{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:ZZ7OYTJ3RLJJJPJ3LG7TGQ7DMC","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":"afbdd8bc6f2ffd026aeb5ec5a7eb273e5a4d70eca98ea153d514eff2637ceff7","cross_cats_sorted":["math.LO"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2021-11-02T16:59:06Z","title_canon_sha256":"a17d2cb7a23d1e2246a5ac7a17a9f8b32f457c0967123dc03ea258d3c0a59969"},"schema_version":"1.0","source":{"id":"2111.01737","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.01737","created_at":"2026-07-05T10:31:37Z"},{"alias_kind":"arxiv_version","alias_value":"2111.01737v4","created_at":"2026-07-05T10:31:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.01737","created_at":"2026-07-05T10:31:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZZ7OYTJ3RLJJ","created_at":"2026-07-05T10:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"ZZ7OYTJ3RLJJJPJ3","created_at":"2026-07-05T10:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"ZZ7OYTJ3","created_at":"2026-07-05T10:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:1d26f737fcf4e9dfb3dd3936d1bcb7fdcb023ccfdd7eec663de2a91ad8fb96e4","target":"graph","created_at":"2026-07-05T10:31:37Z","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/2111.01737/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Over the past several years, numerous authors have explored model theoretically motivated combinatorial conditions that ensure that a graph has an efficient regular decomposition in the sense of Szemer\\'edi. In this paper we set out a research program that explores a corresponding set of questions for 3-uniform hypergraphs, a setting in which useful notions of regularity are significantly more intricate.\n  The main results in this paper concern certain combinatorial properties which arose as natural higher-order generalizations of the order property in parallel work of the authors in the arith","authors_text":"C. Terry, J. Wolf","cross_cats":["math.LO"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2021-11-02T16:59:06Z","title":"Irregular triads in 3-uniform hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.01737","kind":"arxiv","version":4},"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":"sha256:5065e4d4980419800ee27849fd1cb7a386e240ea7434b123b755564bf746ea5c","target":"record","created_at":"2026-07-05T10:31:37Z","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":"afbdd8bc6f2ffd026aeb5ec5a7eb273e5a4d70eca98ea153d514eff2637ceff7","cross_cats_sorted":["math.LO"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2021-11-02T16:59:06Z","title_canon_sha256":"a17d2cb7a23d1e2246a5ac7a17a9f8b32f457c0967123dc03ea258d3c0a59969"},"schema_version":"1.0","source":{"id":"2111.01737","kind":"arxiv","version":4}},"canonical_sha256":"ce7eec4d3b8ad294bd3b59bf3343e3608759aa5f7355c8621c491f4c47c5d539","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce7eec4d3b8ad294bd3b59bf3343e3608759aa5f7355c8621c491f4c47c5d539","first_computed_at":"2026-07-05T10:31:37.689604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:31:37.689604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j4ZXh4DtMob+FDsrkBGDud4Gp3QwZByet0eRppHPS+DekJbT1lElARcRkyz7k/gUljUCNTpcD1RX0/KY93vyBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:31:37.690382Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.01737","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5065e4d4980419800ee27849fd1cb7a386e240ea7434b123b755564bf746ea5c","sha256:1d26f737fcf4e9dfb3dd3936d1bcb7fdcb023ccfdd7eec663de2a91ad8fb96e4"],"state_sha256":"5e836e2f91e230c3326022ff16af4b8a39467e02884711d1362b1c989dcc87ea"}