{"id":"https://openalex.org/W7223347360","doi":"https://doi.org/10.48550/arxiv.2610.30503","title":"The linearity Conjecture","display_name":"The linearity Conjecture","publication_year":2026,"publication_date":"2026-10-21","ids":{"openalex":"https://openalex.org/W7223347360","doi":"https://doi.org/10.48550/arxiv.2610.30503"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.30503","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30503","pdf_url":"https://arxiv.org/pdf/2610.30503","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,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.30503","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009320630","display_name":"P\u00e9ter Sziklai","orcid":"https://orcid.org/0000-0001-5323-0887","observed_orcids":["https://orcid.org/0000-0001-5323-0887"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sziklai, Peter","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5009320630"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.6029999852180481,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.6029999852180481,"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/T10849","display_name":"Finite Group Theory Research","score":0.1282999962568283,"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/T11130","display_name":"Coding theory and cryptography","score":0.09229999780654907,"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/minimal-blocking-sets","display_name":"minimal blocking sets","score":0.9509999752044678},{"id":"https://openalex.org/keywords/projective-plane","display_name":"projective plane","score":0.7929999828338623},{"id":"https://openalex.org/keywords/finite-fields","display_name":"finite fields","score":0.7519999742507935},{"id":"https://openalex.org/keywords/subfields","display_name":"subfields","score":0.7570000290870667}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8432000279426575},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.8389999866485596},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7486000061035156},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5317999720573425},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4894999861717224},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4799000024795532},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44369998574256897},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.3962000012397766},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.3756999969482422},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.32120001316070557},{"id":"https://openalex.org/C144745244","wikidata":"https://www.wikidata.org/wiki/Q4927286","display_name":"Blocking (statistics)","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2784999907016754}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.30503","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30503","pdf_url":"https://arxiv.org/pdf/2610.30503","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,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.30503","doi":"https://doi.org/10.48550/arxiv.2610.30503","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.30503","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,"listed_in":[],"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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.30503","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30503","pdf_url":"https://arxiv.org/pdf/2610.30503","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,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335908","display_name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223347360.pdf","grobid_xml":"https://content.openalex.org/works/W7223347360.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1964404752","https://openalex.org/W2004755185","https://openalex.org/W2019004548","https://openalex.org/W2021647730","https://openalex.org/W2090714405","https://openalex.org/W2133091062","https://openalex.org/W2154186200","https://openalex.org/W2964307994","https://openalex.org/W3202621203","https://openalex.org/W4256178969","https://openalex.org/W7223158911"],"related_works":["https://openalex.org/W1820922198","https://openalex.org/W2090714405","https://openalex.org/W6948232622","https://openalex.org/W7098971758","https://openalex.org/W2181580799","https://openalex.org/W2048349637","https://openalex.org/W3134475546","https://openalex.org/W111208569","https://openalex.org/W2275601737","https://openalex.org/W2981932028"],"abstract_inverted_index":{"The":[0,49],"Linearity":[1,35,89],"Conjecture":[2,36,90],"states":[3],"that":[4],"in":[5],"the":[6,31,34,43,46,75,78,88],"projective":[7],"plane":[8],"PG(2,$q$),":[9],"$q=p^h$,":[10],"every":[11],"minimal":[12],"blocking":[13,47],"set":[14,21],"(w.r.t.":[15],"lines)":[16],"is":[17,42,81],"a":[18,60,71],"linear":[19],"point":[20],"over":[22],"some":[23],"subfield":[24],"of":[25,33,45,74],"${\\mathbb":[26],"F}_q$.":[27],"This":[28],"paper":[29],"contains":[30,51],"proof":[32],"for":[37,62,91],"$p^e\\ne":[38],"3,4$,":[39],"where":[40],"$e$":[41],"exponent":[44],"set.":[48],"text":[50],"3":[52],"concatenated":[53],"parts.":[54],"In":[55,83],"Part":[56,68,84],"0,":[57],"we":[58,86],"give":[59],"guide":[61],"reading":[63],"Parts":[64],"1":[65,69],"and":[66,77],"2.":[67],"develops":[70],"great":[72],"part":[73],"method,":[76],"case":[79],"$p^e=2$":[80],"solved.":[82],"2":[85],"prove":[87],"$p^e\\geq":[92],"5$.":[93]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-24T00:00:00"}