{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:F3AUALM3H7V3OMXBPLHD4OLTSF","short_pith_number":"pith:F3AUALM3","schema_version":"1.0","canonical_sha256":"2ec1402d9b3febb732e17ace3e3973916c28325edbd56381ddf24c0675b939ce","source":{"kind":"arxiv","id":"1908.08237","version":3},"attestation_state":"computed","paper":{"title":"On small balanceable, strongly-balanceable and omnitonal graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christina Zarb, Josef Lauri, Yair Caro","submitted_at":"2019-08-22T07:34:08Z","abstract_excerpt":"In Ramsey theory for graphs we are given a graph $G$ and we are required to find the least $n_0$ such that, for any $n\\geq n_0$, any red/blue colouring of the edges of $K_n$ gives a subgraph $G$ all of whose edges are blue or all are red. Here we shall be requiring that, for any red/blue colouring of the edges of $K_n$, there must be a copy of $G$ such that its edges are partitioned equally as red or blue (or the sizes of the colour classes differs by one in the case when $G$ has an odd number of edges). This introduces the notion of balanceable graphs and the balance number of $G$ which, if i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.08237","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-22T07:34:08Z","cross_cats_sorted":[],"title_canon_sha256":"de3c9036e823e1e324990cd2ee107ffbf6504db1976ca6d1cc2b0b846d64b378","abstract_canon_sha256":"8557c83c999068b7b901b2072599d587c501ac7fda87c57cd85df1e357f6ad1e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:35:01.801159Z","signature_b64":"18NgxzLdZign4Oty0Qg4XqY/Tg4uwRQKn7Hae5cMRno0UEbGCw3ifBR9VZfAIi8ODDGTXXPihoNd2OB5Ei0WDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ec1402d9b3febb732e17ace3e3973916c28325edbd56381ddf24c0675b939ce","last_reissued_at":"2026-07-05T00:35:01.800713Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:35:01.800713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On small balanceable, strongly-balanceable and omnitonal graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christina Zarb, Josef Lauri, Yair Caro","submitted_at":"2019-08-22T07:34:08Z","abstract_excerpt":"In Ramsey theory for graphs we are given a graph $G$ and we are required to find the least $n_0$ such that, for any $n\\geq n_0$, any red/blue colouring of the edges of $K_n$ gives a subgraph $G$ all of whose edges are blue or all are red. Here we shall be requiring that, for any red/blue colouring of the edges of $K_n$, there must be a copy of $G$ such that its edges are partitioned equally as red or blue (or the sizes of the colour classes differs by one in the case when $G$ has an odd number of edges). This introduces the notion of balanceable graphs and the balance number of $G$ which, if i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08237","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.08237/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.08237","created_at":"2026-07-05T00:35:01.800771+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.08237v3","created_at":"2026-07-05T00:35:01.800771+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08237","created_at":"2026-07-05T00:35:01.800771+00:00"},{"alias_kind":"pith_short_12","alias_value":"F3AUALM3H7V3","created_at":"2026-07-05T00:35:01.800771+00:00"},{"alias_kind":"pith_short_16","alias_value":"F3AUALM3H7V3OMXB","created_at":"2026-07-05T00:35:01.800771+00:00"},{"alias_kind":"pith_short_8","alias_value":"F3AUALM3","created_at":"2026-07-05T00:35:01.800771+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2003.04804","citing_title":"On the balanceability of some graph classes","ref_index":9,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F3AUALM3H7V3OMXBPLHD4OLTSF","json":"https://pith.science/pith/F3AUALM3H7V3OMXBPLHD4OLTSF.json","graph_json":"https://pith.science/api/pith-number/F3AUALM3H7V3OMXBPLHD4OLTSF/graph.json","events_json":"https://pith.science/api/pith-number/F3AUALM3H7V3OMXBPLHD4OLTSF/events.json","paper":"https://pith.science/paper/F3AUALM3"},"agent_actions":{"view_html":"https://pith.science/pith/F3AUALM3H7V3OMXBPLHD4OLTSF","download_json":"https://pith.science/pith/F3AUALM3H7V3OMXBPLHD4OLTSF.json","view_paper":"https://pith.science/paper/F3AUALM3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.08237&json=true","fetch_graph":"https://pith.science/api/pith-number/F3AUALM3H7V3OMXBPLHD4OLTSF/graph.json","fetch_events":"https://pith.science/api/pith-number/F3AUALM3H7V3OMXBPLHD4OLTSF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F3AUALM3H7V3OMXBPLHD4OLTSF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F3AUALM3H7V3OMXBPLHD4OLTSF/action/storage_attestation","attest_author":"https://pith.science/pith/F3AUALM3H7V3OMXBPLHD4OLTSF/action/author_attestation","sign_citation":"https://pith.science/pith/F3AUALM3H7V3OMXBPLHD4OLTSF/action/citation_signature","submit_replication":"https://pith.science/pith/F3AUALM3H7V3OMXBPLHD4OLTSF/action/replication_record"}},"created_at":"2026-07-05T00:35:01.800771+00:00","updated_at":"2026-07-05T00:35:01.800771+00:00"}