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For positive integers $n$ and $k$, the expression $aw([n],k)$ denotes the smallest number of colors with which the integers $\\{1,\\ldots,n\\}$ can be colored and still guarantee there is a rainbow arithmetic progression of length $k$. We establish that $aw([n],3)=\\Theta(\\log n)$ and $aw([n],k)=n^{1-o(1)}$ for $k\\geq 4$.\n  For positive integers $n$ and $k$, the expression $aw(Z_n,k)$ denotes the smallest number of colors with which elements of the cyclic group of order $n$ c"},"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":"1404.7232","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-29T04:24:57Z","cross_cats_sorted":[],"title_canon_sha256":"2de046ecdf642294699bb4424ea78f5f274585a13c9cbedac9967f43e071c1ef","abstract_canon_sha256":"a20c8283b4aa0a0a6e603bd520cda70d932028eb5da21edc3cabe099eaeec395"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:08.960862Z","signature_b64":"doqj7G/VZaTpUk5bhOKIYQyZuXNYIdrLDGRd9V4lw1oO+8Eia0CtRuXHqW1a+sAN5qd2p0HogfgYhj923cJaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56021dd54b324f19703797bd03061282d41ea0ab7ffd8abc019b6408f70f8366","last_reissued_at":"2026-05-18T01:23:08.960360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:08.960360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rainbow arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Craig Erickson, Derrick Stolee, Jephian Chin-Hung Lin, Kirsten Hogenson, Leslie Hogben, Lucas Kramer, Michael Young, Nathan Warnberg, Richard L. Kramer, Ryan R. Martin, Steve Butler","submitted_at":"2014-04-29T04:24:57Z","abstract_excerpt":"In this paper, we investigate the anti-Ramsey (more precisely, anti-van der Waerden) properties of arithmetic progressions. For positive integers $n$ and $k$, the expression $aw([n],k)$ denotes the smallest number of colors with which the integers $\\{1,\\ldots,n\\}$ can be colored and still guarantee there is a rainbow arithmetic progression of length $k$. We establish that $aw([n],3)=\\Theta(\\log n)$ and $aw([n],k)=n^{1-o(1)}$ for $k\\geq 4$.\n  For positive integers $n$ and $k$, the expression $aw(Z_n,k)$ denotes the smallest number of colors with which elements of the cyclic group of order $n$ c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7232","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":"1404.7232","created_at":"2026-05-18T01:23:08.960425+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.7232v2","created_at":"2026-05-18T01:23:08.960425+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7232","created_at":"2026-05-18T01:23:08.960425+00:00"},{"alias_kind":"pith_short_12","alias_value":"KYBB3VKLGJHR","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KYBB3VKLGJHRS4BX","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KYBB3VKL","created_at":"2026-05-18T12:28:35.611951+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2307.12154","citing_title":"Hitting sets and colorings of hypergraphs","ref_index":6,"is_internal_anchor":true},{"citing_arxiv_id":"2410.22024","citing_title":"An Unsure Note on an Un-Schur Problem","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KYBB3VKLGJHRS4BXS66QGBQSQL","json":"https://pith.science/pith/KYBB3VKLGJHRS4BXS66QGBQSQL.json","graph_json":"https://pith.science/api/pith-number/KYBB3VKLGJHRS4BXS66QGBQSQL/graph.json","events_json":"https://pith.science/api/pith-number/KYBB3VKLGJHRS4BXS66QGBQSQL/events.json","paper":"https://pith.science/paper/KYBB3VKL"},"agent_actions":{"view_html":"https://pith.science/pith/KYBB3VKLGJHRS4BXS66QGBQSQL","download_json":"https://pith.science/pith/KYBB3VKLGJHRS4BXS66QGBQSQL.json","view_paper":"https://pith.science/paper/KYBB3VKL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.7232&json=true","fetch_graph":"https://pith.science/api/pith-number/KYBB3VKLGJHRS4BXS66QGBQSQL/graph.json","fetch_events":"https://pith.science/api/pith-number/KYBB3VKLGJHRS4BXS66QGBQSQL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KYBB3VKLGJHRS4BXS66QGBQSQL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KYBB3VKLGJHRS4BXS66QGBQSQL/action/storage_attestation","attest_author":"https://pith.science/pith/KYBB3VKLGJHRS4BXS66QGBQSQL/action/author_attestation","sign_citation":"https://pith.science/pith/KYBB3VKLGJHRS4BXS66QGBQSQL/action/citation_signature","submit_replication":"https://pith.science/pith/KYBB3VKLGJHRS4BXS66QGBQSQL/action/replication_record"}},"created_at":"2026-05-18T01:23:08.960425+00:00","updated_at":"2026-05-18T01:23:08.960425+00:00"}