{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BHF3PYGQIVEVPBY726AYZADNDL","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":"4c83986619b75c43b5e420d8ce0fe93ebbd548f472bec9b90d3a2504863aef6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-20T01:06:29Z","title_canon_sha256":"f9e0f4536efcdb47c9338659b8672976151d23775d5fc48c30c81c57ec28d9c1"},"schema_version":"1.0","source":{"id":"1605.06188","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06188","created_at":"2026-05-18T01:14:19Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06188v1","created_at":"2026-05-18T01:14:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06188","created_at":"2026-05-18T01:14:19Z"},{"alias_kind":"pith_short_12","alias_value":"BHF3PYGQIVEV","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BHF3PYGQIVEVPBY7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BHF3PYGQ","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:9578437aa5fe11cc3ff3da54ef9219f8811cd4f1a9d6e5c8dc947cb6e5825338","target":"graph","created_at":"2026-05-18T01:14:19Z","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":"The weighted Ramsey number, ${\\rm wR}(n,k)$, is the minimum $q$ such that there is an assignment of nonnegative real numbers (weights) to the edges of $K_n$ with the total sum of the weights equal to ${n\\choose 2}$ and there is a Red/Blue coloring of edges of the same $K_n$, such that in any complete $k$-vertex subgraph $H$, of $K_n$, the sum of the weights on Red edges in $H$ is at most $q$ and the sum of the weights on Blue edges in $H$ is at most $q$. This concept was introduced recently by Fujisawa and Ota.\n  We provide new bounds on ${\\rm wR}(n,k)$, for $k\\geq 4$ and $n$ large enough and ","authors_text":"Maria Axenovich, Ryan Martin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-20T01:06:29Z","title":"On weighted Ramsey numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06188","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":"sha256:81810cb7efc78381d758297f886114d2036bea6c392f35873559ff2865451328","target":"record","created_at":"2026-05-18T01:14:19Z","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":"4c83986619b75c43b5e420d8ce0fe93ebbd548f472bec9b90d3a2504863aef6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-20T01:06:29Z","title_canon_sha256":"f9e0f4536efcdb47c9338659b8672976151d23775d5fc48c30c81c57ec28d9c1"},"schema_version":"1.0","source":{"id":"1605.06188","kind":"arxiv","version":1}},"canonical_sha256":"09cbb7e0d0454957871fd7818c806d1ae63c7b47b28416451379717c3c22e8c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09cbb7e0d0454957871fd7818c806d1ae63c7b47b28416451379717c3c22e8c2","first_computed_at":"2026-05-18T01:14:19.677936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:19.677936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RlxwF2RW/N+bh23g3UtN/nOMmRq0i4MgGjhG86jYpUu/4i3XpEtNeSbTUorgbXiJnKlGYQ/rcirCzbPNpkLADw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:19.678669Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.06188","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81810cb7efc78381d758297f886114d2036bea6c392f35873559ff2865451328","sha256:9578437aa5fe11cc3ff3da54ef9219f8811cd4f1a9d6e5c8dc947cb6e5825338"],"state_sha256":"a6752b898d4647f5aa0b25be3d181571d31629e02e22ff8cf25491827b41282b"}