{"id":"https://openalex.org/W7168643262","doi":"https://doi.org/10.4230/lipics.itp.2026.26","title":"An End-To-End Verification of Keller\u2019s Conjecture","display_name":"An End-To-End Verification of Keller\u2019s Conjecture","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7168643262","doi":"https://doi.org/10.4230/lipics.itp.2026.26"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:27000","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2026.26","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol382-itp2026/LIPIcs.ITP.2026.26/LIPIcs.ITP.2026.26.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol382-itp2026/LIPIcs.ITP.2026.26/LIPIcs.ITP.2026.26.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038251501","display_name":"James Gallicchio","orcid":"https://orcid.org/0000-0002-0838-3240"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gallicchio, James","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":"https://orcid.org/0000-0002-0838-3240","affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024865188","display_name":"Cayden R. Codel","orcid":"https://orcid.org/0000-0003-3588-4873"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Codel, Cayden","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":"https://orcid.org/0000-0003-3588-4873","affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003483051","display_name":"Jeremy Avigad","orcid":"https://orcid.org/0000-0003-1275-315X"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Avigad, Jeremy","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":"https://orcid.org/0000-0003-1275-315X","affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025921874","display_name":"Marijn J. H. Heule","orcid":"https://orcid.org/0000-0002-5587-8801"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Heule, Marijn J. H.","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":"https://orcid.org/0000-0002-5587-8801","affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.86455499,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.14630000293254852,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.14630000293254852,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.13429999351501465,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.0723000019788742,"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/conjecture","display_name":"Conjecture","score":0.88919997215271},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.52920001745224},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.521399974822998},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.45829999446868896},{"id":"https://openalex.org/keywords/propositional-variable","display_name":"Propositional variable","score":0.40380001068115234},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.38530001044273376},{"id":"https://openalex.org/keywords/propositional-formula","display_name":"Propositional formula","score":0.3734000027179718},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.35530000925064087}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.88919997215271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5558000206947327},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.52920001745224},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.521399974822998},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5063999891281128},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.45829999446868896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4361000061035156},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.40380001068115234},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.398499995470047},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.38530001044273376},{"id":"https://openalex.org/C74640108","wikidata":"https://www.wikidata.org/wiki/Q1372900","display_name":"Propositional formula","level":5,"score":0.3734000027179718},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.35530000925064087},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.3528999984264374},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3221000134944916},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.31630000472068787},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C204795200","wikidata":"https://www.wikidata.org/wiki/Q903282","display_name":"Symmetry breaking","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2777999937534332},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.25999999046325684}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:27000","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2026.26","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol382-itp2026/LIPIcs.ITP.2026.26/LIPIcs.ITP.2026.26.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},{"id":"pmh:doi:10.4230/lipics.itp.2026.26","is_oa":true,"landing_page_url":"https://github.com/FormalSAT/trestle","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"ConferencePaper"},{"id":"doi:10.4230/lipics.itp.2026.26","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.itp.2026.26","pdf_url":null,"source":null,"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":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:27000","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2026.26","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol382-itp2026/LIPIcs.ITP.2026.26/LIPIcs.ITP.2026.26.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8357987069","display_name":"AIMing: A Neuro-Symbolic Approach to Mechanized Mathematical Reasoning","funder_award_id":"2434614","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7168643262.pdf","grobid_xml":"https://content.openalex.org/works/W7168643262.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,85,153],"1930,":[1],"Keller":[2],"conjectured":[3],"that":[4,17],"every":[5],"gap-free":[6],"tiling":[7],"of":[8,51,67,96,108,122,177],"\u211d\u207f":[9],"by":[10,60],"n-dimensional":[11],"unit":[12],"cubes":[13,16],"must":[14],"contain":[15],"fully":[18],"share":[19],"an":[20,90,118],"(n":[21],"-":[22],"1)-dimensional":[23],"face.":[24],"Keller\u2019s":[25,97,109],"conjecture":[26,63,98,110],"holds":[27],"for":[28,34,99,174],"n":[29,35,41],"\u2264":[30],"7":[31],"and":[32,53,78,145,162,184,200],"fails":[33],"\u2265":[36],"8.":[37],"The":[38,56],"final":[39],"case,":[40],"=":[42],"7,":[43],"was":[44,58,158,169],"settled":[45],"in":[46,93],"2020":[47],"using":[48],"a":[49,65,82,105,163],"mix":[50],"traditional":[52],"automated":[54,146],"reasoning.":[55,180],"result":[57],"obtained":[59],"reducing":[61],"the":[62,112,132,141,155,178,190],"to":[64,111,139,188],"set":[66],"clique-existence":[68,113],"problems,":[69,124],"encoding":[70,121],"those":[71,123],"problems":[72],"into":[73],"propositional":[74],"logic,":[75],"breaking":[76],"symmetries,":[77],"solving":[79],"them":[80],"with":[81],"SAT":[83,120],"solver.":[84],"this":[86],"paper,":[87],"we":[88,103,137,186],"present":[89],"end-to-end":[91],"verification":[92],"Lean":[94,161],"4":[95],"all":[100,176],"dimensions.":[101],"First,":[102],"simplify":[104],"prior":[106],"reduction":[107],"problems.":[114],"We":[115,181],"then":[116],"verify":[117],"improved":[119],"as":[125,127],"well":[126],"some":[128],"symmetry":[129,156,179],"reasoning":[130,157,191],"on":[131,171,196],"encoding.":[133],"Throughout":[134],"our":[135],"work,":[136],"sought":[138],"maximize":[140],"synergy":[142],"between":[143,160],"interactive":[144],"techniques":[147],"while":[148],"minimizing":[149],"human":[150],"proof":[151,165],"burden.":[152],"particular,":[154],"split":[159,189],"mechanically-checkable":[164],"system,":[166],"since":[167],"neither":[168],"suitable":[170],"their":[172,197],"own":[173],"verifying":[175],"discuss":[182],"how":[183],"why":[185],"chose":[187],"across":[192],"these":[193],"systems":[194],"based":[195],"relative":[198],"strengths":[199],"weaknesses.":[201]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-17T00:00:00"}