{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:TYXTJHMHPJG3YHG5RUBLCYEKKH","short_pith_number":"pith:TYXTJHMH","schema_version":"1.0","canonical_sha256":"9e2f349d877a4dbc1cdd8d02b1608a51c9cd5ff8f0c0dc76fe81af8e61bcbe74","source":{"kind":"arxiv","id":"2411.14566","version":2},"attestation_state":"computed","paper":{"title":"A canonical Ramsey theorem for even cycles in random graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guilherme O. Mota, Jos\\'e D. Alvarado, Patrick Morris, Y. Kohayakawa","submitted_at":"2024-11-21T20:29:59Z","abstract_excerpt":"The celebrated canonical Ramsey theorem of Erd\\H{o}s and Rado implies that for $2\\leq k\\in \\mathbb{N}$, any colouring of the edges of $K_n$ with $n$ sufficiently large gives a copy of $C_{2k}$ which has one of three canonical colour patterns: monochromatic, rainbow or lexicographic. In this paper we show that if $p=\\omega(n^{-1+1/(2k-1)}\\log n)$, then ${\\mathbf{G}}(n,p)$ will asymptotically almost surely also have the property that any colouring of its edges induces canonical copies of $C_{2k}$. This determines the threshold for the canonical Ramsey property with respect to even cycles, up to "},"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":"2411.14566","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-11-21T20:29:59Z","cross_cats_sorted":[],"title_canon_sha256":"acf635f16780a9e4130652f35041d18d26786ea93cd73bd8ad2630ba884953d9","abstract_canon_sha256":"6703c2e508c780cca35841929d7df0aff166d16c97f98864f214ac4492baeeb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:13:43.979809Z","signature_b64":"bgbeWvRnYnNr6dT9QWCcTjWEB/HRhAyf2ZDtmVVx9Z/yDTbwEwwJAc4glRWiIt9CC7OBB4yW4lLH8GrWHeJzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e2f349d877a4dbc1cdd8d02b1608a51c9cd5ff8f0c0dc76fe81af8e61bcbe74","last_reissued_at":"2026-06-23T03:13:43.979240Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:13:43.979240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A canonical Ramsey theorem for even cycles in random graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guilherme O. Mota, Jos\\'e D. Alvarado, Patrick Morris, Y. Kohayakawa","submitted_at":"2024-11-21T20:29:59Z","abstract_excerpt":"The celebrated canonical Ramsey theorem of Erd\\H{o}s and Rado implies that for $2\\leq k\\in \\mathbb{N}$, any colouring of the edges of $K_n$ with $n$ sufficiently large gives a copy of $C_{2k}$ which has one of three canonical colour patterns: monochromatic, rainbow or lexicographic. In this paper we show that if $p=\\omega(n^{-1+1/(2k-1)}\\log n)$, then ${\\mathbf{G}}(n,p)$ will asymptotically almost surely also have the property that any colouring of its edges induces canonical copies of $C_{2k}$. This determines the threshold for the canonical Ramsey property with respect to even cycles, up to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14566","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.14566/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":"2411.14566","created_at":"2026-06-23T03:13:43.979297+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.14566v2","created_at":"2026-06-23T03:13:43.979297+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14566","created_at":"2026-06-23T03:13:43.979297+00:00"},{"alias_kind":"pith_short_12","alias_value":"TYXTJHMHPJG3","created_at":"2026-06-23T03:13:43.979297+00:00"},{"alias_kind":"pith_short_16","alias_value":"TYXTJHMHPJG3YHG5","created_at":"2026-06-23T03:13:43.979297+00:00"},{"alias_kind":"pith_short_8","alias_value":"TYXTJHMH","created_at":"2026-06-23T03:13:43.979297+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2605.21471","citing_title":"Ramsey properties for tilings in random graphs","ref_index":2,"is_internal_anchor":true},{"citing_arxiv_id":"2510.03084","citing_title":"A sparse canonical van der Waerden theorem","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TYXTJHMHPJG3YHG5RUBLCYEKKH","json":"https://pith.science/pith/TYXTJHMHPJG3YHG5RUBLCYEKKH.json","graph_json":"https://pith.science/api/pith-number/TYXTJHMHPJG3YHG5RUBLCYEKKH/graph.json","events_json":"https://pith.science/api/pith-number/TYXTJHMHPJG3YHG5RUBLCYEKKH/events.json","paper":"https://pith.science/paper/TYXTJHMH"},"agent_actions":{"view_html":"https://pith.science/pith/TYXTJHMHPJG3YHG5RUBLCYEKKH","download_json":"https://pith.science/pith/TYXTJHMHPJG3YHG5RUBLCYEKKH.json","view_paper":"https://pith.science/paper/TYXTJHMH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.14566&json=true","fetch_graph":"https://pith.science/api/pith-number/TYXTJHMHPJG3YHG5RUBLCYEKKH/graph.json","fetch_events":"https://pith.science/api/pith-number/TYXTJHMHPJG3YHG5RUBLCYEKKH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TYXTJHMHPJG3YHG5RUBLCYEKKH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TYXTJHMHPJG3YHG5RUBLCYEKKH/action/storage_attestation","attest_author":"https://pith.science/pith/TYXTJHMHPJG3YHG5RUBLCYEKKH/action/author_attestation","sign_citation":"https://pith.science/pith/TYXTJHMHPJG3YHG5RUBLCYEKKH/action/citation_signature","submit_replication":"https://pith.science/pith/TYXTJHMHPJG3YHG5RUBLCYEKKH/action/replication_record"}},"created_at":"2026-06-23T03:13:43.979297+00:00","updated_at":"2026-06-23T03:13:43.979297+00:00"}