{"id":"https://openalex.org/W7225814028","doi":"https://doi.org/10.5281/zenodo.24141095","title":"Nodal Chamber Equipartition, Critical-Point Index Dichotomy, and Weighted Prime-Simplex Dilogarithm Integrals for Riemann's Xi-Function","display_name":"Nodal Chamber Equipartition, Critical-Point Index Dichotomy, and Weighted Prime-Simplex Dilogarithm Integrals for Riemann's Xi-Function","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225814028","doi":"https://doi.org/10.5281/zenodo.24141095"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24141095","doi":"https://doi.org/10.5281/zenodo.24141095","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24141095","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":null,"license_id":null,"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.24141095","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159549932","display_name":"Thijs Missiaen","orcid":"https://orcid.org/0009-0007-3678-0810","observed_orcids":["https://orcid.org/0009-0007-3678-0810"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Missiaen, Thijs","raw_affiliation_strings":["Independent Researcher, Belgium"],"raw_orcid":"https://orcid.org/0009-0007-3678-0810","affiliations":[{"raw_affiliation_string":"Independent Researcher, Belgium","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159549932"],"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/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/T11428","display_name":"Advanced Mathematical Identities","score":9.999999747378752e-05,"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"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.883899986743927},{"id":"https://openalex.org/C61836697","wikidata":"https://www.wikidata.org/wiki/Q124743","display_name":"Wronskian","level":2,"score":0.7235000133514404},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.6234999895095825},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49810001254081726},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44670000672340393},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.415800005197525},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4083999991416931},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.4027999937534332},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36959999799728394},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.362199991941452},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.3619000017642975},{"id":"https://openalex.org/C58315980","wikidata":"https://www.wikidata.org/wiki/Q179436","display_name":"Asymptote","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C82240120","wikidata":"https://www.wikidata.org/wiki/Q190573","display_name":"Gamma function","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31700000166893005},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.28529998660087585},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C108408018","wikidata":"https://www.wikidata.org/wiki/Q1124546","display_name":"Laguerre polynomials","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.26669999957084656},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.257099986076355},{"id":"https://openalex.org/C43321923","wikidata":"https://www.wikidata.org/wiki/Q864333","display_name":"Transcendental function","level":2,"score":0.2554999887943268},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24141095","doi":"https://doi.org/10.5281/zenodo.24141095","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24141095","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24141096","doi":"https://doi.org/10.5281/zenodo.24141096","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24141096","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24141095","doi":"https://doi.org/10.5281/zenodo.24141095","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24141095","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":null,"license_id":null,"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":[],"abstract_inverted_index":{"Studies":[0],"the":[1,26,44,49,73,79,86,115,160],"Cauchy-Riemann":[2],"nodal":[3],"geometry":[4],"and":[5,56,59,61,84,99,102,139],"Prime-Number-Theorem":[6],"simplex":[7,152],"integrals":[8],"associated":[9],"with":[10,175],"Riemann's":[11],"completed":[12],"zeta":[13],"function":[14,82],"Xi(t":[15],"-":[16],"i*d)":[17],"=":[18,32,34,40,135,155,171],"R(d,t)":[19],"+":[20,37],"i*I(d,t)":[21],"(d":[22],">=":[23],"0)":[24],"under":[25],"canonical":[27],"transverse":[28],"Wronskian":[29,164],"normalization":[30],"W(d,t)":[31],"(1/2)*d_d|Xi(t-id)|^2":[33],"R*d_d":[35,122],"R":[36,123],"I*d_d":[38,127],"I":[39,128],"d*W_tilde(d,t).":[41],"(1)":[42],"Places":[43],"local":[45],"nodal-branch":[46],"dichotomy":[47],"within":[48],"critical-point":[50],"index":[51],"framework":[52],"of":[53,78,89,105],"Craven,":[54],"Csordas,":[55],"Smith":[57],"(1987)":[58],"Ki":[60],"Kim":[62],"(2000),":[63],"certifies":[64],"Case-I":[65],"critical-line":[66],"Laguerre":[67],"defects":[68],"c_1^{DH}(tau_{false,m})":[69],"<":[70,173],"0":[71,108,138],"across":[72],"first":[74],"five":[75],"off-critical":[76],"zeros":[77],"self-dual":[80],"Davenport-Heilbronn":[81],"Xi_DH,":[83],"details":[85],"global":[87],"obstacles":[88],"1-parameter":[90],"heat-flow":[91],"saddle":[92],"collisions,":[93],"unbounded":[94],"hairpin":[95],"components":[96],"(requiring":[97],"Phragmen-Lindelof":[98],"Euler-product":[100],"control),":[101],"Speiser-level":[103],"difficulty":[104],"Xi'":[106],"!=":[107],"on":[109],"d":[110],">":[111,137,157,179],"0.":[112,180],"(2)":[113],"Proves":[114],"unconditional":[116],"50%-50%":[117],"Green-Dirichlet-Neumann":[118],"chamber":[119],"equipartition":[120],"int":[121,126],"dt":[124,129,134],"==":[125,130],"iint_{Omega_k}":[131],"|Xi'|^2":[132],"dd":[133],"(1/2)*W_{Omega_k}(d_0)":[136],"Wronskian-slope":[140],"reciprocity.":[141],"(3)":[142],"Derives":[143],"exact":[144],"closed-form":[145],"Euler":[146],"dilogarithm":[147],"Li_2(2*theta)":[148],"formulas":[149],"contrasting":[150],"factorized":[151],"weights":[153],"(eta_fac^{(2)}(1/6)":[154],"0.676891":[156],"1/2)":[158],"against":[159],"true":[161],"additive":[162],"semiprime":[163],"weight":[165],"(1-u-v)^2,":[166],"which":[167],"collapses":[168],"to":[169],"eta_add^{(2)}(1/6)":[170],"0.150604":[172],"1/2":[174],"polynomial":[176],"deficit":[177],"(1/8)*(1-2*tau)^2*(3-4*tau)":[178]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}
