{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CAW5MN374NIMHFPHAZRO7FHR2Z","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":"b2fad42abbd79190e5e5beca7723f6e3b7046eaa96d855ede66ecfcd3f4c24ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-07T13:42:08Z","title_canon_sha256":"f8d9d489a0a7608fa01059069c44c11f8a5d84470c3ef8fa0849042d34b7536c"},"schema_version":"1.0","source":{"id":"1905.02893","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.02893","created_at":"2026-05-17T23:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1905.02893v2","created_at":"2026-05-17T23:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02893","created_at":"2026-05-17T23:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"CAW5MN374NIM","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"CAW5MN374NIMHFPH","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"CAW5MN37","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:7d65db9fdb69fe007d67ef11b462f635d96142dd0084baabbf637c79bed7bfec","target":"graph","created_at":"2026-05-17T23:40:55Z","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"},"paper":{"abstract_excerpt":"Let $m(n,r)$ denote the minimal number of edges in an $n$-uniform hypergraph which is not $r$-colorable. For the broad history of the problem see [RaiSh]. It is known that for a fixed $n$ the sequence \\[ \\frac{m(n,r)}{r^n} \\] has a limit.\n  The only trivial case is $n=2$ in which $m(2,r) = \\binom{r+1}{2}$. In this note we focus on the case $n=3$. First, we compare the existing methods in this case and then improve the lower bound.","authors_text":"Danila Cherkashin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-07T13:42:08Z","title":"On the Erd{\\H o}s--Hajnal problem in the case of 3-graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02893","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":"sha256:842c65d338a602462fde2af03286953f63738ec1e1467cfcf2b7482b30c0fd0b","target":"record","created_at":"2026-05-17T23:40:55Z","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":"b2fad42abbd79190e5e5beca7723f6e3b7046eaa96d855ede66ecfcd3f4c24ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-07T13:42:08Z","title_canon_sha256":"f8d9d489a0a7608fa01059069c44c11f8a5d84470c3ef8fa0849042d34b7536c"},"schema_version":"1.0","source":{"id":"1905.02893","kind":"arxiv","version":2}},"canonical_sha256":"102dd6377fe350c395e70662ef94f1d67ece04d0863a7971ce4577ec0585e688","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"102dd6377fe350c395e70662ef94f1d67ece04d0863a7971ce4577ec0585e688","first_computed_at":"2026-05-17T23:40:55.136207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:55.136207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gO5bHaeoWF72wWLT9trbAGfkNT8qGw4NFF9Edz8aFUXUgCPEia4seT/VFpcIrajeJjbHQNmC0oUlrGceSS0lDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:55.136896Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.02893","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:842c65d338a602462fde2af03286953f63738ec1e1467cfcf2b7482b30c0fd0b","sha256:7d65db9fdb69fe007d67ef11b462f635d96142dd0084baabbf637c79bed7bfec"],"state_sha256":"0d68c9ffef9de2fcc1622f5f34f4c7d12eb0e89d881efa124b915bee73ede9c4"}