{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2SDZAA64MLTPTRC24SSKQI2KBP","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":"4fa2687b611cbb22f7de0c83de551ca66dbe272a90fe047c41416b8762a180cf","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-02-27T02:00:44Z","title_canon_sha256":"808def7825b37c3896b1eebee5b9e60fdfc3fe377200e9b722589e6d9b84292d"},"schema_version":"1.0","source":{"id":"2402.17137","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.17137","created_at":"2026-07-05T11:50:25Z"},{"alias_kind":"arxiv_version","alias_value":"2402.17137v2","created_at":"2026-07-05T11:50:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.17137","created_at":"2026-07-05T11:50:25Z"},{"alias_kind":"pith_short_12","alias_value":"2SDZAA64MLTP","created_at":"2026-07-05T11:50:25Z"},{"alias_kind":"pith_short_16","alias_value":"2SDZAA64MLTPTRC2","created_at":"2026-07-05T11:50:25Z"},{"alias_kind":"pith_short_8","alias_value":"2SDZAA64","created_at":"2026-07-05T11:50:25Z"}],"graph_snapshots":[{"event_id":"sha256:0e1ff4e1381603f74ce6f46fdc36e54affb9f93a0e784c730d63c640e7c8f3be","target":"graph","created_at":"2026-07-05T11:50:25Z","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/2402.17137/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A set of points $S$ in Euclidean space $\\mathbb{R}^d$ is called \\textit{Ramsey} if any finite partition of $\\mathbb{R}^{\\infty}$ yields a monochromatic copy of $S$. While characterization of Ramsey set remains a major open problem in the area, a stronger ``density'' concept was considered in [J. Amer. Math. Soc. 3, 1--7, 1990]: If $S$ is a $d$-dimensional simplex, then for any $\\mu>0$ there is an integer $d:=d(S,\\mu)$ and finite configuration $X\\subseteq \\mathbb{R}^d$ such that any subconfiguration $Y\\subseteq X$ with $|Y|\\geq \\mu |X|$ contains a copy of $S$. Complementing this, here we show t","authors_text":"Marcelo Sales, Vojt\\v{e}ch R\\\"odl","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-02-27T02:00:44Z","title":"Nowhere dense Ramsey sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.17137","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":"sha256:6db73d24a2001a1f6fc96c94384a217f524a3d45a69003b3bfb4819e1bbd16a6","target":"record","created_at":"2026-07-05T11:50:25Z","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":"4fa2687b611cbb22f7de0c83de551ca66dbe272a90fe047c41416b8762a180cf","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-02-27T02:00:44Z","title_canon_sha256":"808def7825b37c3896b1eebee5b9e60fdfc3fe377200e9b722589e6d9b84292d"},"schema_version":"1.0","source":{"id":"2402.17137","kind":"arxiv","version":2}},"canonical_sha256":"d4879003dc62e6f9c45ae4a4a8234a0be8eafa1fcd4d04f53a57a07b1be1f1c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4879003dc62e6f9c45ae4a4a8234a0be8eafa1fcd4d04f53a57a07b1be1f1c1","first_computed_at":"2026-07-05T11:50:25.825935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:50:25.825935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pZhnNJ0x27mx99UkK0xR74BaBNZhhh8DN14mZyUKcKaW6F7fgJz1yeKt+qYBvfLQVyTqYHjlZqQncAAjL/W/AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:50:25.826452Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.17137","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6db73d24a2001a1f6fc96c94384a217f524a3d45a69003b3bfb4819e1bbd16a6","sha256:0e1ff4e1381603f74ce6f46fdc36e54affb9f93a0e784c730d63c640e7c8f3be"],"state_sha256":"56056c13bf47ea67622199a8e544df2c76acbd8d8dff528de98e48f74114c014"}