{"id":"https://openalex.org/W7224083126","doi":"https://doi.org/10.5281/zenodo.23718290","title":"An injective C*-power series violating the Bieberbach coefficient bound","display_name":"An injective C*-power series violating the Bieberbach coefficient bound","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7224083126","doi":"https://doi.org/10.5281/zenodo.23718290"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23718290","doi":"https://doi.org/10.5281/zenodo.23718290","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23718290","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.23718290","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/T11822","display_name":"Analytic and geometric function theory","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11822","display_name":"Analytic and geometric function theory","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.0017999999690800905,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.0003000000142492354,"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/global-injectivity","display_name":"global injectivity","score":0.7649999856948853},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.7310000061988831},{"id":"https://openalex.org/keywords/lean-formal-verification","display_name":"Lean formal verification","score":0.6330000162124634}],"concepts":[{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.7348999977111816},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7343000173568726},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6398000121116638},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6037999987602234},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47099998593330383},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.4490000009536743},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.4489000141620636},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4399000108242035},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4187999963760376},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.38670000433921814},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.37290000915527344},{"id":"https://openalex.org/C7720571","wikidata":"https://www.wikidata.org/wiki/Q1136880","display_name":"Power of two","level":2,"score":0.3587999939918518},{"id":"https://openalex.org/C99138194","wikidata":"https://www.wikidata.org/wiki/Q183427","display_name":"Hash function","level":2,"score":0.3538999855518341},{"id":"https://openalex.org/C99463465","wikidata":"https://www.wikidata.org/wiki/Q2716519","display_name":"Injective module","level":3,"score":0.3522999882698059},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34549999237060547},{"id":"https://openalex.org/C134757568","wikidata":"https://www.wikidata.org/wiki/Q274089","display_name":"Heap (data structure)","level":2,"score":0.3398999869823456},{"id":"https://openalex.org/C154441711","wikidata":"https://www.wikidata.org/wiki/Q1782332","display_name":"Divisible group","level":5,"score":0.3312000036239624},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.32919999957084656},{"id":"https://openalex.org/C96865113","wikidata":"https://www.wikidata.org/wiki/Q2946816","display_name":"Certificate","level":2,"score":0.3230000138282776},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30320000648498535},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27950000762939453},{"id":"https://openalex.org/C9395851","wikidata":"https://www.wikidata.org/wiki/Q177929","display_name":"Stack (abstract data type)","level":2,"score":0.263700008392334},{"id":"https://openalex.org/C43364308","wikidata":"https://www.wikidata.org/wiki/Q8799","display_name":"Byte","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.25529998540878296},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.25450000166893005},{"id":"https://openalex.org/C2776848632","wikidata":"https://www.wikidata.org/wiki/Q853463","display_name":"Clipping (morphology)","level":2,"score":0.25189998745918274},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23718290","doi":"https://doi.org/10.5281/zenodo.23718290","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23718290","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.23718291","doi":"https://doi.org/10.5281/zenodo.23718291","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23718291","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.23718290","doi":"https://doi.org/10.5281/zenodo.23718290","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23718290","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/W2011690209","https://openalex.org/W2188350974","https://openalex.org/W7166663746","https://openalex.org/W2050140563","https://openalex.org/W2086777251","https://openalex.org/W2026173588","https://openalex.org/W4241825571","https://openalex.org/W4238665156","https://openalex.org/W7100346995","https://openalex.org/W2049245282"],"abstract_inverted_index":{"A":[0,28],"normalized":[1,165],"norm-entire":[2],"power":[3],"series":[4],"on":[5],"C([0,1],C)":[6],"is":[7,74,112],"globally":[8],"injective":[9],"and":[10,58,95,118,125,138,144,160,178],"has":[11],"an":[12],"everywhere":[13],"norm-convergent":[14],"formal":[15,92],"derivative":[16],"series,":[17],"but":[18],"its":[19],"second":[20],"coefficient":[21],"violates":[22],"the":[23,45,85,91,98],"general":[24],"C*-Bieberbach":[25],"order":[26],"bound.":[27],"continuous":[29],"exponential":[30],"period":[31],"anchored":[32],"at":[33],"zero":[34],"proves":[35,44],"global":[36],"injectivity":[37],"without":[38],"assuming":[39],"univalent":[40],"scalar":[41],"fibers.":[42],"Lean":[43,82],"full":[46],"source":[47,150,166],"Conjecture":[48],"1.2/1.4":[49],"counterexample":[50],"as":[51],"one":[52],"common":[53],"outcome.":[54],"Invertible-coefficient,":[55],"polynomial,":[56],"Robertson":[57],"Lebedev\u2013Milin":[59],"variants":[60],"remain":[61],"unclaimed.":[62],"AI-assisted":[63],"preprint":[64],"by":[65],"Myeongjin":[66],"Kang,":[67],"with":[68,141],"no":[69,169,179],"affiliation.":[70],"Internal":[71],"AI":[72],"review":[73],"not":[75,107,174],"external":[76],"journal":[77],"peer":[78],"review.":[79],"The":[80,130],"accompanying":[81],"certificate":[83],"covers":[84],"precise":[86],"scoped":[87],"main":[88],"statement;":[89],"inspect":[90],"endpoint,":[93],"assumptions":[94],"provenance":[96],"in":[97],"supporting":[99,132],"package.":[100],"Prior-art":[101],"investigations":[102],"are":[103,128],"documented":[104],"bounded":[105],"searches,":[106],"worldwide-priority":[108,175],"certification.":[109],"Original":[110],"prose":[111],"offered":[113],"under":[114,121],"CC":[115],"BY":[116],"4.0":[117],"original":[119,135],"code/Lean":[120],"MIT;":[122],"third-party":[123,149],"rights":[124],"existing":[126],"notices":[127],"preserved.":[129],"public":[131],"ZIP":[133],"contains":[134],"proof":[136],"sources":[137],"verification":[139],"evidence,":[140],"bibliographic":[142],"links":[143],"hashes":[145],"instead":[146],"of":[147],"redistributed":[148],"manuscripts.":[151],"Recorded":[152],"prior-art/source-access":[153],"limits:":[154],"DirectPreprintsPDF403":[155],"persists;":[156],"actual":[157],"authorZenodo6917925":[158],"bytes":[159],"fresh":[161],"live":[162],"md5":[163],"verified,":[164],"text":[167],"agrees,":[168],"binaryidentityclaim;":[170],"Bounded":[171],"citation/web/superposition/registry":[172],"screen,":[173],"certification;":[176],"SemanticScholar429":[177],"exhaustive":[180],"subscription-index":[181],"search":[182]},"counts_by_year":[],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2026-10-29T00:00:00"}
