{"id":"https://openalex.org/W7163652905","doi":"https://doi.org/10.48550/arxiv.2606.06136","title":"A Finite Certificate for the Positive $n=9$ Vasc Inequality","display_name":"A Finite Certificate for the Positive $n=9$ Vasc Inequality","publication_year":2026,"publication_date":"2026-06-04","ids":{"openalex":"https://openalex.org/W7163652905","doi":"https://doi.org/10.48550/arxiv.2606.06136"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.06136","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.06136","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.06136","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137930222","display_name":"Dakai Guo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo, Dakai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137976274","display_name":"Ruichen Qiu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qiu, Ruichen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137931692","display_name":"Yichuan Cao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cao, Yichuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5050890628","display_name":"Ruyong Feng","orcid":"https://orcid.org/0000-0001-6508-8486"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Feng, Ruyong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T11435","display_name":"Polynomial and algebraic computation","score":0.6711999773979187,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.6711999773979187,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0754999965429306,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.03849999979138374,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/certificate","display_name":"Certificate","score":0.6424000263214111},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.5011000037193298},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.439300000667572},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.3617999851703644},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.3425999879837036},{"id":"https://openalex.org/keywords/midpoint","display_name":"Midpoint","score":0.3296999931335449}],"concepts":[{"id":"https://openalex.org/C96865113","wikidata":"https://www.wikidata.org/wiki/Q2946816","display_name":"Certificate","level":2,"score":0.6424000263214111},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6284999847412109},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.5011000037193298},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.439300000667572},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40560001134872437},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36579999327659607},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.3617999851703644},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3425999879837036},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33009999990463257},{"id":"https://openalex.org/C34130140","wikidata":"https://www.wikidata.org/wiki/Q1645406","display_name":"Midpoint","level":2,"score":0.3296999931335449},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.32910001277923584},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.30630001425743103},{"id":"https://openalex.org/C519991488","wikidata":"https://www.wikidata.org/wiki/Q28865","display_name":"Python (programming language)","level":2,"score":0.29010000824928284},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.28519999980926514},{"id":"https://openalex.org/C154504017","wikidata":"https://www.wikidata.org/wiki/Q853614","display_name":"Identifier","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.26660001277923584},{"id":"https://openalex.org/C50942859","wikidata":"https://www.wikidata.org/wiki/Q4967193","display_name":"Rectification","level":3,"score":0.2624000012874603},{"id":"https://openalex.org/C199521495","wikidata":"https://www.wikidata.org/wiki/Q181487","display_name":"Audit","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.06136","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.06136","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.06136","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.06136","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":[{"display_name":"Reduced inequalities","score":0.5125523805618286,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2,7,19,25,29,50,65,74,103,114],"positive-real":[3],"$n=9$":[4],"case":[5,75],"of":[6],"Vasc":[8],"cyclic":[9,39],"inequality.":[10],"The":[11,82],"proof":[12],"was":[13],"obtained":[14],"with":[15],"human-guided":[16],"assistance":[17],"from":[18],"AI":[20],"agent":[21],"MechMath":[22,61],"Agent":[23,62],"Team:":[24],"human-readable":[26],"part":[27,52],"reduces":[28],"rational":[30],"inequality":[31],"to":[32],"a":[33,38,54,110,120],"homogeneous":[34],"polynomial":[35],"inequality,":[36],"fixes":[37],"maximum,":[40],"and":[41,79,94,106,109,119],"parametrizes":[42],"each":[43],"sorted":[44,59],"fixed-maximum":[45],"cone":[46],"by":[47],"cumulative":[48],"gaps;":[49],"finite":[51],"is":[53],"certificate":[55,66,84],"covering":[56],"all":[57],"$8!=40320$":[58],"cones.":[60],"Team":[63],"generated":[64],"verification":[67,77,107],"workflow":[68],"through":[69],"Python":[70],"tool":[71],"calls,":[72],"including":[73],"split,":[76],"programs,":[78],"terminal":[80],"classifications.":[81],"published":[83],"has":[85],"$36815$":[86],"coefficient":[87],"leaves,":[88,93],"$2236$":[89],"ordinary":[90],"Polya":[91],"multiplier":[92],"$1269$":[95],"AM-GM":[96],"midpoint":[97],"overlay":[98],"leaves.":[99],"Human":[100],"authors":[101],"audited":[102],"mathematical":[104],"reductions":[105],"logic,":[108],"separate":[111],"artifact":[112],"contains":[113],"certificate,":[115],"an":[116],"independent":[117],"verifier,":[118],"from-source":[121],"rebuild":[122],"route.":[123]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-06T00:00:00"}
