{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QHUZ7273A4BLN6BIRKHXAITCOY","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":"f324994c6ea315d8ad718b22126c502f6cca5178d9c9b267efc9d690a03c071c","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-19T22:35:40Z","title_canon_sha256":"3f96d32d296dae7f7a36c72d65ec3e31c75e268b6a4b94436da529dda0d9e8ae"},"schema_version":"1.0","source":{"id":"1805.07670","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07670","created_at":"2026-05-17T23:47:07Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07670v2","created_at":"2026-05-17T23:47:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07670","created_at":"2026-05-17T23:47:07Z"},{"alias_kind":"pith_short_12","alias_value":"QHUZ7273A4BL","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QHUZ7273A4BLN6BI","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QHUZ7273","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:26e53db62f81f45c8029abb274f89702a84630ef8d64a6453bf3141f42c830be","target":"graph","created_at":"2026-05-17T23:47:07Z","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":"This paper considers the difficulty in the set-system approach to generalizing graph theory. These difficulties arise categorically as the category of set-system hypergraphs is shown not to be cartesian closed and lacks enough projective objects, unlike the category of directed multigraphs (i.e. quivers). The category of incidence hypergraphs is introduced as a \"graph-like\" remedy for the set-system issues so that hypergraphs may be studied by their locally graphic behavior via homomorphisms that allow an edge of the domain to be mapped into a subset of an edge in the codomain. Moreover, it is","authors_text":"Lucas J. Rusnak, Will Grilliette","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-19T22:35:40Z","title":"Incidence hypergraphs: The categorical inconsistency of set-systems and a characterization of quiver exponentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07670","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":"sha256:5b02b4d950289f6d27397c7cf25a6181a33dd38bee0118dd92303d55ee4c7147","target":"record","created_at":"2026-05-17T23:47:07Z","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":"f324994c6ea315d8ad718b22126c502f6cca5178d9c9b267efc9d690a03c071c","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-19T22:35:40Z","title_canon_sha256":"3f96d32d296dae7f7a36c72d65ec3e31c75e268b6a4b94436da529dda0d9e8ae"},"schema_version":"1.0","source":{"id":"1805.07670","kind":"arxiv","version":2}},"canonical_sha256":"81e99febfb0702b6f8288a8f70226276007aeb6653887a481bea8f91878673e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81e99febfb0702b6f8288a8f70226276007aeb6653887a481bea8f91878673e9","first_computed_at":"2026-05-17T23:47:07.450831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:07.450831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LsFDQ0x7vVANBJSpYXEJrjzyzIRi85hWGCp3P3J24xmuyRAbPTDW5bTVqUeEA6TJqT52gbWYndFXiLn3HNv+BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:07.451487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07670","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b02b4d950289f6d27397c7cf25a6181a33dd38bee0118dd92303d55ee4c7147","sha256:26e53db62f81f45c8029abb274f89702a84630ef8d64a6453bf3141f42c830be"],"state_sha256":"aa853ff3853dfd193e9f30e5d95b49dc717c90f9c43a8f236d26cbada386d268"}