{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MM3UC5ZWJH7EXZ6VEAUBNIOFMM","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":"e68ba93e6c94d2f23974f46df25c7634a40891492ddb7a0a0389d65ea8547a0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-30T17:52:44Z","title_canon_sha256":"36a3a45a17a605884cbaacb99ee1ba00d033a7f18f9cc84e8c1be7e804b8a511"},"schema_version":"1.0","source":{"id":"1212.6756","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6756","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6756v1","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6756","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"pith_short_12","alias_value":"MM3UC5ZWJH7E","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MM3UC5ZWJH7EXZ6V","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MM3UC5ZW","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:58f1e8b4740358bb9301cc36f944151563916ea33186eaefb0fa74c5e368d4da","target":"graph","created_at":"2026-05-18T03:37:31Z","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 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 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 R^k such that any two disjoint edges of H can be separated by a hyperplane normal to one of the axes. We show that the separation d","authors_text":"Deepak Rajendraprasad, L. Sunil Chandran, Manu Basavaraju, Rogers Mathew","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-30T17:52:44Z","title":"Pairwise Suitable Family of Permutations and Boxicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6756","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":"sha256:0a514fe5c91b23211e07fa941e7a0b876f5f3a6f17421db386c365827448911f","target":"record","created_at":"2026-05-18T03:37:31Z","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":"e68ba93e6c94d2f23974f46df25c7634a40891492ddb7a0a0389d65ea8547a0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-30T17:52:44Z","title_canon_sha256":"36a3a45a17a605884cbaacb99ee1ba00d033a7f18f9cc84e8c1be7e804b8a511"},"schema_version":"1.0","source":{"id":"1212.6756","kind":"arxiv","version":1}},"canonical_sha256":"633741773649fe4be7d5202816a1c56334cf3d987875115b58f455419d6e5207","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"633741773649fe4be7d5202816a1c56334cf3d987875115b58f455419d6e5207","first_computed_at":"2026-05-18T03:37:31.005192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:31.005192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AM1NqDc3xLX1WhoqmiQeoO1/jFlVpNBj3r4EbCBOrSSjWPV7CnYB+rI3GdmxoS0P0HrxUNkOhAxzbUrQrHqDBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:31.005874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6756","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a514fe5c91b23211e07fa941e7a0b876f5f3a6f17421db386c365827448911f","sha256:58f1e8b4740358bb9301cc36f944151563916ea33186eaefb0fa74c5e368d4da"],"state_sha256":"aade35748d149e5c5385cf9b53493160c66a15aa1f8b586323056047f39fa74f"}