{"id":"https://openalex.org/W7225794119","doi":"https://doi.org/10.5281/zenodo.24126172","title":"Paper 125D: Multiplicative Packets, Defect Orbitals, and Radial Euler Cancellation Exact Three-Owner Identities, Bright\u2013Dark Coordinates, and the Primitive Rank-One Boundary","display_name":"Paper 125D: Multiplicative Packets, Defect Orbitals, and Radial Euler Cancellation Exact Three-Owner Identities, Bright\u2013Dark Coordinates, and the Primitive Rank-One Boundary","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225794119","doi":"https://doi.org/10.5281/zenodo.24126172"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24126172","doi":"https://doi.org/10.5281/zenodo.24126172","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24126172","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.24126172","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/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"}},{"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":0.7321000099182129},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5016000270843506},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.46219998598098755},{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.4174000024795532},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.38370001316070557},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3675999939441681},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.3662000000476837},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3431999981403351},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32260000705718994},{"id":"https://openalex.org/C2780757906","wikidata":"https://www.wikidata.org/wiki/Q5276676","display_name":"Dilation (metric space)","level":2,"score":0.3183000087738037},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.3167000114917755},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.31360000371932983},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.2937999963760376},{"id":"https://openalex.org/C154399039","wikidata":"https://www.wikidata.org/wiki/Q1780921","display_name":"Orthogonal complement","level":3,"score":0.2822999954223633},{"id":"https://openalex.org/C154483964","wikidata":"https://www.wikidata.org/wiki/Q825857","display_name":"Riemann sphere","level":3,"score":0.27250000834465027},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.2540000081062317}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24126172","doi":"https://doi.org/10.5281/zenodo.24126172","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24126172","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.24126173","doi":"https://doi.org/10.5281/zenodo.24126173","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24126173","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.24126172","doi":"https://doi.org/10.5281/zenodo.24126172","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24126172","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":{"We":[0],"derive":[1],"exact":[2,179,185],"multiplicative":[3],"decompositions":[4],"that":[5],"retain":[6],"internal":[7],"M\u00f6bius":[8,48,65],"cancellation":[9],"beforeestimating":[10],"the":[11,89,111,119,169,175,178,195],"near-resonance":[12],"energy":[13,109],"inherited":[14],"from":[15],"Paper":[16],"125C.":[17],"Three":[18],"prime-factor":[19],"coordinatesgive":[20],"finite":[21,94,152],"packets":[22,39,105,142],"with":[23,84],"explicit":[24],"support-boundary":[25],"terms.":[26],"Their":[27],"individual":[28],"packet":[29,172],"energies":[30],"have":[31],"afixed":[32],"logarithmic":[33],"bound,":[34],"while":[35],"completed":[36],"odd-numerator,":[37],"odd-denominator":[38],"at":[40,77],"a":[41,62,92,107,192],"commonfrequency":[42],"cancel":[43],"exactly.":[44],"A":[45],"cubic":[46],"truncated":[47],"identity":[49,95],"is":[50],"reorganized":[51],"into":[52,61],"components":[53],"withnested":[54],"support.":[55],"Each":[56],"reduced":[57],"channel":[58],"also":[59],"factors":[60],"universal":[63],"double":[64],"convolution":[66],"and":[67,151,159,174,187],"anabsolutely":[68],"summable":[69],"arithmetic":[70,126],"correction.":[71],"The":[72,163,183],"associated":[73],"Dirichlet":[74],"series":[75],"has":[76],"least":[78],"two":[79,99],"zeros":[80],"atits":[81],"density":[82],"boundary,":[83],"an":[85,124,129,145,160],"additional":[86],"zero":[87],"in":[88],"odd\u2013odd":[90],"case;":[91],"separate":[93],"reducesthat":[96],"case":[97],"to":[98,177],"radial":[100,134],"boundary":[101],"bands.":[102],"Ordered":[103],"Euler":[104],"satisfy":[106],"positive":[108],"identityin":[110],"dilation-invariant":[112],"continuous":[113,171],"norm.":[114],"Descending":[115],"prime":[116],"order":[117],"minimizes":[118],"specified":[120],"scalarpacket":[121],"cost,":[122],"not":[123,191],"arbitrary":[125],"energy.":[127],"On":[128],"active":[130],"primitive":[131],"shell,":[132],"integer":[133],"samplingleaves":[135],"only":[136],"one":[137],"coordinate,":[138],"so":[139],"further":[140],"dilation":[141],"cannot":[143],"create":[144],"independent":[146],"sampled":[147],"radialprofile.":[148],"Archived":[149],"diagnostics":[150],"recomputations":[153],"illustrate":[154],"this":[155],"distinction":[156],"between":[157,166],"improvedcoordinates":[158],"actual":[161],"bound.":[162],"signed":[164],"interactions":[165],"distinct":[167],"frequencies,":[168],"transferfrom":[170],"norms,":[173],"return":[176],"complement":[180],"remain":[181],"unresolved.":[182],"papersupplies":[184],"identities":[186],"scoped":[188],"component":[189],"estimates,":[190],"proof":[193],"of":[194],"Riemann":[196],"hypothesis.":[197]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}
