{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HORNYUWCVAVME4TV77W3XNLIRM","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":"615e39db785130927feabddc74c979f80699bb21a076e585c451d98b8d7ade7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-16T06:12:58Z","title_canon_sha256":"b552f0f339096206edcbba3466e5ce4ffda900dd78aba3b05f139fada6c079d5"},"schema_version":"1.0","source":{"id":"1804.05511","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05511","created_at":"2026-05-17T23:40:20Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05511v2","created_at":"2026-05-17T23:40:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05511","created_at":"2026-05-17T23:40:20Z"},{"alias_kind":"pith_short_12","alias_value":"HORNYUWCVAVM","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HORNYUWCVAVME4TV","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HORNYUWC","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:3b8fa0abf3b29bf31371c955da4e7d22c6341eed10a3d3d278cdedcf70741afc","target":"graph","created_at":"2026-05-17T23:40:20Z","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":"The hypergraph regularity lemma -- the extension of Szemer\\'edi's graph regularity lemma to the setting of $k$-uniform hypergraphs -- is one of the most celebrated combinatorial results obtained in the past decade. By now there are several (very different) proofs of this lemma, obtained by Gowers, by Nagle-R\\\"odl-Schacht-Skokan and by Tao. Unfortunately, what all these proofs have in common is that they yield regular partitions whose order is given by the $k$-th Ackermann function. We show that such Ackermann-type bounds are unavoidable for every $k \\ge 2$, thus confirming a prediction of Tao.","authors_text":"Asaf Shapira, Guy Moshkovitz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-16T06:12:58Z","title":"A Tight Bound for Hypergraph Regularity I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05511","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":"sha256:3b61c9b7a73ff3dbf4d8546e7eea4f54b86205c7c811fa58119468aedcd5c209","target":"record","created_at":"2026-05-17T23:40:20Z","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":"615e39db785130927feabddc74c979f80699bb21a076e585c451d98b8d7ade7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-16T06:12:58Z","title_canon_sha256":"b552f0f339096206edcbba3466e5ce4ffda900dd78aba3b05f139fada6c079d5"},"schema_version":"1.0","source":{"id":"1804.05511","kind":"arxiv","version":2}},"canonical_sha256":"3ba2dc52c2a82ac27275ffedbbb5688b2cbc4ebc6b53fcc192036c6b18b7b185","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ba2dc52c2a82ac27275ffedbbb5688b2cbc4ebc6b53fcc192036c6b18b7b185","first_computed_at":"2026-05-17T23:40:20.793937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:20.793937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KH0CtIU7HmmG1xTeKyjLXMgvlQNJwUYMzXteX/JxPKqd5Trx6cntT4QmxVJzvv6MzVgN31zI8AH4IDWESsSXAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:20.794670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.05511","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b61c9b7a73ff3dbf4d8546e7eea4f54b86205c7c811fa58119468aedcd5c209","sha256:3b8fa0abf3b29bf31371c955da4e7d22c6341eed10a3d3d278cdedcf70741afc"],"state_sha256":"7562bc538b52019a1ed2c226b58242f07b9d3ff297f08e23271af39a37987fd1"}