{"id":"https://openalex.org/W7225001377","doi":"https://doi.org/10.5281/zenodo.23827152","title":"Sharp mixed-potential Fourier pairs and planar universal optimality","display_name":"Sharp mixed-potential Fourier pairs and planar universal optimality","publication_year":2026,"publication_date":"2026-10-30","ids":{"openalex":"https://openalex.org/W7225001377","doi":"https://doi.org/10.5281/zenodo.23827152"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23827152","doi":"https://doi.org/10.5281/zenodo.23827152","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23827152","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":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23827152","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002564364","display_name":"Barry Z. Cynamon","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Cynamon, Barry Z.","raw_affiliation_strings":["Weidenbaum Center, Washington University in St. Louis"],"raw_orcid":"https://orcid.org/0009-0009-5778-0005","affiliations":[{"raw_affiliation_string":"Weidenbaum Center, Washington University in St. Louis","institution_ids":["https://openalex.org/I204465549"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002564364"],"corresponding_institution_ids":["https://openalex.org/I204465549"],"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.3698999881744385,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.3698999881744385,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.10589999705553055,"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/T11166","display_name":"Analytic Number Theory Research","score":0.09380000084638596,"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":[{"id":"https://openalex.org/keywords/energy-comparison","display_name":"energy comparison","score":0.6259999871253967},{"id":"https://openalex.org/keywords/representing-measures","display_name":"representing measures","score":0.4519999921321869},{"id":"https://openalex.org/keywords/periodic-configurations","display_name":"periodic configurations","score":0.5759999752044678},{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi tessellation","score":0.7080000042915344},{"id":"https://openalex.org/keywords/lean-formal-verification","display_name":"Lean formal verification","score":0.4050000011920929}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7742000222206116},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.525600016117096},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5239999890327454},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.503000020980835},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.45179998874664307},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4043000042438507},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.40380001068115234},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.39730000495910645},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.392300009727478},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37599998712539673},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36410000920295715},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.36329999566078186},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.3472999930381775},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.33340001106262207},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.33340001106262207},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3305000066757202},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.3278999924659729},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C62100291","wikidata":"https://www.wikidata.org/wiki/Q1936288","display_name":"Total variation","level":2,"score":0.31060001254081726},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3001999855041504},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.29100000858306885},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C2777183706","wikidata":"https://www.wikidata.org/wiki/Q630771","display_name":"Subvariety","level":3,"score":0.28349998593330383},{"id":"https://openalex.org/C2777630202","wikidata":"https://www.wikidata.org/wiki/Q5527840","display_name":"Gaussian measure","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.26100000739097595}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23827152","doi":"https://doi.org/10.5281/zenodo.23827152","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23827152","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":"Preprint"},{"id":"doi:10.5281/zenodo.23827153","doi":"https://doi.org/10.5281/zenodo.23827153","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23827153","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":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23827152","doi":"https://doi.org/10.5281/zenodo.23827152","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23827152","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":"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":["https://openalex.org/W7225005005","https://openalex.org/W7135195220","https://openalex.org/W7221337613","https://openalex.org/W7225002436","https://openalex.org/W7221480911","https://openalex.org/W7223771293","https://openalex.org/W7223664836","https://openalex.org/W3103274847","https://openalex.org/W2911697850","https://openalex.org/W7221774315"],"abstract_inverted_index":{"We":[0],"study":[1],"planar":[2],"energy":[3,20,75],"comparison":[4,21],"and":[5,22,37,45,80,96,115,141,149,160,163,180,188,216,252,279,301,304],"sharp":[6],"Fourier":[7,55,83],"auxiliaries":[8],"for":[9,85,211],"completely":[10],"monotone":[11],"potentials":[12],"of":[13,39,120,232],"squared":[14],"distance.":[15],"The":[16,153,221],"attributed":[17],"OpenAI":[18,270],"Math":[19,271],"Gaussian":[23,99,140],"construction":[24],"cover":[25],"locally":[26],"finite":[27,46,158,161,168],"density-one":[28],"configurations,":[29,91],"including":[30,107],"nonperiodic":[31],"competitors":[32],"without":[33],"a":[34,157],"separation":[35],"bound":[36,103],"cases":[38],"infinite":[40,70],"energy.":[41],"For":[42,89],"positive":[43,65],"density":[44],"triangular":[47],"reference":[48,74,164],"energy,":[49],"we":[50],"construct":[51],"one":[52],"real":[53],"radial":[54],"pair":[56],"satisfying":[57],"all":[58],"sixteen":[59],"auxiliary":[60],"conclusions":[61],"simultaneously.":[62],"A":[63],"common":[64],"representing":[66,170],"measure":[67],"may":[68],"have":[69],"total":[71,169],"mass.":[72,171],"Finite":[73],"also":[76],"yields":[77],"physical":[78],"integrability":[79],"the":[81,86,97,118,126,197,233,268,288,298],"reverse":[82],"identity":[84,95],"same":[87],"pair.":[88],"periodic":[90,109],"an":[92,135,228],"exact":[93],"excess":[94,147],"selected":[98],"family's":[100],"first-cell":[101],"margins":[102],"ordered":[104],"short":[105],"pairs,":[106],"nonzero":[108,142],"self-images.":[110],"Actual":[111],"Voronoi":[112],"facets,":[113],"deletion,":[114],"reinsertion":[116],"control":[117],"fraction":[119,182],"defective":[121],"closed":[122],"six-neighbor":[123],"neighborhoods":[124],"on":[125],"original":[127,250],"period":[128],"cell.":[129],"An":[130,172],"explicit":[131,173],"geometric":[132],"coefficient":[133],"has":[134],"inverse-square":[136],"tolerance":[137,179],"bound.":[138],"Its":[139],"positive-mixture":[143],"consequences":[144],"give":[145],"cube-root":[146],"estimates":[148],"separate":[150,192],"zero-excess":[151],"endpoints.":[152],"mixture":[154],"statement":[155,303],"requires":[156],"potential":[159],"competitor":[162],"energies,":[165],"but":[166],"not":[167,225,293],"ninth-root":[174],"consequence":[175],"makes":[176],"both":[177],"local":[178],"exceptional":[181],"tend":[183],"to":[184,284],"zero.":[185],"Global":[186],"alignment":[187],"equality":[189],"classification":[190],"remain":[191,219],"tasks.":[193],"Formal":[194],"proof":[195],"companion:":[196],"Lean":[198],"software":[199],"package":[200,214],"is":[201,208],"identified":[202,269],"by":[203],"reserved":[204],"DOI":[205],"10.5281/zenodo.23826711.":[206],"It":[207],"being":[209],"prepared":[210],"release;":[212],"complete":[213,234],"qualification":[215],"independent":[217],"replay":[218],"pending.":[220],"formal":[222],"companion":[223],"does":[224,292],"yet":[226],"establish":[227],"independently":[229],"replayed":[230],"verification":[231],"manuscript.":[235],"2020":[236],"Mathematics":[237],"Subject":[238],"Classification:":[239],"Primary":[240],"52C15;":[241],"Secondary":[242],"42B10,":[243],"52C05.":[244],"License":[245,276],"scope:":[246],"Barry":[247],"Z.":[248],"Cynamon\u2019s":[249],"text":[251],"figures":[253],"are":[254],"licensed":[255],"under":[256],"Creative":[257],"Commons":[258],"Attribution":[259],"4.0":[260],"International":[261],"(CC":[262],"BY":[263,290],"4.0).":[264],"Material":[265],"adapted":[266],"from":[267],"sources":[272],"retains":[273],"its":[274],"Apache":[275],"2.0":[277],"terms":[278],"attribution.":[280],"These":[281],"licenses":[282],"apply":[283],"their":[285],"respective":[286],"material;":[287],"CC":[289],"grant":[291],"relicense":[294],"upstream":[295],"material.":[296],"See":[297],"manuscript\u2019s":[299],"attribution":[300],"assistance":[302],"Appendix":[305],"B.1.":[306]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-11-01T00:00:00"}