{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:3G2HQO23YR24H4AD5QTREJACIE","short_pith_number":"pith:3G2HQO23","schema_version":"1.0","canonical_sha256":"d9b4783b5bc475c3f003ec27122402410a91de5d0222e0062aad867fe0a50e53","source":{"kind":"arxiv","id":"2502.03864","version":2},"attestation_state":"computed","paper":{"title":"On zero-sum Ramsey numbers modulo 3","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xandru Mifsud, Yair Caro","submitted_at":"2025-02-06T08:25:28Z","abstract_excerpt":"We start with a systematic study of the zero-sum Ramsey numbers. For a graph $G$ with $0 \\ (\\!\\!\\!\\!\\mod 3)$ edges, the zero-sum Ramsey number is defined as the smallest positive integer $R(G, \\mathbb{Z}_3)$ such that for every $n \\geq R(G, \\mathbb{Z}_3)$ and every edge-colouring $f$ of $K_n$ using $\\mathbb{Z}_3$, there is a zero-sum copy of $G$ in $K_n$ coloured by $f$, that is: $\\sum_{e \\in E(G)} f(e) \\equiv 0 \\ (\\!\\!\\!\\!\\mod 3)$.\n  Only sporadic results are known for these Ramsey numbers, and we discover many new ones. In particular we prove that for every forest $F$ on $n$ vertices and wit"},"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":"2502.03864","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-06T08:25:28Z","cross_cats_sorted":[],"title_canon_sha256":"615760805e6cdef7ae4ba4ced2cd88265a7e50730b2ebb8c9f13b8d99c883954","abstract_canon_sha256":"bd80ddf6d35631956f177c97aa62018f241d9819837a6aeac4b0ea8c0106bdc6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:09:07.199777Z","signature_b64":"HnAtaoR7zHML2gFcemmtwdCA3YNV8/oenE51NCIt+pMJQfMguvvEXnSOagVjP4uHl9cqHWcEpFeqfQLYt573Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9b4783b5bc475c3f003ec27122402410a91de5d0222e0062aad867fe0a50e53","last_reissued_at":"2026-06-12T01:09:07.199122Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:09:07.199122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On zero-sum Ramsey numbers modulo 3","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xandru Mifsud, Yair Caro","submitted_at":"2025-02-06T08:25:28Z","abstract_excerpt":"We start with a systematic study of the zero-sum Ramsey numbers. For a graph $G$ with $0 \\ (\\!\\!\\!\\!\\mod 3)$ edges, the zero-sum Ramsey number is defined as the smallest positive integer $R(G, \\mathbb{Z}_3)$ such that for every $n \\geq R(G, \\mathbb{Z}_3)$ and every edge-colouring $f$ of $K_n$ using $\\mathbb{Z}_3$, there is a zero-sum copy of $G$ in $K_n$ coloured by $f$, that is: $\\sum_{e \\in E(G)} f(e) \\equiv 0 \\ (\\!\\!\\!\\!\\mod 3)$.\n  Only sporadic results are known for these Ramsey numbers, and we discover many new ones. In particular we prove that for every forest $F$ on $n$ vertices and wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.03864","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/2502.03864/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":"2502.03864","created_at":"2026-06-12T01:09:07.199210+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.03864v2","created_at":"2026-06-12T01:09:07.199210+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.03864","created_at":"2026-06-12T01:09:07.199210+00:00"},{"alias_kind":"pith_short_12","alias_value":"3G2HQO23YR24","created_at":"2026-06-12T01:09:07.199210+00:00"},{"alias_kind":"pith_short_16","alias_value":"3G2HQO23YR24H4AD","created_at":"2026-06-12T01:09:07.199210+00:00"},{"alias_kind":"pith_short_8","alias_value":"3G2HQO23","created_at":"2026-06-12T01:09:07.199210+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.14954","citing_title":"On zero-sum Ramsey numbers of cycles and wheels","ref_index":11,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3G2HQO23YR24H4AD5QTREJACIE","json":"https://pith.science/pith/3G2HQO23YR24H4AD5QTREJACIE.json","graph_json":"https://pith.science/api/pith-number/3G2HQO23YR24H4AD5QTREJACIE/graph.json","events_json":"https://pith.science/api/pith-number/3G2HQO23YR24H4AD5QTREJACIE/events.json","paper":"https://pith.science/paper/3G2HQO23"},"agent_actions":{"view_html":"https://pith.science/pith/3G2HQO23YR24H4AD5QTREJACIE","download_json":"https://pith.science/pith/3G2HQO23YR24H4AD5QTREJACIE.json","view_paper":"https://pith.science/paper/3G2HQO23","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.03864&json=true","fetch_graph":"https://pith.science/api/pith-number/3G2HQO23YR24H4AD5QTREJACIE/graph.json","fetch_events":"https://pith.science/api/pith-number/3G2HQO23YR24H4AD5QTREJACIE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3G2HQO23YR24H4AD5QTREJACIE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3G2HQO23YR24H4AD5QTREJACIE/action/storage_attestation","attest_author":"https://pith.science/pith/3G2HQO23YR24H4AD5QTREJACIE/action/author_attestation","sign_citation":"https://pith.science/pith/3G2HQO23YR24H4AD5QTREJACIE/action/citation_signature","submit_replication":"https://pith.science/pith/3G2HQO23YR24H4AD5QTREJACIE/action/replication_record"}},"created_at":"2026-06-12T01:09:07.199210+00:00","updated_at":"2026-06-12T01:09:07.199210+00:00"}