{"id":"https://openalex.org/W7225620731","doi":"https://doi.org/10.5281/zenodo.24085683","title":"A Unitary Scattering Perspective on the Riemann Hypothesis","display_name":"A Unitary Scattering Perspective on the Riemann Hypothesis","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225620731","doi":"https://doi.org/10.5281/zenodo.24085683"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24085683","doi":"https://doi.org/10.5281/zenodo.24085683","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24085683","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24085683","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161328786","display_name":"H.P. Chen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chen, H.P.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5161328786"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":1.0,"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":1.0,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","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"}},{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.9959999918937683},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.9229999780654907},{"id":"https://openalex.org/keywords/prime-numbers","display_name":"prime numbers","score":0.5730000138282776},{"id":"https://openalex.org/keywords/resonance-poles","display_name":"resonance poles","score":0.8339999914169312},{"id":"https://openalex.org/keywords/critical-line","display_name":"critical line","score":0.8579999804496765},{"id":"https://openalex.org/keywords/spectral-interpretation","display_name":"spectral interpretation","score":0.4020000100135803},{"id":"https://openalex.org/keywords/conditional-proof","display_name":"conditional proof","score":0.47099998593330383}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7746999859809875},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.6449999809265137},{"id":"https://openalex.org/C130295795","wikidata":"https://www.wikidata.org/wiki/Q3550684","display_name":"Unitarity","level":2,"score":0.5799000263214111},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.5163999795913696},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.48429998755455017},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4530999958515167},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.44429999589920044},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4339999854564667},{"id":"https://openalex.org/C154483964","wikidata":"https://www.wikidata.org/wiki/Q825857","display_name":"Riemann sphere","level":3,"score":0.4250999987125397},{"id":"https://openalex.org/C67105901","wikidata":"https://www.wikidata.org/wiki/Q903737","display_name":"Scattering theory","level":3,"score":0.42100000381469727},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.3882000148296356},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3813000023365021},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.37130001187324524},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.34940001368522644},{"id":"https://openalex.org/C48902493","wikidata":"https://www.wikidata.org/wiki/Q2152235","display_name":"Riemann Xi function","level":3,"score":0.32829999923706055},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.3271999955177307},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3188000023365021},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29649999737739563},{"id":"https://openalex.org/C2776605787","wikidata":"https://www.wikidata.org/wiki/Q5186739","display_name":"Critical line","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C188313703","wikidata":"https://www.wikidata.org/wiki/Q1972470","display_name":"Unitary operator","level":3,"score":0.2680000066757202},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C115047598","wikidata":"https://www.wikidata.org/wiki/Q54505","display_name":"Quantum field theory","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25929999351501465},{"id":"https://openalex.org/C153013531","wikidata":"https://www.wikidata.org/wiki/Q1322810","display_name":"Scattering amplitude","level":3,"score":0.258899986743927},{"id":"https://openalex.org/C151602998","wikidata":"https://www.wikidata.org/wiki/Q485287","display_name":"Analytic continuation","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2574999928474426},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.25360000133514404},{"id":"https://openalex.org/C161094330","wikidata":"https://www.wikidata.org/wiki/Q581505","display_name":"S-matrix","level":3,"score":0.25270000100135803},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.250900000333786}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.24085683","doi":"https://doi.org/10.5281/zenodo.24085683","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24085683","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.24085684","doi":"https://doi.org/10.5281/zenodo.24085684","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24085684","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.24102553","doi":"https://doi.org/10.5281/zenodo.24102553","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24102553","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24085683","doi":"https://doi.org/10.5281/zenodo.24085683","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24085683","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"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/W7083629174","https://openalex.org/W7160432228","https://openalex.org/W7125791138","https://openalex.org/W6944247361","https://openalex.org/W7155366133","https://openalex.org/W7106228905","https://openalex.org/W7154839231","https://openalex.org/W1824108706","https://openalex.org/W7155645059","https://openalex.org/W7204232647"],"abstract_inverted_index":{"This":[0,97,130],"paper":[1],"constructs":[2],"a":[3,132],"closed":[4,84],"unitary":[5],"scattering":[6,25,35,86,125],"dynamical":[7],"system":[8,81],"of":[9,20,28,46,82],"the":[10,17,21,29,37,42,50,64,78,83,92],"prime":[11,47],"multiplicative":[12],"semigroup,":[13],"and":[14,53,69,122],"equivalently":[15],"defines":[16],"non-trivial":[18],"zeros":[19],"Riemann":[22,93],"\u03b6-function":[23],"as":[24],"resonance":[26],"states":[27],"arithmetic":[30,85],"system.":[31],"Based":[32],"on":[33,106],"standard":[34,123],"unitarity,":[36],"Wigner\u2013Weisskopf":[38],"coupling":[39],"sum":[40],"rule,":[41],"asymptotic":[43],"uniform":[44],"distribution":[45],"logarithmic":[48],"frequencies,":[49],"large-sieve":[51],"inequality":[52],"phase-winding":[54],"index":[55],"analysis,":[56],"all":[57],"zero":[58],"configurations":[59],"that":[60],"may":[61],"deviate":[62],"from":[63],"critical":[65],"line":[66],"are":[67,128],"exhausted":[68],"ruled":[70],"out.":[71],"The":[72],"strict":[73],"conclusion":[74],"is":[75,99,131],"obtained:":[76],"Within":[77],"self-consistent":[79],"axiomatic":[80],"model":[87],"defined":[88],"in":[89],"this":[90],"paper,":[91],"Hypothesis":[94],"holds":[95],"completely.":[96],"work":[98],"fully":[100],"independent.":[101],"It":[102],"does":[103],"not":[104,136],"rely":[105],"any":[107],"external":[108],"fundamental":[109],"physical":[110],"models,":[111],"topological":[112],"theories":[113],"or":[114],"philosophical":[115],"frameworks.":[116],"Only":[117],"classical":[118],"analytic":[119],"number":[120],"theory":[121],"quantum":[124],"spectral":[126],"tools":[127],"adopted.":[129],"conditional":[133],"rigorous":[134],"argument,":[135],"an":[137],"unconditional":[138],"mathematical":[139],"proof.":[140]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
