{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZRXDWXBA5OQVJOYTCZ7BNM7TF5","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":"07cd5c9e096f27971ea83b003794c12a6003a5318a4632430bcb2cea80d7f4a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-08-28T11:58:58Z","title_canon_sha256":"eec8b6995ebbe6d299dfdd9b3ed2419d90e8348499f0ee58188ee4c6a399a69e"},"schema_version":"1.0","source":{"id":"2508.20696","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.20696","created_at":"2026-07-05T12:00:58Z"},{"alias_kind":"arxiv_version","alias_value":"2508.20696v1","created_at":"2026-07-05T12:00:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.20696","created_at":"2026-07-05T12:00:58Z"},{"alias_kind":"pith_short_12","alias_value":"ZRXDWXBA5OQV","created_at":"2026-07-05T12:00:58Z"},{"alias_kind":"pith_short_16","alias_value":"ZRXDWXBA5OQVJOYT","created_at":"2026-07-05T12:00:58Z"},{"alias_kind":"pith_short_8","alias_value":"ZRXDWXBA","created_at":"2026-07-05T12:00:58Z"}],"graph_snapshots":[{"event_id":"sha256:e2395c1cce13a7683bcef0acbd0231f3c638909260103e73c8fe9835088a7bd2","target":"graph","created_at":"2026-07-05T12:00:58Z","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/2508.20696/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the 1980s, Erd\\H{o}s and S\\'os first introduced an extremal problem on hypergraphs with density constraints. Given an $r$-uniform hypergraph $F$ (or $r$-graph for short), its uniform Tur\\'an density $\\pi_u(F)$ is the smallest value of $d$ in which every hypergraph $H$ in which every linear-sized subhypergraph of $H$ has edge density at least $d$ contains $F$ as a subgraph. The first non-zero value of $\\pi_u(F)$ was not found until 30 years later.\n  Progress in studying the set of values of the uniform Tur\\'an density of $r$-graphs has been uneven in terms of $r$: to this day there are infin","authors_text":"Ander Lamaison","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-08-28T11:58:58Z","title":"Uniform Tur\\'an density beyond 3-graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.20696","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":"sha256:9ebf202d61a90d9a10b95c7d4b91c041002d1f22b2f6fd0cfada5df1f37169d2","target":"record","created_at":"2026-07-05T12:00:58Z","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":"07cd5c9e096f27971ea83b003794c12a6003a5318a4632430bcb2cea80d7f4a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-08-28T11:58:58Z","title_canon_sha256":"eec8b6995ebbe6d299dfdd9b3ed2419d90e8348499f0ee58188ee4c6a399a69e"},"schema_version":"1.0","source":{"id":"2508.20696","kind":"arxiv","version":1}},"canonical_sha256":"cc6e3b5c20eba154bb13167e16b3f32f6ed65263acf82b7eeba8c6e279719539","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc6e3b5c20eba154bb13167e16b3f32f6ed65263acf82b7eeba8c6e279719539","first_computed_at":"2026-07-05T12:00:58.147188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:00:58.147188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ZMfQlE+UQFkcQ2BxOjgnxOwj+ifSUNZBVEV1NvkUcMDr7PmgyNODz1QERZxkkeaXLeZAPlgCKtarnZuw5HAAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:00:58.147681Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.20696","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ebf202d61a90d9a10b95c7d4b91c041002d1f22b2f6fd0cfada5df1f37169d2","sha256:e2395c1cce13a7683bcef0acbd0231f3c638909260103e73c8fe9835088a7bd2"],"state_sha256":"178d4a0b3bd3b111947474650afcff5b87e4f2fa9dcb02463bb81f78c5a0a27c"}