{"id":"https://openalex.org/W7225625220","doi":"https://doi.org/10.5281/zenodo.24090930","title":"Every three-coloring of R^7 contains a monochromatic unit square","display_name":"Every three-coloring of R^7 contains a monochromatic unit square","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225625220","doi":"https://doi.org/10.5281/zenodo.24090930"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24090930","doi":"https://doi.org/10.5281/zenodo.24090930","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24090930","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","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24090930","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157916437","display_name":"Carson Crocker","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Crocker, Carson","raw_affiliation_strings":["Independent researcher"],"raw_orcid":"https://orcid.org/0009-0009-2790-1187","affiliations":[{"raw_affiliation_string":"Independent researcher","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5157916437"],"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.8848000168800354,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.8848000168800354,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.023499999195337296,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.019899999722838402,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/drat-trim","display_name":"drat-trim","score":0.890999972820282},{"id":"https://openalex.org/keywords/lean-4-formal-verification","display_name":"Lean 4 formal verification","score":0.8529999852180481},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"computer-assisted proof","score":0.7900000214576721}],"concepts":[{"id":"https://openalex.org/C40833965","wikidata":"https://www.wikidata.org/wiki/Q6901438","display_name":"Monochromatic color","level":2,"score":0.6686999797821045},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6162999868392944},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5715000033378601},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.515999972820282},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5062000155448914},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42640000581741333},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4174000024795532},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.40149998664855957},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.3790999948978424},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.36039999127388},{"id":"https://openalex.org/C2776900844","wikidata":"https://www.wikidata.org/wiki/Q8028383","display_name":"Witness","level":2,"score":0.34700000286102295},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3465000092983246},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.33480000495910645},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3273000121116638},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3154999911785126},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C2778751112","wikidata":"https://www.wikidata.org/wiki/Q835016","display_name":"Window (computing)","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28850001096725464},{"id":"https://openalex.org/C2777831296","wikidata":"https://www.wikidata.org/wiki/Q12518","display_name":"Tower","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24090930","doi":"https://doi.org/10.5281/zenodo.24090930","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24090930","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.24090931","doi":"https://doi.org/10.5281/zenodo.24090931","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24090931","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.24090930","doi":"https://doi.org/10.5281/zenodo.24090930","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24090930","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/W7224429513","https://openalex.org/W4403370445","https://openalex.org/W7223280068","https://openalex.org/W7223235793","https://openalex.org/W3185786588","https://openalex.org/W7224136849","https://openalex.org/W7172244398","https://openalex.org/W7164935395","https://openalex.org/W2896809962","https://openalex.org/W7223031129"],"abstract_inverted_index":{"Every":[0],"coloring":[1],"of":[2,19,47],"R^7":[3],"with":[4],"three":[5],"colors":[6],"contains":[7],"a":[8,65,68,104],"monochromatic":[9],"unit":[10],"square,":[11],"so":[12,100],"d(3)":[13,31],"<=":[14,32],"7":[15],"in":[16],"the":[17,43,57,79,111,119,123],"notation":[18],"Gasarch,":[20],"Gezalyan":[21],"and":[22,34,74,76,117],"Parker":[23],"(SIGACT":[24],"News":[25],"56(3),":[26],"2025),":[27],"whose":[28],"column":[29],"gives":[30],"10":[33],"asks":[35],"for":[36],"better":[37],"upper":[38],"bounds.":[39],"The":[40],"witness":[41],"is":[42,64,102],"64":[44],"even-weight":[45],"points":[46],"{0,1}^7":[48],"scaled":[49],"by":[50],"1/sqrt(2).":[51],"A":[52,81],"short":[53],"hand":[54],"argument":[55],"reduces":[56],"claim":[58],"to":[59],"117":[60],"finite":[61],"cases.":[62],"This":[63],"computer-assisted":[66],"proof:":[67],"SAT":[69],"solver":[70],"refutes":[71],"each":[72],"case,":[73],"drat-trim":[75],"lrat-check":[77],"accept":[78],"proofs.":[80],"separate":[82],"Lean":[83],"4":[84],"proof":[85],"has":[86,128],"no":[87],"sorry;":[88],"it":[89,101],"trusts":[90],"compiled":[91],"code":[92],"at":[93],"118":[94],"steps":[95],"(117":[96],"bv_decide,":[97],"1":[98],"native_decide),":[99],"not":[103],"kernel-only":[105],"proof.":[106],"Running":[107],"\"bash":[108],"verify_all.sh\"":[109],"repeats":[110],"checks.":[112],"I":[113],"direct":[114],"AI":[115],"agents":[116],"built":[118],"checks;":[120],"Claude":[121],"did":[122],"detailed":[124],"work.":[125],"No":[126],"mathematician":[127],"refereed":[129],"this.":[130]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
