{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:4NECLZLRWEAG6UTEX6WT574ROH","short_pith_number":"pith:4NECLZLR","schema_version":"1.0","canonical_sha256":"e34825e571b1006f5264bfad3eff9171ffdc259bbfd0a3d3f3f36ed9d41ec886","source":{"kind":"arxiv","id":"2203.10003","version":1},"attestation_state":"computed","paper":{"title":"On flag spheres with few equators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lorenzo Venturello","submitted_at":"2022-03-18T15:04:10Z","abstract_excerpt":"In this note we construct a flag simplicial $3$-sphere $\\Delta$ with the following properties: - $\\Delta$ is not a suspension; - $\\Delta$ has no edge that can be contracted to obtain another flag sphere; - The only equators (induced subcomplexes which are spheres of codimension $1$) of $\\Delta$ are vertex links. Our construction has $12$ vertices, the minimum number of vertices such a simplicial complex can have. This answers a question posed by Chudnovsky and Nevo."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2203.10003","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-03-18T15:04:10Z","cross_cats_sorted":[],"title_canon_sha256":"704aabedcbd52a70fc84ce944390de283928380a9bd4aa3775bcc35af36f6001","abstract_canon_sha256":"cdf36a0eac80a209911db75840ad4cfd6f0ff4305f59f082ae700bffaa387361"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:06:26.681527Z","signature_b64":"VWS4e0sKh+N58WgoEGGjMDXAS7jqFVMzcSp3HVRhToguROpl4VmVN82YdiZdUYTKXXRZwQdqlswubRu5hOA7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e34825e571b1006f5264bfad3eff9171ffdc259bbfd0a3d3f3f36ed9d41ec886","last_reissued_at":"2026-07-05T04:06:26.681020Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:06:26.681020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On flag spheres with few equators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lorenzo Venturello","submitted_at":"2022-03-18T15:04:10Z","abstract_excerpt":"In this note we construct a flag simplicial $3$-sphere $\\Delta$ with the following properties: - $\\Delta$ is not a suspension; - $\\Delta$ has no edge that can be contracted to obtain another flag sphere; - The only equators (induced subcomplexes which are spheres of codimension $1$) of $\\Delta$ are vertex links. Our construction has $12$ vertices, the minimum number of vertices such a simplicial complex can have. This answers a question posed by Chudnovsky and Nevo."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.10003","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.10003/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2203.10003","created_at":"2026-07-05T04:06:26.681090+00:00"},{"alias_kind":"arxiv_version","alias_value":"2203.10003v1","created_at":"2026-07-05T04:06:26.681090+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.10003","created_at":"2026-07-05T04:06:26.681090+00:00"},{"alias_kind":"pith_short_12","alias_value":"4NECLZLRWEAG","created_at":"2026-07-05T04:06:26.681090+00:00"},{"alias_kind":"pith_short_16","alias_value":"4NECLZLRWEAG6UTE","created_at":"2026-07-05T04:06:26.681090+00:00"},{"alias_kind":"pith_short_8","alias_value":"4NECLZLR","created_at":"2026-07-05T04:06:26.681090+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.16905","citing_title":"Lower bounds on the $g$-numbers of spheres without large missing faces","ref_index":35,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4NECLZLRWEAG6UTEX6WT574ROH","json":"https://pith.science/pith/4NECLZLRWEAG6UTEX6WT574ROH.json","graph_json":"https://pith.science/api/pith-number/4NECLZLRWEAG6UTEX6WT574ROH/graph.json","events_json":"https://pith.science/api/pith-number/4NECLZLRWEAG6UTEX6WT574ROH/events.json","paper":"https://pith.science/paper/4NECLZLR"},"agent_actions":{"view_html":"https://pith.science/pith/4NECLZLRWEAG6UTEX6WT574ROH","download_json":"https://pith.science/pith/4NECLZLRWEAG6UTEX6WT574ROH.json","view_paper":"https://pith.science/paper/4NECLZLR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2203.10003&json=true","fetch_graph":"https://pith.science/api/pith-number/4NECLZLRWEAG6UTEX6WT574ROH/graph.json","fetch_events":"https://pith.science/api/pith-number/4NECLZLRWEAG6UTEX6WT574ROH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4NECLZLRWEAG6UTEX6WT574ROH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4NECLZLRWEAG6UTEX6WT574ROH/action/storage_attestation","attest_author":"https://pith.science/pith/4NECLZLRWEAG6UTEX6WT574ROH/action/author_attestation","sign_citation":"https://pith.science/pith/4NECLZLRWEAG6UTEX6WT574ROH/action/citation_signature","submit_replication":"https://pith.science/pith/4NECLZLRWEAG6UTEX6WT574ROH/action/replication_record"}},"created_at":"2026-07-05T04:06:26.681090+00:00","updated_at":"2026-07-05T04:06:26.681090+00:00"}