{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KJZ4BKPUV3ETII2UBRDA3M6UAH","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":"7ece477448194acd21caf4f3e7513696ccb34812e20d3b9889973ff4df9061bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-17T12:50:37Z","title_canon_sha256":"bb21ba97939322ac84a9dbe6872ee58deae745a13af382c2883b75d0732ffda8"},"schema_version":"1.0","source":{"id":"1512.05565","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05565","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05565v1","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05565","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"KJZ4BKPUV3ET","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KJZ4BKPUV3ETII2U","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KJZ4BKPU","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:1fb17eb22480a43920f7e8afff92ee5fb41b2e2c2e9d616aaf78e46c3d71c962","target":"graph","created_at":"2026-05-18T01:24:09Z","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":"A subposet $Q'$ of a poset $Q$ is a copy of a poset $P$ if there is a bijection $f$ between elements of $P$ and $Q'$ such that $x\\leq y$ in $P$ iff $f(x)\\leq f(y)$ in $Q'$. For posets $P, P'$, let the poset Ramsey number $R(P,P')$ be the smallest $N$ such that no matter how the elements of the Boolean lattice $Q_N$ are colored red and blue, there is a copy of $P$ with all red elements or a copy of $P'$ with all blue elements. We provide some general bounds on $R(P,P')$ and focus on the situation when $P$ and $P'$ are both Boolean lattices. In addition, we give asymptotically tight bounds for t","authors_text":"Maria Axenovich, Stefan Walzer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-17T12:50:37Z","title":"Boolean lattices: Ramsey properties and embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05565","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:b15bbd948ed70d5776ddc3849c5903b6915db2c5803d260300aa76a2c2adb1b7","target":"record","created_at":"2026-05-18T01:24:09Z","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":"7ece477448194acd21caf4f3e7513696ccb34812e20d3b9889973ff4df9061bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-17T12:50:37Z","title_canon_sha256":"bb21ba97939322ac84a9dbe6872ee58deae745a13af382c2883b75d0732ffda8"},"schema_version":"1.0","source":{"id":"1512.05565","kind":"arxiv","version":1}},"canonical_sha256":"5273c0a9f4aec93423540c460db3d401e88f68cc38d8dd317c14f413ee1c8254","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5273c0a9f4aec93423540c460db3d401e88f68cc38d8dd317c14f413ee1c8254","first_computed_at":"2026-05-18T01:24:09.787889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:09.787889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EYdSExH3LEFdNk/9/RP/5FDfd8fZUFx5NLViw7cKhsmoVo4YvFd+MnmgDMLowDBaOGpnynMYBzv/r84K4tXFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:09.788535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05565","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b15bbd948ed70d5776ddc3849c5903b6915db2c5803d260300aa76a2c2adb1b7","sha256:1fb17eb22480a43920f7e8afff92ee5fb41b2e2c2e9d616aaf78e46c3d71c962"],"state_sha256":"927f0cd2655404bfa80717bb1672f1e0b4b6dd3ebbae96d05293d190b2521590"}