{"id":"https://openalex.org/W7208747814","doi":"https://doi.org/10.48550/arxiv.2609.03489","title":"Another counterexample to the Nerves of Steel Conjecture","display_name":"Another counterexample to the Nerves of Steel Conjecture","publication_year":2026,"publication_date":"2026-09-03","ids":{"openalex":"https://openalex.org/W7208747814","doi":"https://doi.org/10.48550/arxiv.2609.03489"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.03489","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03489","pdf_url":"https://arxiv.org/pdf/2609.03489","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/2609.03489","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086285555","display_name":"Kevin Coulembier","orcid":"https://orcid.org/0000-0003-0996-3965","observed_orcids":["https://orcid.org/0000-0003-0996-3965"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Coulembier, Kevin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5086285555"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.7401999831199646,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.7401999831199646,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.19429999589920044,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.00860000029206276,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/prime-spectrum","display_name":"prime spectrum","score":0.7639999985694885},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.8289999961853027},{"id":"https://openalex.org/keywords/support-theory","display_name":"support theory","score":0.49399998784065247}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.9854000210762024},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8756999969482422},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7414000034332275},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.6416000127792358},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.600600004196167},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5695000290870667},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.5145000219345093},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5055000185966492},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43560001254081726},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4032999873161316},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.30169999599456787},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2621999979019165}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.03489","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03489","pdf_url":"https://arxiv.org/pdf/2609.03489","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.2609.03489","doi":"https://doi.org/10.48550/arxiv.2609.03489","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.03489","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.03489","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03489","pdf_url":"https://arxiv.org/pdf/2609.03489","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":[{"id":"https://openalex.org/G4767662469","display_name":"Developing an analytic theory of monoidal categories","funder_award_id":"DP250100762","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7208747814.pdf","grobid_xml":"https://content.openalex.org/works/W7208747814.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4414988016","https://openalex.org/W7141429283","https://openalex.org/W7162399486"],"related_works":["https://openalex.org/W4413982877","https://openalex.org/W4414988016","https://openalex.org/W3203483521","https://openalex.org/W7106861486","https://openalex.org/W7221176124","https://openalex.org/W7165685846","https://openalex.org/W2613384594","https://openalex.org/W4403705273","https://openalex.org/W4407238412","https://openalex.org/W3187091039"],"abstract_inverted_index":{"In":[0,65],"[B2]":[1],"Balmer":[2],"introduced":[3],"the":[4,14,27,36,52,73,81],"homological":[5],"spectrum":[6],"of":[7,16,33,45],"a":[8,60,70],"rigid":[9],"tensor-triangulated":[10],"category,":[11],"and":[12,57],"had":[13],"``nerves":[15],"steel''":[17],"not":[18],"to":[19,39,59,72,80],"conjecture":[20,53,82],"that":[21],"it":[22],"was":[23,54,88],"in":[24,50,76,91],"bijection":[25],"with":[26],"prime":[28],"spectrum,":[29],"despite":[30],"an":[31],"``avalanche":[32],"examples''.":[34],"Naturally,":[35],"statement":[37],"came":[38],"be":[40],"known":[41],"as":[42],"Balmer's":[43],"Nerves":[44],"Steel":[46],"Conjecture.":[47],"More":[48],"recently,":[49],"[NVY]":[51],"stated":[55],"explicitly":[56],"extended":[58],"more":[61],"general":[62],"non-symmetric":[63],"context.":[64],"this":[66],"paper":[67],"we":[68],"provide":[69],"counterexample":[71,87],"original":[74],"suggestion":[75],"[B2],":[77],"so":[78],"also":[79],"from":[83],"[NVY].":[84],"A":[85],"first":[86],"recently":[89],"constructed":[90],"[BHR].":[92]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-05T00:00:00"}
