{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HDFZF4TKHSUKW2JOSBV5MXQO7X","short_pith_number":"pith:HDFZF4TK","schema_version":"1.0","canonical_sha256":"38cb92f26a3ca8ab692e906bd65e0efdcbde20c5da4c0a24e5b5b9f7174ab557","source":{"kind":"arxiv","id":"1309.6686","version":1},"attestation_state":"computed","paper":{"title":"Packing Posets in the Boolean Lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew P. Dove, Jerrold R. Griggs","submitted_at":"2013-09-25T22:36:09Z","abstract_excerpt":"We are interested in maximizing the number of pairwise unrelated copies of a poset $P$ in the family of all subsets of $[n]$. We prove that for any $P$ the maximum number of unrelated copies of $P$ is asymptotic to a constant times the largest binomial coefficient. Moreover, the constant has the form $\\frac{1}{c(P)}$, where $c(P)$ is the size of the smallest convex closure over all embeddings of $P$ into the Boolean lattice."},"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":"1309.6686","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-25T22:36:09Z","cross_cats_sorted":[],"title_canon_sha256":"0dbd97fdc6a9a6c2f4361249d2f4e9e02f9292b9a65ff6bc193a226ae11abd3d","abstract_canon_sha256":"657a46b0388c7297aa4e474cb311e3ee7047463afaace6448f8a8ccb27a80f37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:10.874366Z","signature_b64":"PIcvkmRF6sOKcpc0bjOgAINoGm8xOzgr4/frx0oa3p0gN8oZrJVQD7f8F25429qI8T3kTra4ZAdhudqyTL0rDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38cb92f26a3ca8ab692e906bd65e0efdcbde20c5da4c0a24e5b5b9f7174ab557","last_reissued_at":"2026-05-18T03:12:10.873590Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:10.873590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Packing Posets in the Boolean Lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew P. Dove, Jerrold R. Griggs","submitted_at":"2013-09-25T22:36:09Z","abstract_excerpt":"We are interested in maximizing the number of pairwise unrelated copies of a poset $P$ in the family of all subsets of $[n]$. We prove that for any $P$ the maximum number of unrelated copies of $P$ is asymptotic to a constant times the largest binomial coefficient. Moreover, the constant has the form $\\frac{1}{c(P)}$, where $c(P)$ is the size of the smallest convex closure over all embeddings of $P$ into the Boolean lattice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6686","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":"1309.6686","created_at":"2026-05-18T03:12:10.873761+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.6686v1","created_at":"2026-05-18T03:12:10.873761+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6686","created_at":"2026-05-18T03:12:10.873761+00:00"},{"alias_kind":"pith_short_12","alias_value":"HDFZF4TKHSUK","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HDFZF4TKHSUKW2JO","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HDFZF4TK","created_at":"2026-05-18T12:27:46.883200+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/HDFZF4TKHSUKW2JOSBV5MXQO7X","json":"https://pith.science/pith/HDFZF4TKHSUKW2JOSBV5MXQO7X.json","graph_json":"https://pith.science/api/pith-number/HDFZF4TKHSUKW2JOSBV5MXQO7X/graph.json","events_json":"https://pith.science/api/pith-number/HDFZF4TKHSUKW2JOSBV5MXQO7X/events.json","paper":"https://pith.science/paper/HDFZF4TK"},"agent_actions":{"view_html":"https://pith.science/pith/HDFZF4TKHSUKW2JOSBV5MXQO7X","download_json":"https://pith.science/pith/HDFZF4TKHSUKW2JOSBV5MXQO7X.json","view_paper":"https://pith.science/paper/HDFZF4TK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.6686&json=true","fetch_graph":"https://pith.science/api/pith-number/HDFZF4TKHSUKW2JOSBV5MXQO7X/graph.json","fetch_events":"https://pith.science/api/pith-number/HDFZF4TKHSUKW2JOSBV5MXQO7X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HDFZF4TKHSUKW2JOSBV5MXQO7X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HDFZF4TKHSUKW2JOSBV5MXQO7X/action/storage_attestation","attest_author":"https://pith.science/pith/HDFZF4TKHSUKW2JOSBV5MXQO7X/action/author_attestation","sign_citation":"https://pith.science/pith/HDFZF4TKHSUKW2JOSBV5MXQO7X/action/citation_signature","submit_replication":"https://pith.science/pith/HDFZF4TKHSUKW2JOSBV5MXQO7X/action/replication_record"}},"created_at":"2026-05-18T03:12:10.873761+00:00","updated_at":"2026-05-18T03:12:10.873761+00:00"}