{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:H6OQGXZP4SN6ATMAN5TMCT7Y5E","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":"6266d23ab9a0230c30b703b957386b506bf656627b8cb4c29100c5c9c995edf0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-15T22:33:34Z","title_canon_sha256":"1a367bc01d001c55a3aa546d3d3601890a91d58a21a92e061b24726c415127c6"},"schema_version":"1.0","source":{"id":"1905.06459","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.06459","created_at":"2026-05-17T23:46:02Z"},{"alias_kind":"arxiv_version","alias_value":"1905.06459v1","created_at":"2026-05-17T23:46:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.06459","created_at":"2026-05-17T23:46:02Z"},{"alias_kind":"pith_short_12","alias_value":"H6OQGXZP4SN6","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"H6OQGXZP4SN6ATMA","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"H6OQGXZP","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:96219ea02a4068e21284505631e0b3bbcba2eb6c3b916221c9dfe17014f2b34f","target":"graph","created_at":"2026-05-17T23:46:02Z","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":"An Euler tour of a hypergraph is a closed walk that traverses every edge exactly once; if a hypergraph admits such a walk, then it is called eulerian. Although this notion is one of the progenitors of graph theory --- dating back to the eighteenth century --- treatment of this subject has only begun on hypergraphs in the last decade. Other authors have produced results about rank-2 universal cycles and 1-overlap cycles, which are equivalent to our definition of Euler tours. In contrast, an Euler family is a collection of nontrivial closed walks that jointly traverse every edge of the hypergrap","authors_text":"Andrew Wagner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-15T22:33:34Z","title":"Eulerian Properties of Design Hypergraphs and Hypergraphs with Small Edge Cuts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06459","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:da7d1f9bd602c06efd6ca7431a1fcc74401385b89b0ad657423efe62e6de5e38","target":"record","created_at":"2026-05-17T23:46:02Z","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":"6266d23ab9a0230c30b703b957386b506bf656627b8cb4c29100c5c9c995edf0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-15T22:33:34Z","title_canon_sha256":"1a367bc01d001c55a3aa546d3d3601890a91d58a21a92e061b24726c415127c6"},"schema_version":"1.0","source":{"id":"1905.06459","kind":"arxiv","version":1}},"canonical_sha256":"3f9d035f2fe49be04d806f66c14ff8e9153b0418f1913386d1481f87bbe06f0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f9d035f2fe49be04d806f66c14ff8e9153b0418f1913386d1481f87bbe06f0d","first_computed_at":"2026-05-17T23:46:02.338574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:02.338574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Aa1+MIdisHXDX8zRbHuk6Dkkcgz+DkvZcfWd7qlni/i9bUxkGsn/kRPlGKetAMXJX79Co7mA/bKvkqUBm+gzDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:02.339371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.06459","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da7d1f9bd602c06efd6ca7431a1fcc74401385b89b0ad657423efe62e6de5e38","sha256:96219ea02a4068e21284505631e0b3bbcba2eb6c3b916221c9dfe17014f2b34f"],"state_sha256":"1a67fa4bb0a396d84ff60608770f79c932e47320a9448e4fe42b16d1626a87bf"}