{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XE6LAD4TI5ICMJY22WSLUUZYFQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"085553caf19f95aada23d676c43188d3ad9ec73d0a4ebf1087eac1355abe0765","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-24T12:26:22Z","title_canon_sha256":"54e8680b3d611c3d55dafc6b94771393dfee2d26e631afdd6be292a2924e8b41"},"schema_version":"1.0","source":{"id":"1204.5355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5355","created_at":"2026-05-18T03:57:13Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5355v1","created_at":"2026-05-18T03:57:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5355","created_at":"2026-05-18T03:57:13Z"},{"alias_kind":"pith_short_12","alias_value":"XE6LAD4TI5IC","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XE6LAD4TI5ICMJY2","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XE6LAD4T","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:21e6d3a0bbfa03c76e6cef61f91c6326c9d7175127c1110cb0b5c63490414d59","target":"graph","created_at":"2026-05-18T03:57:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For a given finite poset $P$, $La(n,P)$ denotes the largest size of a family $\\mathcal{F}$ of subsets of $[n]$ not containing $P$ as a weak subposet. We exactly determine $La(n,P)$ for infinitely many $P$ posets. These posets are built from seven base posets using two operations. For arbitrary posets, an upper bound is given for $La(n,P)$ depending on $|P|$ and the size of the longest chain in $P$. To prove these theorems we introduce a new method, counting the intersections of $\\mathcal{F}$ with double chains, rather than chains.","authors_text":"D\\'aniel T. Nagy, P\\'eter Burcsi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-24T12:26:22Z","title":"The method of double chains for largest families with excluded subposets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5355","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8b581955d2732fed65f5869bf57c50f5ea75cf055797a0daf7c689ae9fc23683","target":"record","created_at":"2026-05-18T03:57:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"085553caf19f95aada23d676c43188d3ad9ec73d0a4ebf1087eac1355abe0765","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-24T12:26:22Z","title_canon_sha256":"54e8680b3d611c3d55dafc6b94771393dfee2d26e631afdd6be292a2924e8b41"},"schema_version":"1.0","source":{"id":"1204.5355","kind":"arxiv","version":1}},"canonical_sha256":"b93cb00f93475026271ad5a4ba53382c31a8a7814a72760d59e8d0ed0c5d838d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b93cb00f93475026271ad5a4ba53382c31a8a7814a72760d59e8d0ed0c5d838d","first_computed_at":"2026-05-18T03:57:13.451266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:13.451266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nxgmvkkUmOmsqU8fW9xQw1Wt+e4gmI/ONEmxzCqwKAhLkgEit48K3J8pYcE7uRBRdRfSMva3qfkUBzc5cYh/CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:13.451749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b581955d2732fed65f5869bf57c50f5ea75cf055797a0daf7c689ae9fc23683","sha256:21e6d3a0bbfa03c76e6cef61f91c6326c9d7175127c1110cb0b5c63490414d59"],"state_sha256":"27f6ff02b16cb32a8aadee790d08578c1fa5ed2b02645d5501e62648b4f7d6da"}