{"id":"https://openalex.org/W7225817035","doi":"https://doi.org/10.5281/zenodo.24126292","title":"Paper 125F: The Abel\u2013Hardy Abscissa of a M\u00f6bius Moving-Window Field A Positive-Energy Criterion for the Rightmost Zeta Zero, Zero Multiplicity, and the Riemann Hypothesis","display_name":"Paper 125F: The Abel\u2013Hardy Abscissa of a M\u00f6bius Moving-Window Field A Positive-Energy Criterion for the Rightmost Zeta Zero, Zero Multiplicity, and the Riemann Hypothesis","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225817035","doi":"https://doi.org/10.5281/zenodo.24126292"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24126292","doi":"https://doi.org/10.5281/zenodo.24126292","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24126292","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.24126292","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134672110","display_name":"Michael Sarnowski","orcid":"https://orcid.org/0009-0005-4210-6027","observed_orcids":["https://orcid.org/0009-0005-4210-6027"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sarnowski, Michael","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0005-4210-6027","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5134672110"],"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.0,"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"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8501999974250793},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.5781999826431274},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5285999774932861},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.508400022983551},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.46860000491142273},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.4250999987125397},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.41839998960494995},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.4138000011444092},{"id":"https://openalex.org/C92788228","wikidata":"https://www.wikidata.org/wiki/Q3777923","display_name":"Multiplicative group","level":3,"score":0.4047999978065491},{"id":"https://openalex.org/C27783845","wikidata":"https://www.wikidata.org/wiki/Q5421272","display_name":"Explicit formulae","level":2,"score":0.4020000100135803},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3995000123977661},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.39910000562667847},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3880000114440918},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3709999918937683},{"id":"https://openalex.org/C48902493","wikidata":"https://www.wikidata.org/wiki/Q2152235","display_name":"Riemann Xi function","level":3,"score":0.3702000081539154},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.3596999943256378},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.3463999927043915},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.3449000120162964},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3411000072956085},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.2939999997615814},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C18556879","wikidata":"https://www.wikidata.org/wiki/Q753035","display_name":"Riemann surface","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.27390000224113464},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.2718000113964081},{"id":"https://openalex.org/C35861355","wikidata":"https://www.wikidata.org/wiki/Q4791135","display_name":"Arithmetic zeta function","level":3,"score":0.26989999413490295},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.2694000005722046}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24126292","doi":"https://doi.org/10.5281/zenodo.24126292","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24126292","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.24126293","doi":"https://doi.org/10.5281/zenodo.24126293","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24126293","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.24126292","doi":"https://doi.org/10.5281/zenodo.24126292","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24126292","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":[],"abstract_inverted_index":{"A":[0,60,108,132],"positive":[1],"logarithmically":[2],"weighted":[3],"energy":[4,127,171],"of":[5,19,34,143,191],"a":[6,105],"smoothed":[7],"M\u00f6bius":[8],"moving-window":[9],"field":[10],"has":[11],"aconvergence":[12],"boundary":[13],"equal":[14],"to":[15],"the":[16,20,30,40,43,51,56,65,84,90,137,192],"right":[17],"edge":[18],"nontrivial":[21],"zeta":[22,58,75],"zeros,":[23],"shifted":[24],"by":[25,55],"one":[26],"half.":[27],"The":[28,98,146,169],"fieldretains":[29],"primitive":[31],"observation":[32,44,53],"geometry":[33],"Paper":[35],"125E":[36],"while":[37,162],"smoothing":[38],"both":[39],"shell":[41],"boundaryand":[42],"window.":[45],"Its":[46],"Hilbert-valued":[47],"Laplace":[48],"transform":[49],"is":[50,100,128,195],"Mellin":[52],"vectordivided":[54],"Riemann":[57,193],"function.":[59],"convolution":[61],"argument":[62],"shows":[63],"that":[64],"vector":[66],"cannot":[67],"vanishidentically":[68],"at":[69,181],"any":[70],"spectral":[71,138],"parameter,":[72],"so":[73],"every":[74],"zero":[76,142,182],"remains":[77,176],"observable.":[78],"Explicit":[79],"vertical-growthand":[80],"contour":[81],"arguments":[82],"establish":[83],"weighted-energy":[85],"abscissa,":[86],"and":[87,154],"Plancherel":[88],"gives":[89],"associatedpositive":[91],"vertical-line":[92],"identity":[93],"on":[94],"its":[95],"valid":[96],"half-plane.":[97],"result":[99],"an":[101,121,166],"exact":[102],"Riemann-hypothesiscriterion":[103],"without":[104],"simplicity":[106],"assumption.":[107],"multiplicative":[109],"correlation":[110],"formula":[111],"holds":[112],"absolutely":[113],"inits":[114],"initial":[115],"range;":[116],"finite-time":[117],"Gram":[118],"forms":[119],"provide":[120],"unambiguous":[122],"monotone":[123],"extension":[124],"wherever":[125],"thefull":[126],"finite":[129,151],"or":[130,189],"infinite.":[131],"separate":[133],"local":[134],"calculation":[135],"identifies":[136],"growth":[139],"caused":[140],"bya":[141],"given":[144],"multiplicity.":[145],"retained":[147],"fifty-zero":[148],"figures":[149],"illustrate":[150],"Abel":[152],"averaging,":[153],"acomplete":[155],"standard-library":[156],"implementation":[157],"reproduces":[158],"their":[159],"original":[160],"discretization":[161],"distinguishingnumerical":[163],"refinement":[164],"from":[165],"infinite-spectrum":[167],"estimate.":[168],"required":[170],"finiteness":[172],"for":[173],"everypositive":[174],"weight":[175],"unproved.":[177],"No":[178],"uniform":[179],"bound":[180],"weight,":[183],"sharp-window":[184],"error":[185],"estimate,new":[186],"zero-free":[187],"half-plane,":[188],"proof":[190],"hypothesis":[194],"claimed.":[196]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}
