{"id":"https://openalex.org/W7212423398","doi":"https://doi.org/10.5281/zenodo.22731872","title":"Structure-Preserving Coefficient\u2013Operator\u2013Mellin Transport Theorem","display_name":"Structure-Preserving Coefficient\u2013Operator\u2013Mellin Transport Theorem","publication_year":2026,"publication_date":"2026-09-13","ids":{"openalex":"https://openalex.org/W7212423398","doi":"https://doi.org/10.5281/zenodo.22731872"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22731872","doi":"https://doi.org/10.5281/zenodo.22731872","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22731872","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","license_id":"https://openalex.org/licenses/cc-by-nc","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.22731872","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147346860","display_name":"Aaron Woffinden","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Woffinden, Aaron","raw_affiliation_strings":["Institute of Unitive Cross-Domain Morphology"],"raw_orcid":"https://orcid.org/0009-0008-4415-7436","affiliations":[{"raw_affiliation_string":"Institute of Unitive Cross-Domain Morphology","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5147346860"],"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":0.9312000274658203,"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":0.9312000274658203,"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":0.033799998462200165,"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/T14500","display_name":"Advanced Mathematical Theories","score":0.007400000002235174,"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/dirichlet-convolution","display_name":"Dirichlet convolution","score":0.8209999799728394},{"id":"https://openalex.org/keywords/mellin-transform","display_name":"Mellin transform","score":0.8429999947547913},{"id":"https://openalex.org/keywords/composition-of-operators","display_name":"composition of operators","score":0.6620000004768372},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.9399999976158142},{"id":"https://openalex.org/keywords/dirichlet-series","display_name":"Dirichlet series","score":0.5479999780654907},{"id":"https://openalex.org/keywords/dirichlet-l-functions","display_name":"Dirichlet L-functions","score":0.4869999885559082},{"id":"https://openalex.org/keywords/dirichlet-eta-function","display_name":"Dirichlet eta function","score":0.5210000276565552},{"id":"https://openalex.org/keywords/dirichlet-beta-function","display_name":"Dirichlet beta function","score":0.6069999933242798}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.730400025844574},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5536999702453613},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5533000230789185},{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.39969998598098755},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.3961000144481659},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.3903999924659729},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37940001487731934},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.37549999356269836},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.375},{"id":"https://openalex.org/C151602998","wikidata":"https://www.wikidata.org/wiki/Q485287","display_name":"Analytic continuation","level":2,"score":0.3630000054836273},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.36160001158714294},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.36039999127388},{"id":"https://openalex.org/C21513729","wikidata":"https://www.wikidata.org/wiki/Q5156798","display_name":"Composition operator","level":4,"score":0.35260000824928284},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.3515999913215637},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.34220001101493835},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.34220001101493835},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3353999853134155},{"id":"https://openalex.org/C65630602","wikidata":"https://www.wikidata.org/wiki/Q2278680","display_name":"Shift operator","level":4,"score":0.320499986410141},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3151000142097473},{"id":"https://openalex.org/C82916341","wikidata":"https://www.wikidata.org/wiki/Q6934990","display_name":"Multiplication operator","level":3,"score":0.31139999628067017},{"id":"https://openalex.org/C79587385","wikidata":"https://www.wikidata.org/wiki/Q2638931","display_name":"Convolution theorem","level":5,"score":0.3100000023841858},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C40231798","wikidata":"https://www.wikidata.org/wiki/Q1333743","display_name":"Composition (language)","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.2976999878883362},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.22731872","doi":"https://doi.org/10.5281/zenodo.22731872","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22731872","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","license_id":"https://openalex.org/licenses/cc-by-nc","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.22731873","doi":"https://doi.org/10.5281/zenodo.22731873","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22731873","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","license_id":"https://openalex.org/licenses/cc-by-nc","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.22731872","doi":"https://doi.org/10.5281/zenodo.22731872","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22731872","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","license_id":"https://openalex.org/licenses/cc-by-nc","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.7578350901603699,"display_name":"Peace, justice, and strong institutions","id":"https://metadata.un.org/sdg/16"}],"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":{"Structure-Preserving":[0,387,444],"Coefficient\u2013Operator\u2013Mellin":[1,388,445],"Transport":[2,389,446],"Theorem":[3,164,390],"One":[4],"Composition":[5],"Law,":[6],"Three":[7,92],"Working":[8],"Realizations":[9,93],"This":[10,317],"theorem":[11,168,262,302,318],"establishes":[12],"an":[13,192,201],"explicit,":[14],"invertible":[15],"transport":[16,225,252,299,335,395],"among":[17,396],"three":[18,149,154,240,365,438],"classical":[19,241],"realizations":[20,156],"of":[21,141,157,321,353],"multiplicative":[22],"arithmetic:":[23],"arithmetic":[24,35,59,193],"coefficients,":[25],"scale-transfer":[26,40,119,134,399],"operators,":[27,120],"and":[28,79,227,267,293,401,429],"Dirichlet/Mellin":[29,44,402],"symbols.":[30,145],"Its":[31],"central":[32],"correspondence":[33],"is:":[34],"coefficients":[36],"under":[37,42,46,457],"Dirichlet":[38,104,122,144,397],"convolution\u2194":[39],"operators":[41],"composition\u2194":[43],"symbols":[45],"multiplication":[47,140],"The":[48,91,113,167,232,261,386],"point":[49],"is":[50,98,116,184,234,245,297,319,348,405],"operational:":[51],"Move":[52],"the":[53,56,65,84,89,107,133,142,158,163,220,239,264,301,311,322,331,349,358,381,419,422,433,437],"identity.":[54],"Keep":[55],"law.":[57,110],"An":[58],"relation":[60,203],"can":[61],"be":[62,195,204,216,408],"moved":[63],"into":[64,139,172,197,206,219,248,418],"representation":[66,170,420],"where":[67,121,421],"its":[68],"relevant":[69,265],"operation":[70,424],"becomes":[71,124,425],"easiest":[72,187],"to":[73,181,188,314,407],"see":[74],"or":[75,280],"manipulate,":[76],"worked":[77],"there,":[78,428],"transported":[80,217],"back":[81],"while":[82],"preserving":[83],"compositional":[85,268,360],"structure":[86,309],"established":[87],"by":[88,100,118],"theorem.":[90],"Coefficient":[94],"space":[95,112,129],"Arithmetic":[96,316,325],"information":[97,115],"encoded":[99],"coefficient":[101],"sequences,":[102],"with":[103,254],"convolution":[105,123,194],"as":[106,410],"native":[108,363],"composition":[109,138],"Operator":[111],"same":[114,159,332,359],"represented":[117],"ordinary":[125],"operator":[126,137,198,202],"composition.":[127],"Mellin/Dirichlet":[128],"Mellin":[130],"monomials":[131],"diagonalize":[132],"action,":[135],"converting":[136],"corresponding":[143],"These":[146],"are":[147,153],"not":[148,236,272,306],"unrelated":[150],"descriptions.":[151],"They":[152],"working":[155],"algebraic":[160,266],"mechanism.":[161],"What":[162],"Makes":[165],"Possible":[166],"turns":[169],"choice":[171],"a":[173,179,210,249,255,392,411,416],"usable":[174],"mathematical":[175,367,412],"move.":[176],"It":[177,244,270,404],"allows":[178],"researcher":[180],"ask:":[182],"Where":[183],"this":[185],"identity":[186],"work":[189,427],"with?":[190],"Can":[191,200,209],"converted":[196],"composition?":[199],"diagonalized":[205],"scalar":[207],"multiplication?":[208],"result":[211],"obtained":[212],"in":[213,356,364],"one":[214],"realization":[215],"faithfully":[218],"others?":[221],"Which":[222],"features":[223],"survive":[224],"automatically,":[226],"which":[228],"require":[229,289],"additional":[230,308],"structure?":[231],"contribution":[233],"therefore":[235],"merely":[237],"that":[238,274,354,435],"ingredients":[242],"exist.":[243],"their":[246,290],"assembly":[247],"single":[250],"explicit":[251],"instrument":[253],"stated":[256],"preservation":[257],"boundary.":[258,312],"Preservation":[259],"Boundary":[260],"preserves":[263],"structure.":[269],"does":[271],"assert":[273],"every":[275],"metric,":[276],"geometric,":[277],"spectral,":[278],"topological,":[279],"analytic":[281],"property":[282],"automatically":[283],"transfers":[284],"between":[285],"realizations.":[286,439],"Such":[287],"properties":[288],"own":[291],"hypotheses":[292],"arguments.":[294],"That":[295],"distinction":[296],"deliberate:":[298],"what":[300],"actually":[303],"preserves;":[304],"do":[305],"smuggle":[307],"across":[310],"Relation":[313],"Relation-Primary":[315,324],"AP-001":[320,347],"larger":[323],"(RPA)":[326],"research":[327,333],"architecture.":[328],"RPA":[329],"generalizes":[330],"motion:":[334],"\u2192":[336,338,341,343,345],"compare":[337],"measure":[339],"loss":[340],"lift":[342],"cross-constrain":[344],"exclude":[346],"cleanest":[350],"exact":[351],"example":[352],"architecture":[355],"action:":[357],"law":[361,434],"made":[362],"different":[366],"habitats.":[368],"Parent":[369],"architecture:Relation-Primary":[370],"Arithmetic:":[371],"Moving":[372],"Problems":[373],"Across":[374],"Representations":[375],"\u2014":[376],"A":[377],"133-Component":[378],"Architecture":[379],"Toward":[380],"Riemann":[382],"HypothesisDOI:":[383],"10.5281/zenodo.22731871":[384],"Summary":[385],"provides":[391],"faithful":[393],"three-way":[394],"convolution,":[398],"composition,":[400],"multiplication.":[403],"designed":[406],"used":[409],"switching":[413],"device:":[414],"move":[415],"problem":[417],"needed":[423],"native,":[426],"return":[430],"without":[431],"losing":[432],"connects":[436],"Citation:":[440],"Woffinden,":[441],"A.":[442],"(2026).":[443],"Theorem,":[447],"v1.0.":[448],"Zenodo.":[449],"DOI:":[450],"10.5281/zenodo.22731873License:":[451],"\u00a9":[452],"2026":[453],"Aaron":[454],"Woffinden.":[455],"Released":[456],"CC":[458],"BY-NC":[459],"4.0.":[460]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-09-14T00:00:00"}
