{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:3A3I5MZD2SPZB452NO52E24XPA","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":"897c5b53435c7e08e0b4fa8f88f8742fdb2757667f921e0598a23647384f1f3a","cross_cats_sorted":["cs.DM","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-07-22T02:55:56Z","title_canon_sha256":"873952730acc6e28e1e89dfd99c71b10667a3d84dbeb717ef32806d25b47347b"},"schema_version":"1.0","source":{"id":"2207.10850","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.10850","created_at":"2026-07-05T04:42:40Z"},{"alias_kind":"arxiv_version","alias_value":"2207.10850v1","created_at":"2026-07-05T04:42:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.10850","created_at":"2026-07-05T04:42:40Z"},{"alias_kind":"pith_short_12","alias_value":"3A3I5MZD2SPZ","created_at":"2026-07-05T04:42:40Z"},{"alias_kind":"pith_short_16","alias_value":"3A3I5MZD2SPZB452","created_at":"2026-07-05T04:42:40Z"},{"alias_kind":"pith_short_8","alias_value":"3A3I5MZD","created_at":"2026-07-05T04:42:40Z"}],"graph_snapshots":[{"event_id":"sha256:2cdfeb6ee7e790b82c0eeb6deb960ade6f2a62d0a86ebe9235480fb36fe3c6a7","target":"graph","created_at":"2026-07-05T04:42:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2207.10850/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The hypergraph Moore bound is an elegant statement that characterizes the extremal trade-off between the girth - the number of hyperedges in the smallest cycle or even cover (a subhypergraph with all degrees even) and size - the number of hyperedges in a hypergraph. For graphs (i.e., $2$-uniform hypergraphs), a bound tight up to the leading constant was proven in a classical work of Alon, Hoory and Linial [AHL02]. For hypergraphs of uniformity $k>2$, an appropriate generalization was conjectured by Feige [Fei08]. The conjecture was settled up to an additional $\\log^{4k+1} n$ factor in the size","authors_text":"Jun-Ting Hsieh, Pravesh K. Kothari, Sidhanth Mohanty","cross_cats":["cs.DM","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-07-22T02:55:56Z","title":"A simple and sharper proof of the hypergraph Moore bound"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.10850","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":"sha256:434cf05f23679f54e91c5d6ec8c83ca3dda50e86c95042907d65ab1df859cec6","target":"record","created_at":"2026-07-05T04:42:40Z","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":"897c5b53435c7e08e0b4fa8f88f8742fdb2757667f921e0598a23647384f1f3a","cross_cats_sorted":["cs.DM","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-07-22T02:55:56Z","title_canon_sha256":"873952730acc6e28e1e89dfd99c71b10667a3d84dbeb717ef32806d25b47347b"},"schema_version":"1.0","source":{"id":"2207.10850","kind":"arxiv","version":1}},"canonical_sha256":"d8368eb323d49f90f3ba6bbba26b977832da0afe33ef0fe03d1f3d6eb190e865","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8368eb323d49f90f3ba6bbba26b977832da0afe33ef0fe03d1f3d6eb190e865","first_computed_at":"2026-07-05T04:42:40.213261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:42:40.213261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jQPAW/uCfCdehh0Wblgib+ju+wTwNeWoGagi8lUWsJI4BaqXtr0aSo39SGteKdVMrJM2jV4fqcdFxap/UgemAA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:42:40.213661Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.10850","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:434cf05f23679f54e91c5d6ec8c83ca3dda50e86c95042907d65ab1df859cec6","sha256:2cdfeb6ee7e790b82c0eeb6deb960ade6f2a62d0a86ebe9235480fb36fe3c6a7"],"state_sha256":"453fea7d29c244911cbd6012cf1e7b008665e3ccd0d338d84d08e41af4960849"}