{"id":"https://openalex.org/W7224091807","doi":"https://doi.org/10.5281/zenodo.23718214","title":"A Hermitian counterexample to C*-algebraic Novak positivity","display_name":"A Hermitian counterexample to C*-algebraic Novak positivity","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7224091807","doi":"https://doi.org/10.5281/zenodo.23718214"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23718214","doi":"https://doi.org/10.5281/zenodo.23718214","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23718214","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.23718214","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158066045","display_name":"Myeongjin Kang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kang, Myeongjin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5158066045"],"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.7333999872207642,"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"}},"topics":[{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.7333999872207642,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.1996999979019165,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.018200000748038292,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/positive-semidefinite-kernels","display_name":"positive semidefinite kernels","score":0.8920000195503235},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.8569999933242798},{"id":"https://openalex.org/keywords/self-adjoint-operators","display_name":"self-adjoint operators","score":0.7540000081062317},{"id":"https://openalex.org/keywords/matrix-valued-kernels","display_name":"matrix-valued kernels","score":0.5180000066757202},{"id":"https://openalex.org/keywords/exponential-kernel","display_name":"exponential kernel","score":0.5180000066757202},{"id":"https://openalex.org/keywords/lean-formal-verification","display_name":"Lean formal verification","score":0.640999972820282}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6771000027656555},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.5957000255584717},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.559499979019165},{"id":"https://openalex.org/C2780882242","wikidata":"https://www.wikidata.org/wiki/Q14235582","display_name":"Literal (mathematical logic)","level":2,"score":0.4668999910354614},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46389999985694885},{"id":"https://openalex.org/C96865113","wikidata":"https://www.wikidata.org/wiki/Q2946816","display_name":"Certificate","level":2,"score":0.4404999911785126},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42410001158714294},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4228000044822693},{"id":"https://openalex.org/C43169469","wikidata":"https://www.wikidata.org/wiki/Q580922","display_name":"Preprint","level":2,"score":0.39480000734329224},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.39340001344680786},{"id":"https://openalex.org/C99138194","wikidata":"https://www.wikidata.org/wiki/Q183427","display_name":"Hash function","level":2,"score":0.35830000042915344},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34860000014305115},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.3391000032424927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33219999074935913},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3257000148296356},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3176000118255615},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3061999976634979},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C2777588356","wikidata":"https://www.wikidata.org/wiki/Q1868414","display_name":"Local property","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2671000063419342}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23718214","doi":"https://doi.org/10.5281/zenodo.23718214","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23718214","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.23718215","doi":"https://doi.org/10.5281/zenodo.23718215","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23718215","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.23718214","doi":"https://doi.org/10.5281/zenodo.23718214","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23718214","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4297795839","https://openalex.org/W7224105073","https://openalex.org/W2519767062","https://openalex.org/W1976351612","https://openalex.org/W2520469937","https://openalex.org/W625168834","https://openalex.org/W7202158269","https://openalex.org/W4415036734","https://openalex.org/W1517121229","https://openalex.org/W1770973883"],"abstract_inverted_index":{"We":[0],"construct":[1],"four":[2],"self-adjoint":[3],"inputs":[4],"with":[5,62,135],"two":[6],"coordinates":[7],"in":[8,55,91,155],"M_2(C)":[9],"for":[10],"which":[11],"the":[12,39,79,85,92],"literal":[13],"exponential-defined":[14],"Novak":[15,43],"kernel":[16],"is":[17,30,68,106,166],"Hermitian":[18],"but":[19],"not":[20,69,101],"positive":[21],"semidefinite.":[22],"An":[23],"explicit":[24],"quadratic":[25],"form":[26],"equals":[27],"cos(pi*sqrt(15))-3":[28],"and":[29,41,50,89,112,119,132,138,170],"at":[31],"most":[32],"-2.":[33],"This":[34],"refutes":[35],"Krishna's":[36],"C*-algebraic":[37],"extension;":[38],"scalar":[40],"commutative":[42],"theorems":[44],"are":[45,53,97,122],"unaffected.":[46],"The":[47,74,124],"matrix":[48],"construction":[49],"exact":[51],"failure":[52],"proved":[54],"Lean.":[56],"AI-assisted":[57],"preprint":[58],"by":[59,180],"Myeongjin":[60],"Kang,":[61],"no":[63],"affiliation.":[64],"Internal":[65],"AI":[66],"review":[67],"external":[70],"journal":[71],"peer":[72],"review.":[73],"accompanying":[75],"Lean":[76],"certificate":[77],"covers":[78],"precise":[80],"scoped":[81],"main":[82],"statement;":[83],"inspect":[84],"formal":[86],"endpoint,":[87],"assumptions":[88],"provenance":[90],"supporting":[93,126],"package.":[94],"Prior-art":[95],"investigations":[96],"documented":[98],"bounded":[99],"searches,":[100],"worldwide-priority":[102],"certification.":[103],"Original":[104],"prose":[105],"offered":[107],"under":[108,115],"CC":[109],"BY":[110],"4.0":[111],"original":[113,129],"code/Lean":[114],"MIT;":[116],"third-party":[117,143],"rights":[118],"existing":[120],"notices":[121],"preserved.":[123],"public":[125],"ZIP":[127],"contains":[128],"proof":[130],"sources":[131],"verification":[133],"evidence,":[134],"bibliographic":[136],"links":[137],"hashes":[139],"instead":[140],"of":[141],"redistributed":[142],"source":[144],"manuscripts.":[145],"Recorded":[146],"prior-art/source-access":[147],"limits:":[148],"No":[149,183],"prior":[150],"full":[151],"source-conjecture":[152],"refutation":[153],"found":[154],"inspected":[156],"primary/citing":[157],"literature.":[158],"Classical":[159],"radial-kernel":[160],"mechanisms":[161],"credited;":[162],"Semantic":[163],"Scholar":[164],"corpus":[165],"incomplete,":[167],"subscription":[168],"indexes":[169],"systematic":[171],"non-English":[172],"search":[173],"unavailable.":[174],"Independent":[175],"numerical":[176],"precision/index-comment":[177],"errors":[178],"reconciled":[179],"parent":[181],"addendum.":[182],"absolute":[184],"worldwide":[185],"priority":[186],"certified.":[187]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2026-10-29T00:00:00"}
