{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:NP43X3CS5EPAWDBHQPMGAXILRM","short_pith_number":"pith:NP43X3CS","schema_version":"1.0","canonical_sha256":"6bf9bbec52e91e0b0c2783d8605d0b8b3fdd737c79bc27c2feb8318483648d6a","source":{"kind":"arxiv","id":"2404.02024","version":3},"attestation_state":"computed","paper":{"title":"Growth of regular partitions 3: strong regularity and the vertex partition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"C. Terry","submitted_at":"2024-04-02T15:14:24Z","abstract_excerpt":"We consider here the strong regularity for $3$-uniform hypergraphs developed by Frankl, Gowers, Kohayakawa, Nagle, R\\\"{o}dl, Skokan, and Schacht. This type of regular decomposition comes with two components, a partition of the vertices, and a partition of the pairs of vertices. The data of a regular decomposition also includes two parameters measuring quasirandomness, a fixed constant $\\epsilon_1>0$, and a function $\\epsilon_2:\\mathbb{N}\\rightarrow (0,1]$. We define two growth functions associated to a hereditary property $\\mathcal{H}$ of $3$-uniform hypergraphs: $T_{\\mathcal{H}}(\\epsilon_1,\\e"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2404.02024","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-04-02T15:14:24Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"aca01a28a30e94c5f15a8e126596cfb8af3e6daf431e5ae5e4375a6b8155176c","abstract_canon_sha256":"38242c637eacdf025eec64aff867d13f9787bf02eb5c60e981cf78d5a39da858"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:47:11.414246Z","signature_b64":"OkpndWs8XGTJichzE0yBfqtqdQOJfXrndvDt1eNL28eis2xx+UcgymnVLXp2ap/Ht9QrWZjbbiE5Ja/KnSJGAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bf9bbec52e91e0b0c2783d8605d0b8b3fdd737c79bc27c2feb8318483648d6a","last_reissued_at":"2026-07-05T11:47:11.413733Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:47:11.413733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Growth of regular partitions 3: strong regularity and the vertex partition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"C. Terry","submitted_at":"2024-04-02T15:14:24Z","abstract_excerpt":"We consider here the strong regularity for $3$-uniform hypergraphs developed by Frankl, Gowers, Kohayakawa, Nagle, R\\\"{o}dl, Skokan, and Schacht. This type of regular decomposition comes with two components, a partition of the vertices, and a partition of the pairs of vertices. The data of a regular decomposition also includes two parameters measuring quasirandomness, a fixed constant $\\epsilon_1>0$, and a function $\\epsilon_2:\\mathbb{N}\\rightarrow (0,1]$. We define two growth functions associated to a hereditary property $\\mathcal{H}$ of $3$-uniform hypergraphs: $T_{\\mathcal{H}}(\\epsilon_1,\\e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.02024","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.02024/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2404.02024","created_at":"2026-07-05T11:47:11.413798+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.02024v3","created_at":"2026-07-05T11:47:11.413798+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.02024","created_at":"2026-07-05T11:47:11.413798+00:00"},{"alias_kind":"pith_short_12","alias_value":"NP43X3CS5EPA","created_at":"2026-07-05T11:47:11.413798+00:00"},{"alias_kind":"pith_short_16","alias_value":"NP43X3CS5EPAWDBH","created_at":"2026-07-05T11:47:11.413798+00:00"},{"alias_kind":"pith_short_8","alias_value":"NP43X3CS","created_at":"2026-07-05T11:47:11.413798+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.09969","citing_title":"Regularity for hypergraphs with bounded VC$_2$ dimension","ref_index":62,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NP43X3CS5EPAWDBHQPMGAXILRM","json":"https://pith.science/pith/NP43X3CS5EPAWDBHQPMGAXILRM.json","graph_json":"https://pith.science/api/pith-number/NP43X3CS5EPAWDBHQPMGAXILRM/graph.json","events_json":"https://pith.science/api/pith-number/NP43X3CS5EPAWDBHQPMGAXILRM/events.json","paper":"https://pith.science/paper/NP43X3CS"},"agent_actions":{"view_html":"https://pith.science/pith/NP43X3CS5EPAWDBHQPMGAXILRM","download_json":"https://pith.science/pith/NP43X3CS5EPAWDBHQPMGAXILRM.json","view_paper":"https://pith.science/paper/NP43X3CS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.02024&json=true","fetch_graph":"https://pith.science/api/pith-number/NP43X3CS5EPAWDBHQPMGAXILRM/graph.json","fetch_events":"https://pith.science/api/pith-number/NP43X3CS5EPAWDBHQPMGAXILRM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NP43X3CS5EPAWDBHQPMGAXILRM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NP43X3CS5EPAWDBHQPMGAXILRM/action/storage_attestation","attest_author":"https://pith.science/pith/NP43X3CS5EPAWDBHQPMGAXILRM/action/author_attestation","sign_citation":"https://pith.science/pith/NP43X3CS5EPAWDBHQPMGAXILRM/action/citation_signature","submit_replication":"https://pith.science/pith/NP43X3CS5EPAWDBHQPMGAXILRM/action/replication_record"}},"created_at":"2026-07-05T11:47:11.413798+00:00","updated_at":"2026-07-05T11:47:11.413798+00:00"}