{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5TY6Y6FN3GRKOSFNESO3WLFL6F","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":"3c1636bd84ca4e888e67af58cd872cb4161af6bed997922085024225f577bdee","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-06-03T16:26:59Z","title_canon_sha256":"78f4c5d0a4d7d42ee68e608b627a9179ce0fe6753acab116a3ecac14be76f18e"},"schema_version":"1.0","source":{"id":"2406.01499","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.01499","created_at":"2026-07-05T08:26:40Z"},{"alias_kind":"arxiv_version","alias_value":"2406.01499v1","created_at":"2026-07-05T08:26:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.01499","created_at":"2026-07-05T08:26:40Z"},{"alias_kind":"pith_short_12","alias_value":"5TY6Y6FN3GRK","created_at":"2026-07-05T08:26:40Z"},{"alias_kind":"pith_short_16","alias_value":"5TY6Y6FN3GRKOSFN","created_at":"2026-07-05T08:26:40Z"},{"alias_kind":"pith_short_8","alias_value":"5TY6Y6FN","created_at":"2026-07-05T08:26:40Z"}],"graph_snapshots":[{"event_id":"sha256:38506abb4b54e4a24ebb9b871a527b97f65ac51fe9a8a4e21a41d49b33bfbddd","target":"graph","created_at":"2026-07-05T08:26:40Z","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/2406.01499/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many problems in extremal combinatorics can be reduced to determining the independence number of a specific auxiliary hypergraph. We present two such problems, one from discrete geometry and one from hypergraph Tur\\'an theory. Using results on hypergraph colorings by Cooper-Mubayi and Li-Postle, we demonstrate that for those two problems the trivial lower bound on the independence number can be improved upon:\n  Erd\\H{o}s, Graham, Ruzsa and Taylor asked to determine the largest size, denoted by $g(n)$, of a subset $P$ of the grid $[n]^2$ such that every pair of points in $P$ span a different sl","authors_text":"Felix Christian Clemen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-06-03T16:26:59Z","title":"Applications of Sparse Hypergraph Colorings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.01499","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:a87e53f2832f2526a2c76e4d78db4b0b2f0eca71067cc1b2d9929cdd5a0ab20b","target":"record","created_at":"2026-07-05T08:26:40Z","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":"3c1636bd84ca4e888e67af58cd872cb4161af6bed997922085024225f577bdee","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-06-03T16:26:59Z","title_canon_sha256":"78f4c5d0a4d7d42ee68e608b627a9179ce0fe6753acab116a3ecac14be76f18e"},"schema_version":"1.0","source":{"id":"2406.01499","kind":"arxiv","version":1}},"canonical_sha256":"ecf1ec78add9a2a748ad249dbb2cabf16d4a5763a1e5a989b69e077cab40983f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecf1ec78add9a2a748ad249dbb2cabf16d4a5763a1e5a989b69e077cab40983f","first_computed_at":"2026-07-05T08:26:40.523103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:26:40.523103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZlfxvCb05L9KHl4M/CO/IJ/pO5n13Om27msGxqPdzZ1HNEJ6zPkAJociBlcO0DCln0ZIl896yfrh2dB3fx5RBw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:26:40.523591Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.01499","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a87e53f2832f2526a2c76e4d78db4b0b2f0eca71067cc1b2d9929cdd5a0ab20b","sha256:38506abb4b54e4a24ebb9b871a527b97f65ac51fe9a8a4e21a41d49b33bfbddd"],"state_sha256":"0d8fedde5eca1eee59fa2690d232018c7db0c4219777c4fc9aff65826b1189f7"}