{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WEMUUIVVT4TFUQDV4KANLGU7QY","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":"ab70f85dabd80487961e941527ea6f400754e613b57bf7d9d17dc1b529c3d621","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-10-19T12:31:28Z","title_canon_sha256":"23ab197fdc54eb644d6e71f889794c23a38c680f744a4d2aeb25f94be309cca3"},"schema_version":"1.0","source":{"id":"2310.12685","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.12685","created_at":"2026-07-05T08:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"2310.12685v2","created_at":"2026-07-05T08:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.12685","created_at":"2026-07-05T08:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"WEMUUIVVT4TF","created_at":"2026-07-05T08:42:53Z"},{"alias_kind":"pith_short_16","alias_value":"WEMUUIVVT4TFUQDV","created_at":"2026-07-05T08:42:53Z"},{"alias_kind":"pith_short_8","alias_value":"WEMUUIVV","created_at":"2026-07-05T08:42:53Z"}],"graph_snapshots":[{"event_id":"sha256:e18657f9cbf0c992132043d6f04b5ddc3b7551e3748d477d4bfe0c71892564a5","target":"graph","created_at":"2026-07-05T08:42:53Z","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/2310.12685/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For positive integers $m$ and $n$, the Zarankiewicz number $Z_{2,2}(m,n)$ can be defined as the maximum total degree of a linear hypergraph with $m$ vertices and $n$ edges. Guy determined $Z_{2,2}(m,n)$ for all $n \\geq \\binom{m}{2}/3+O(m)$. Here, we extend this by determining $Z_{2,2}(m,n)$ for all $n \\geq \\binom{m}{2}/3$ and, when $m$ is large, for all $n \\geq \\binom{m}{2}/6+O(m)$.","authors_text":"Adam Mammoliti, Daniel Horsley, Guangzhou Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-10-19T12:31:28Z","title":"Zarankiewicz numbers near the triple system threshold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.12685","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":"sha256:9da89ae026c6751ac80407b748d037466b34a422416321075a54b80b56cd7c0d","target":"record","created_at":"2026-07-05T08:42:53Z","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":"ab70f85dabd80487961e941527ea6f400754e613b57bf7d9d17dc1b529c3d621","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-10-19T12:31:28Z","title_canon_sha256":"23ab197fdc54eb644d6e71f889794c23a38c680f744a4d2aeb25f94be309cca3"},"schema_version":"1.0","source":{"id":"2310.12685","kind":"arxiv","version":2}},"canonical_sha256":"b1194a22b59f265a4075e280d59a9f861fdba2137fb735177443c08c6c306c1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1194a22b59f265a4075e280d59a9f861fdba2137fb735177443c08c6c306c1e","first_computed_at":"2026-07-05T08:42:53.178073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:42:53.178073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dIjSZ2+0D/CVJHsYEotErbJukeVRp4uq+vKFp5uCmXQ3A1iXjL3u/ic54Hs2wzxRCQ2KmK0RA/9iNLrH6zFiCA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:42:53.178548Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.12685","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9da89ae026c6751ac80407b748d037466b34a422416321075a54b80b56cd7c0d","sha256:e18657f9cbf0c992132043d6f04b5ddc3b7551e3748d477d4bfe0c71892564a5"],"state_sha256":"fec401d410b81dcd72a57df677d7fe87e71914051a98d3a28a7c5b9b13222cfc"}