22262031","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.22665523","doi":"https://doi.org/10.5281/zenodo.22665523","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22665523","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.22695289","doi":"https://doi.org/10.5281/zenodo.22695289","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22695289","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.22878730","doi":"https://doi.org/10.5281/zenodo.22878730","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22878730","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.23767201","doi":"https://doi.org/10.5281/zenodo.23767201","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23767201","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.23815893","doi":"https://doi.org/10.5281/zenodo.23815893","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23815893","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.23872093","doi":"https://doi.org/10.5281/zenodo.23872093","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23872093","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.23922416","doi":"https://doi.org/10.5281/zenodo.23922416","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23922416","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.24163995","doi":"https://doi.org/10.5281/zenodo.24163995","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24163995","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.22262030","doi":"https://doi.org/10.5281/zenodo.22262030","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22262030","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7213945044","https://openalex.org/W7117151740","https://openalex.org/W7203945544","https://openalex.org/W7151010924","https://openalex.org/W7163935126","https://openalex.org/W7214077515","https://openalex.org/W7153528370","https://openalex.org/W7164329060","https://openalex.org/W7111036641","https://openalex.org/W7117360319"],"abstract_inverted_index":{"EARLY/ROUGH":[0],"DRAFTS":[1],"BELOW.":[2],"SEE":[3],"VERSION":[4],"9":[5],"REORGANIZATION":[6],":":[7],"Inspired":[8],"by":[9,39,125,135,169,198,216,331,348],"Dimensional":[10],"Mechanics,":[11],"Riemann":[12,131,144,338],"I":[13],"constructs":[14],"a":[15,60,85],"new":[16],"observable":[17],"D_C":[18,49],"measuring":[19],"how":[20],"well":[21],"the":[22,27,35,68,73,77,98,105,123,138,153,209,219,224,255,259,269,274,280,311,315,319,328,332,337,340],"finite":[23,261,307,352],"Euler":[24,262],"product":[25],"satisfies":[26],"functional":[28],"equation.":[29],"It":[30,253],"equals":[31],"1":[32],"exactly":[33],"on":[34,231],"critical":[36,74],"line,":[37],"prime":[38],"prime,":[40],"and":[41,67,177,189,205,250],"deviates":[42],"off":[43],"it.":[44],"The":[45,115,164,193,227,238,264,284,322],"correction":[46,266,342],"identity":[47],"R_C":[48,57,127],"=":[50,95,159,183],"R_C(1\u2212s)":[51],"shows":[52],"any":[53],"off-line":[54],"zero":[55],"requires":[56],"to":[58,91,111,223,288],"absorb":[59],"growing":[61],"discrepancy.":[62],"A":[63,295],"non-circular":[64],"proto-zero":[65],"filtration":[66],"variance":[69],"asymmetry":[70],"theorem":[71],"establish":[72],"line":[75],"as":[76,119,146,203,208,318],"unique":[78],"locus":[79],"where":[80,233],"zeros":[81],"can":[82,276],"form.":[83],"Independently,":[84],"curvature":[86],"reformulation":[87],"proves":[88],"RH":[89,108],"equivalent":[90],"positivity":[92,102],"of":[93,113,212,258,282],"u":[94],"F_\u03c3\u03c3/F":[96],"throughout":[97],"strip,":[99],"with":[100,161,174,314],"boundary":[101],"established":[103],"via":[104],"Hadamard":[106],"product.":[107,263],"is":[109,167,229,248,254,268,279,344],"reduced":[110],"noncompensation":[112,207],"R_C.":[114,283],"Realizability":[116,139,324],"Principle,":[117],"stated":[118],"an":[120,170],"axiom,":[121],"closes":[122,327,336],"gap":[124,275,330],"denying":[126],"independent":[128,346],"tail":[129],"freedom.":[130],"II,":[132],"also":[133,214],"inspired":[134,215],"DM,":[136,217],"develops":[137],"Principle":[140,325],"(axiom":[141],"used":[142],"in":[143,310],"I)":[145],"standalone":[147],"foundations.":[148],"Iterated":[149],"prime-counting":[150],"enters":[151],"{0,1,2,3};":[152],"parity":[154,187],"recursion":[155],"stabilizes":[156],"at":[157,304,351],"x*":[158],"(3+\u221a13)/2":[160],"floor":[162,240],"3.":[163],"same":[165,323,333],"point":[166],"forced":[168],"S\u00b3":[171],"shell":[172],"equilibrium":[173],"Spin(3)":[175],"texture":[176],"locked":[178],"topological":[179],"core,":[180],"selecting":[181],"d":[182],"3":[184],"uniquely":[185],"through":[186,272],"survival":[188],"\u03c0\u2083(S\u00b3)":[190],"\u2245":[191],"\u2124.":[192],"principle":[194],"classifies":[195],"mathematical":[196],"statements":[197],"frame,":[199],"absorbs":[200],"G\u00f6del":[201],"incompleteness":[202],"frame-dependent,":[204],"identifies":[206],"structural":[210],"consequence":[211],"closure.Yang-Mills,":[213],"applies":[218],"identical":[220],"reduction":[221],"architecture":[222],"mass":[225],"gap.":[226],"theory":[228],"built":[230],"S\u00b3_R":[232],"compactness":[234],"gives":[235],"analytic":[236],"control.":[237],"Casimir":[239],"\u03b4_E":[241],"\u2265":[242],"c_E":[243],"g\u00b2":[244],"C_{2,min}(G)":[245],">":[246],"0":[247],"algebraic":[249],"cannot":[251],"vanish.":[252],"Yang-Mills":[256,329],"analog":[257,281],"zero-free":[260],"magnetic":[265],"\u03b4_B":[267],"only":[270],"channel":[271,343],"which":[273,278],"die,":[277],"entire":[285],"problem":[286],"reduces":[287],"one":[289],"inequality:":[290],"|\u03b4_B|":[291],"\u2264":[292],"(1\u2212\u03b5)":[293],"\u03b4_E.":[294],"truncated":[296],"SU(2)":[297],"lattice":[298],"diagnostic":[299],"confirms":[300],"|\u03b4_B/\u03b4_E|":[301],"<":[302],"0.16":[303],"every":[305],"tested":[306],"system":[308,320],"size":[309],"strong-coupling":[312],"regime,":[313],"ratio":[316],"decelerating":[317],"grows.":[321],"idea":[326],"mechanism":[334],"that":[335],"Hypothesis:":[339],"infinite-volume":[341],"denied":[345],"existence":[347],"arithmetic":[349],"closure":[350],"radius.":[353]},"counts_by_year":[],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2026-09-03T00:00:00"}