{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:RIGIDBWVIA3NRU5OWM25L4PI5K","short_pith_number":"pith:RIGIDBWV","schema_version":"1.0","canonical_sha256":"8a0c8186d54036d8d3aeb335d5f1e8ea9f3d94efdc563ebb6f356ec36a7413d1","source":{"kind":"arxiv","id":"1307.3312","version":1},"attestation_state":"computed","paper":{"title":"Boolean algebras and Lubell functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kevin G. Milans, Linyuan Lu, Travis Johnston","submitted_at":"2013-07-12T03:21:44Z","abstract_excerpt":"Let $2^{[n]}$ denote the power set of $[n]:=\\{1,2,..., n\\}$. A collection $\\B\\subset 2^{[n]}$ forms a $d$-dimensional {\\em Boolean algebra} if there exist pairwise disjoint sets $X_0, X_1,..., X_d \\subseteq [n]$, all non-empty with perhaps the exception of $X_0$, so that $\\B={X_0\\cup \\bigcup_{i\\in I} X_i\\colon I\\subseteq [d]}$. Let $b(n,d)$ be the maximum cardinality of a family $\\F\\subset 2^X$ that does not contain a $d$-dimensional Boolean algebra. Gunderson, R\\\"odl, and Sidorenko proved that $b(n,d) \\leq c_d n^{-1/2^d} \\cdot 2^n$ where $c_d= 10^d 2^{-2^{1-d}}d^{d-2^{-d}}$.\n  In this paper, "},"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":"1307.3312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-12T03:21:44Z","cross_cats_sorted":[],"title_canon_sha256":"9d6403a33632da770c75bc7b577a8793a8d32e0d0c9f257dc0082f66b30ea195","abstract_canon_sha256":"342a35ded36e4d0e458e727d8a4b28494326030f2234dfa96ea9df41e6588776"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:39.502082Z","signature_b64":"2kQhUoh2jHH4YrCUXtS0KO/IlrBpCufaBzLjaUTU7RtzHgRU7U1sXWGyWry6UVlW/dcwLpNRODS1k1kcy18sBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a0c8186d54036d8d3aeb335d5f1e8ea9f3d94efdc563ebb6f356ec36a7413d1","last_reissued_at":"2026-05-18T03:18:39.501673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:39.501673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boolean algebras and Lubell functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kevin G. Milans, Linyuan Lu, Travis Johnston","submitted_at":"2013-07-12T03:21:44Z","abstract_excerpt":"Let $2^{[n]}$ denote the power set of $[n]:=\\{1,2,..., n\\}$. A collection $\\B\\subset 2^{[n]}$ forms a $d$-dimensional {\\em Boolean algebra} if there exist pairwise disjoint sets $X_0, X_1,..., X_d \\subseteq [n]$, all non-empty with perhaps the exception of $X_0$, so that $\\B={X_0\\cup \\bigcup_{i\\in I} X_i\\colon I\\subseteq [d]}$. Let $b(n,d)$ be the maximum cardinality of a family $\\F\\subset 2^X$ that does not contain a $d$-dimensional Boolean algebra. Gunderson, R\\\"odl, and Sidorenko proved that $b(n,d) \\leq c_d n^{-1/2^d} \\cdot 2^n$ where $c_d= 10^d 2^{-2^{1-d}}d^{d-2^{-d}}$.\n  In this paper, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3312","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":""},"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":"1307.3312","created_at":"2026-05-18T03:18:39.501737+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.3312v1","created_at":"2026-05-18T03:18:39.501737+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3312","created_at":"2026-05-18T03:18:39.501737+00:00"},{"alias_kind":"pith_short_12","alias_value":"RIGIDBWVIA3N","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"RIGIDBWVIA3NRU5O","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"RIGIDBWV","created_at":"2026-05-18T12:27:57.521954+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RIGIDBWVIA3NRU5OWM25L4PI5K","json":"https://pith.science/pith/RIGIDBWVIA3NRU5OWM25L4PI5K.json","graph_json":"https://pith.science/api/pith-number/RIGIDBWVIA3NRU5OWM25L4PI5K/graph.json","events_json":"https://pith.science/api/pith-number/RIGIDBWVIA3NRU5OWM25L4PI5K/events.json","paper":"https://pith.science/paper/RIGIDBWV"},"agent_actions":{"view_html":"https://pith.science/pith/RIGIDBWVIA3NRU5OWM25L4PI5K","download_json":"https://pith.science/pith/RIGIDBWVIA3NRU5OWM25L4PI5K.json","view_paper":"https://pith.science/paper/RIGIDBWV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.3312&json=true","fetch_graph":"https://pith.science/api/pith-number/RIGIDBWVIA3NRU5OWM25L4PI5K/graph.json","fetch_events":"https://pith.science/api/pith-number/RIGIDBWVIA3NRU5OWM25L4PI5K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RIGIDBWVIA3NRU5OWM25L4PI5K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RIGIDBWVIA3NRU5OWM25L4PI5K/action/storage_attestation","attest_author":"https://pith.science/pith/RIGIDBWVIA3NRU5OWM25L4PI5K/action/author_attestation","sign_citation":"https://pith.science/pith/RIGIDBWVIA3NRU5OWM25L4PI5K/action/citation_signature","submit_replication":"https://pith.science/pith/RIGIDBWVIA3NRU5OWM25L4PI5K/action/replication_record"}},"created_at":"2026-05-18T03:18:39.501737+00:00","updated_at":"2026-05-18T03:18:39.501737+00:00"}