{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XSH2NK75EZV52ANMSL6EKHGWC2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"38ad542d495d7e447f923b0b5c085b18b65c7dae35c7aa16b15777a32f890919","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-22T14:05:49Z","title_canon_sha256":"d457de40d7fc3e378150ac807a376fddf739a65a5e4cffc194e5f23451c45c06"},"schema_version":"1.0","source":{"id":"1408.5296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5296","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5296v1","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5296","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"XSH2NK75EZV5","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XSH2NK75EZV52ANM","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XSH2NK75","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:64bc8004095176b5033342753fbbb237de4e292701f08b9aa4254ac0dd5882a3","target":"graph","created_at":"2026-05-18T00:14:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Erdos and Sos proposed a problem of determining the maximum number F(n) of rainbow triangles in 3-edge-colored complete graphs on n vertices. They conjectured that F(n) = F(a)+ F(b)+F(c)+F(d)+abc+abd+acd+bcd, where a+b+c+d = n and a, b, c, d are as equal as possible. We prove that the conjectured recurrence holds for sufficiently large n. We also prove the conjecture for n = 4k for all k. These results imply that lim F(n) n^3/6 = 0.4, and determine the unique limit object. In the proof we use flag algebras combined with stability arguments.","authors_text":"Bernard Lidicky, Florian Pfender, Jan Volec, Jozsef Balogh, Michael Young, Ping Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-22T14:05:49Z","title":"Rainbow triangles in three-colored graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5296","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9e745c99648d5ad110815dc6965bd4a698d369e7f120f417d3fc6ef5a163aa57","target":"record","created_at":"2026-05-18T00:14:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"38ad542d495d7e447f923b0b5c085b18b65c7dae35c7aa16b15777a32f890919","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-22T14:05:49Z","title_canon_sha256":"d457de40d7fc3e378150ac807a376fddf739a65a5e4cffc194e5f23451c45c06"},"schema_version":"1.0","source":{"id":"1408.5296","kind":"arxiv","version":1}},"canonical_sha256":"bc8fa6abfd266bdd01ac92fc451cd616a4920dfbbcf973f1d20cb5361639b9da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc8fa6abfd266bdd01ac92fc451cd616a4920dfbbcf973f1d20cb5361639b9da","first_computed_at":"2026-05-18T00:14:29.393430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:29.393430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2SfbOUuYP8Tc4Amd71TwrG8Gzfs/sDvGfuGIyQJ9VjrRMJkrsInwb/wNkOazcTdemsY0FwP5xjlkqjpqv4EwAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:29.394162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e745c99648d5ad110815dc6965bd4a698d369e7f120f417d3fc6ef5a163aa57","sha256:64bc8004095176b5033342753fbbb237de4e292701f08b9aa4254ac0dd5882a3"],"state_sha256":"6d0a3cdc985985e491f34b31e52a62ac9dde62ad25320b0d67b31f7bc6baa0a3"}