{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CKIRNAJLNIN4YXLI42M6SIQ5XC","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":"370af6a8a4867c0475579c48518c37515809a5513ce23529c9a982b54556884c","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-17T11:07:57Z","title_canon_sha256":"02c299c2ada385ec8c40474f8eef3e9e3a2e789ae3733c9ddaf52c7ccec7ec49"},"schema_version":"1.0","source":{"id":"1404.4486","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4486","created_at":"2026-05-18T02:53:55Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4486v2","created_at":"2026-05-18T02:53:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4486","created_at":"2026-05-18T02:53:55Z"},{"alias_kind":"pith_short_12","alias_value":"CKIRNAJLNIN4","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CKIRNAJLNIN4YXLI","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CKIRNAJL","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:643dcb5722c3e848ac9f653b1eb25cf96aa5724cd9672857fd3862b283928e42","target":"graph","created_at":"2026-05-18T02:53:55Z","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 family $\\mathcal{F}$ of permutations of the vertices of a hypergraph $H$ is called 'pairwise suitable' for $H$ if, for every pair of disjoint edges in $H$, there exists a permutation in $\\mathcal{F}$ in which all the vertices in one edge precede those in the other. The cardinality of a smallest such family of permutations for $H$ is called the 'separation dimension' of $H$ and is denoted by $\\pi(H)$. Equivalently, $\\pi(H)$ is the smallest natural number $k$ so that the vertices of $H$ can be embedded in $\\mathbb{R}^k$ such that any two disjoint edges of $H$ can be separated by a hyperplane n","authors_text":"Deepak Rajendraprasad, L. Sunil Chandran, Manu Basavaraju, Martin Charles Golumbic, Rogers Mathew","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-17T11:07:57Z","title":"Boxicity and separation dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4486","kind":"arxiv","version":2},"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":"sha256:1752fbf258fe5cb113b80c20164f7dd8fd3b209035e501a8ae7a8e8af96a191d","target":"record","created_at":"2026-05-18T02:53:55Z","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":"370af6a8a4867c0475579c48518c37515809a5513ce23529c9a982b54556884c","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-17T11:07:57Z","title_canon_sha256":"02c299c2ada385ec8c40474f8eef3e9e3a2e789ae3733c9ddaf52c7ccec7ec49"},"schema_version":"1.0","source":{"id":"1404.4486","kind":"arxiv","version":2}},"canonical_sha256":"129116812b6a1bcc5d68e699e9221db8a305170d113973f7656ac7b9b8eb6ff7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"129116812b6a1bcc5d68e699e9221db8a305170d113973f7656ac7b9b8eb6ff7","first_computed_at":"2026-05-18T02:53:55.612506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:55.612506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mEfpHCBx+yS9DeaVvLfNh1iYQNouCATN47/nfcOOrTu1KffxXM+uMcpAPJGIbPABIJog6DAbK7JRyH9BhgqSDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:55.613278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4486","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1752fbf258fe5cb113b80c20164f7dd8fd3b209035e501a8ae7a8e8af96a191d","sha256:643dcb5722c3e848ac9f653b1eb25cf96aa5724cd9672857fd3862b283928e42"],"state_sha256":"c543b6a09b9ae1a30e3e5cc6a6d4250952c305e846fae192d3871d421e9c6bf0"}