{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CBTNOKMZFZGUWHJAMZ44PMPR57","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":"8ba263e05831ad1198ab2cfd06e3d194b97dc0d53656964d7e2742d5268813ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-02T13:11:17Z","title_canon_sha256":"12b80af1366e662ea805e7546d628e43a5d132f80bfb8e3a6208ad608ba61c58"},"schema_version":"1.0","source":{"id":"1908.00837","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00837","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00837v3","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00837","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"CBTNOKMZFZGU","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_16","alias_value":"CBTNOKMZFZGUWHJA","created_at":"2026-07-05T00:39:13Z"},{"alias_kind":"pith_short_8","alias_value":"CBTNOKMZ","created_at":"2026-07-05T00:39:13Z"}],"graph_snapshots":[{"event_id":"sha256:ea9e33b34b2f2db6e767fe5c29e5bc39bfae1404af6261ab31a30de97ad5ceee","target":"graph","created_at":"2026-07-05T00:39:13Z","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/1908.00837/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is known that in any $r$-coloring of the edges of a complete $r$-uniform hypergraph, there exists a spanning monochromatic component. Given a Steiner triple system on $n$ vertices, what is the largest monochromatic component one can guarantee in an arbitrary 3-coloring of the edges?\n  Gy\\'arf\\'as proved that $(2n+3)/3$ is an absolute lower bound and that this lower bound is best possible for infinitely many $n$. On the other hand, we prove that for almost all Steiner triple systems the lower bound is actually $(1-o(1))n$. We obtain this result as a consequence of a more general theorem whic","authors_text":"Louis DeBiasio, Michael Tait","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-02T13:11:17Z","title":"Large monochromatic components in 3-edge-colored Steiner triple systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00837","kind":"arxiv","version":3},"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":"sha256:806478d750429938cb10a55a9d08342d327f121bc730394dd6ac44d80f10ac72","target":"record","created_at":"2026-07-05T00:39:13Z","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":"8ba263e05831ad1198ab2cfd06e3d194b97dc0d53656964d7e2742d5268813ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-02T13:11:17Z","title_canon_sha256":"12b80af1366e662ea805e7546d628e43a5d132f80bfb8e3a6208ad608ba61c58"},"schema_version":"1.0","source":{"id":"1908.00837","kind":"arxiv","version":3}},"canonical_sha256":"1066d729992e4d4b1d206679c7b1f1efcbb842cb345dc532cc58eaeff6427db3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1066d729992e4d4b1d206679c7b1f1efcbb842cb345dc532cc58eaeff6427db3","first_computed_at":"2026-07-05T00:39:13.152495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:39:13.152495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vhEeKdfXAVC9l/2OlMIJeHsfE8vNWpNi7BkegiPMfECouK52ezGMNC7lM8TKdFlrl9U2GuDdMk8RPTBHXK8ODw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:39:13.152973Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.00837","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:806478d750429938cb10a55a9d08342d327f121bc730394dd6ac44d80f10ac72","sha256:ea9e33b34b2f2db6e767fe5c29e5bc39bfae1404af6261ab31a30de97ad5ceee"],"state_sha256":"49e05eb86d8416575a1a4abce5f1cb44497075f2d2779f4c715e43f2929b2eaa"}