{"id":"https://openalex.org/W7159589524","doi":"https://doi.org/10.48550/arxiv.2604.27645","title":"An Exact 56-Addition, Rank-23 Scheme for General 3*3 Matrix Multiplication","display_name":"An Exact 56-Addition, Rank-23 Scheme for General 3*3 Matrix Multiplication","publication_year":2026,"publication_date":"2026-04-30","ids":{"openalex":"https://openalex.org/W7159589524","doi":"https://doi.org/10.48550/arxiv.2604.27645"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.27645","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.27645","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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.2604.27645","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028439227","display_name":"Yinqi Sun","orcid":"https://orcid.org/0009-0000-3783-5472"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sun, Yinqi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5028439227"],"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":0.6273999810218811,"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":0.6273999810218811,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.19189999997615814,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.0544000007212162,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.5587000250816345},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5160999894142151},{"id":"https://openalex.org/keywords/scalar-multiplication","display_name":"Scalar multiplication","score":0.5077000260353088},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5047000050544739},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4657000005245209},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.44600000977516174},{"id":"https://openalex.org/keywords/noncommutative-geometry","display_name":"Noncommutative geometry","score":0.4422999918460846},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.43689998984336853}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6324999928474426},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.5587000250816345},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5160999894142151},{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.5077000260353088},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5047000050544739},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47130000591278076},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4657000005245209},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.44600000977516174},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.4422999918460846},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.43689998984336853},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.4269999861717224},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4099000096321106},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4032999873161316},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.38999998569488525},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3538999855518341},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3474999964237213},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.3416999876499176},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.305400013923645},{"id":"https://openalex.org/C110342517","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Constant coefficients","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C206470798","wikidata":"https://www.wikidata.org/wiki/Q2634506","display_name":"Kleene algebra","level":2,"score":0.27489998936653137},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.2619999945163727},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2587999999523163},{"id":"https://openalex.org/C2780876879","wikidata":"https://www.wikidata.org/wiki/Q3054749","display_name":"Meaning (existential)","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.27645","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.27645","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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.2604.27645","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.27645","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"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],"present":[1],"a":[2,18],"rank-$23$":[3,40],"algorithm":[4,43],"for":[5,17],"general":[6],"$3\\times3$":[7],"matrix":[8],"multiplication":[9],"that":[10,58],"uses":[11],"$56$":[12],"additions/subtractions":[13],"and":[14,38,74,82,86],"$23$":[15],"multiplications,":[16],"total":[19],"of":[20,35],"$79$":[21],"scalar":[22],"operations":[23],"in":[24,62],"the":[25,32,68,75,79],"standard":[26],"bilinear":[27],"straight-line":[28,80],"model.":[29],"This":[30],"improves":[31],"recent":[33],"sequence":[34],"$60$-,":[36],"$59$-,":[37],"$58$-addition":[39],"schemes.":[41],"The":[42],"works":[44],"over":[45,72],"arbitrary":[46],"associative,":[47],"possibly":[48],"noncommutative,":[49],"coefficient":[50,60],"rings.":[51],"Its":[52],"tensor":[53],"coefficients":[54],"are":[55],"ternary,":[56],"meaning":[57],"every":[59],"lies":[61],"$\\{-1,0,1\\}$.":[63],"Correctness":[64],"is":[65],"certified":[66],"by":[67],"$729$":[69],"Brent":[70],"equations":[71],"$\\mathbb{Z}$,":[73],"verifier":[76],"also":[77],"expands":[78],"program":[81],"performs":[83],"additional":[84],"finite-field":[85],"noncommutative":[87],"implementation":[88],"tests.":[89]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-02T00:00:00"}
