{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NHKK24BAT4F5TIKT6NDTVEQ62A","short_pith_number":"pith:NHKK24BA","schema_version":"1.0","canonical_sha256":"69d4ad70209f0bd9a153f3473a921ed03049d9c6b3abe3aacb6203177752b7d9","source":{"kind":"arxiv","id":"1708.07369","version":2},"attestation_state":"computed","paper":{"title":"Ramsey-nice families of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alon Naor, Dan Hefetz, Gal Kronenberg, Michal Amir, Noga Alon, Penny Haxell, Ron Aharoni, Zilin Jiang","submitted_at":"2017-08-24T12:14:51Z","abstract_excerpt":"For a finite family $\\mathcal{F}$ of fixed graphs let $R_k(\\mathcal{F})$ be the smallest integer $n$ for which every $k$-coloring of the edges of the complete graph $K_n$ yields a monochromatic copy of some $F\\in\\mathcal{F}$. We say that $\\mathcal{F}$ is $k$-nice if for every graph $G$ with $\\chi(G)=R_k(\\mathcal{F})$ and for every $k$-coloring of $E(G)$ there exists a monochromatic copy of some $F\\in\\mathcal{F}$. It is easy to see that if $\\mathcal{F}$ contains no forest, then it is not $k$-nice for any $k$. It seems plausible to conjecture that a (weak) converse holds, namely, for any finite "},"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":"1708.07369","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-24T12:14:51Z","cross_cats_sorted":[],"title_canon_sha256":"64e197d751734ae9c3721506e1035d49f3caa6da1687533b0eeadabafefb2905","abstract_canon_sha256":"26ee792545bf38caf61b360d6a6fb2b0ba8325f73704bab36812dac82096b66b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:35.083398Z","signature_b64":"itrQ5rTw7qZG6YjDCotnzOTSPyNUN+676SbXpiEfTpmK45SW7ycKybM5KVtYjufzNd8BNypkbbpcPtvXBurdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69d4ad70209f0bd9a153f3473a921ed03049d9c6b3abe3aacb6203177752b7d9","last_reissued_at":"2026-05-18T00:12:35.082695Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:35.082695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ramsey-nice families of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alon Naor, Dan Hefetz, Gal Kronenberg, Michal Amir, Noga Alon, Penny Haxell, Ron Aharoni, Zilin Jiang","submitted_at":"2017-08-24T12:14:51Z","abstract_excerpt":"For a finite family $\\mathcal{F}$ of fixed graphs let $R_k(\\mathcal{F})$ be the smallest integer $n$ for which every $k$-coloring of the edges of the complete graph $K_n$ yields a monochromatic copy of some $F\\in\\mathcal{F}$. We say that $\\mathcal{F}$ is $k$-nice if for every graph $G$ with $\\chi(G)=R_k(\\mathcal{F})$ and for every $k$-coloring of $E(G)$ there exists a monochromatic copy of some $F\\in\\mathcal{F}$. It is easy to see that if $\\mathcal{F}$ contains no forest, then it is not $k$-nice for any $k$. It seems plausible to conjecture that a (weak) converse holds, namely, for any finite "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07369","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1708.07369","created_at":"2026-05-18T00:12:35.082806+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.07369v2","created_at":"2026-05-18T00:12:35.082806+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07369","created_at":"2026-05-18T00:12:35.082806+00:00"},{"alias_kind":"pith_short_12","alias_value":"NHKK24BAT4F5","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"NHKK24BAT4F5TIKT","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"NHKK24BA","created_at":"2026-05-18T12:31:31.346846+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NHKK24BAT4F5TIKT6NDTVEQ62A","json":"https://pith.science/pith/NHKK24BAT4F5TIKT6NDTVEQ62A.json","graph_json":"https://pith.science/api/pith-number/NHKK24BAT4F5TIKT6NDTVEQ62A/graph.json","events_json":"https://pith.science/api/pith-number/NHKK24BAT4F5TIKT6NDTVEQ62A/events.json","paper":"https://pith.science/paper/NHKK24BA"},"agent_actions":{"view_html":"https://pith.science/pith/NHKK24BAT4F5TIKT6NDTVEQ62A","download_json":"https://pith.science/pith/NHKK24BAT4F5TIKT6NDTVEQ62A.json","view_paper":"https://pith.science/paper/NHKK24BA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.07369&json=true","fetch_graph":"https://pith.science/api/pith-number/NHKK24BAT4F5TIKT6NDTVEQ62A/graph.json","fetch_events":"https://pith.science/api/pith-number/NHKK24BAT4F5TIKT6NDTVEQ62A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NHKK24BAT4F5TIKT6NDTVEQ62A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NHKK24BAT4F5TIKT6NDTVEQ62A/action/storage_attestation","attest_author":"https://pith.science/pith/NHKK24BAT4F5TIKT6NDTVEQ62A/action/author_attestation","sign_citation":"https://pith.science/pith/NHKK24BAT4F5TIKT6NDTVEQ62A/action/citation_signature","submit_replication":"https://pith.science/pith/NHKK24BAT4F5TIKT6NDTVEQ62A/action/replication_record"}},"created_at":"2026-05-18T00:12:35.082806+00:00","updated_at":"2026-05-18T00:12:35.082806+00:00"}