{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:O2QY4LRYI7UU4I5OYGQE6PBNZY","short_pith_number":"pith:O2QY4LRY","canonical_record":{"source":{"id":"1708.04504","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T14:14:50Z","cross_cats_sorted":[],"title_canon_sha256":"8ab6bb7b2a2765a3c414aa44f228dfcd5cf161fc8e8d740ed0124597c53baa71","abstract_canon_sha256":"31f5a4f314923f224c92dd36ecf5cf6ab5670d6dfae4b7ca8b77d8e3c5f3b9bd"},"schema_version":"1.0"},"canonical_sha256":"76a18e2e3847e94e23aec1a04f3c2dce3e591481c2d72a6002ad2e6aa41a7452","source":{"kind":"arxiv","id":"1708.04504","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04504","created_at":"2026-05-17T23:47:12Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04504v2","created_at":"2026-05-17T23:47:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04504","created_at":"2026-05-17T23:47:12Z"},{"alias_kind":"pith_short_12","alias_value":"O2QY4LRYI7UU","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O2QY4LRYI7UU4I5O","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O2QY4LRY","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:O2QY4LRYI7UU4I5OYGQE6PBNZY","target":"record","payload":{"canonical_record":{"source":{"id":"1708.04504","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T14:14:50Z","cross_cats_sorted":[],"title_canon_sha256":"8ab6bb7b2a2765a3c414aa44f228dfcd5cf161fc8e8d740ed0124597c53baa71","abstract_canon_sha256":"31f5a4f314923f224c92dd36ecf5cf6ab5670d6dfae4b7ca8b77d8e3c5f3b9bd"},"schema_version":"1.0"},"canonical_sha256":"76a18e2e3847e94e23aec1a04f3c2dce3e591481c2d72a6002ad2e6aa41a7452","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:12.824963Z","signature_b64":"1/Zgu7XykK9xSjW/o3ggZnxk4Zn0VumWNMpdO8BqVl8ss22PaJ382tEKRXu/TDoJwbA86a/nGw8YMrxRsmxuDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76a18e2e3847e94e23aec1a04f3c2dce3e591481c2d72a6002ad2e6aa41a7452","last_reissued_at":"2026-05-17T23:47:12.824555Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:12.824555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.04504","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"shnTYt5mx5GVs1fRqWESYZcUN7XUoRZfDzkV6Sacm+CEQtwg4f3qVjr2eH2o480BvJAfoKPrvCUdviUrFnrBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:53:21.390998Z"},"content_sha256":"c1a45c7f8dda40d6c8ee48f2ac40907517a0dd496a3b117bc61705dfd8d9bf36","schema_version":"1.0","event_id":"sha256:c1a45c7f8dda40d6c8ee48f2ac40907517a0dd496a3b117bc61705dfd8d9bf36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:O2QY4LRYI7UU4I5OYGQE6PBNZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Directed Ramsey number for trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Matija Bucic, Shoham Letzter","submitted_at":"2017-08-15T14:14:50Z","abstract_excerpt":"In this paper, we study Ramsey-type problems for directed graphs. We first consider the $k$-colour oriented Ramsey number of $H$, denoted by $\\overrightarrow{R}(H,k)$, which is the least $n$ for which every $k$-edge-coloured tournament on $n$ vertices contains a monochromatic copy of $H$. We prove that $ \\overrightarrow{R}(T,k) \\le c_k|T|^k$ for any oriented tree $T$. This is a generalisation of a similar result for directed paths by Chv\\'atal and by Gy\\'arf\\'as and Lehel, and answers a question of Yuster. In general, it is tight up to a constant factor.\n  We also consider the $k$-colour direc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04504","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hLTaBunWF/De/0yPpuSkiiMwj5WrhJ0C19gnsvKX6GQuKWJ7FVEP1N7fNOoHbLYlQ8Fn+8/AXXMvREeJIWC8Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:53:21.391368Z"},"content_sha256":"e4590052d74612ed577f699c7911d94ee9888bd12023a9137adbc57406c9e7e4","schema_version":"1.0","event_id":"sha256:e4590052d74612ed577f699c7911d94ee9888bd12023a9137adbc57406c9e7e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O2QY4LRYI7UU4I5OYGQE6PBNZY/bundle.json","state_url":"https://pith.science/pith/O2QY4LRYI7UU4I5OYGQE6PBNZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O2QY4LRYI7UU4I5OYGQE6PBNZY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T09:53:21Z","links":{"resolver":"https://pith.science/pith/O2QY4LRYI7UU4I5OYGQE6PBNZY","bundle":"https://pith.science/pith/O2QY4LRYI7UU4I5OYGQE6PBNZY/bundle.json","state":"https://pith.science/pith/O2QY4LRYI7UU4I5OYGQE6PBNZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O2QY4LRYI7UU4I5OYGQE6PBNZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:O2QY4LRYI7UU4I5OYGQE6PBNZY","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":"31f5a4f314923f224c92dd36ecf5cf6ab5670d6dfae4b7ca8b77d8e3c5f3b9bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T14:14:50Z","title_canon_sha256":"8ab6bb7b2a2765a3c414aa44f228dfcd5cf161fc8e8d740ed0124597c53baa71"},"schema_version":"1.0","source":{"id":"1708.04504","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04504","created_at":"2026-05-17T23:47:12Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04504v2","created_at":"2026-05-17T23:47:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04504","created_at":"2026-05-17T23:47:12Z"},{"alias_kind":"pith_short_12","alias_value":"O2QY4LRYI7UU","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O2QY4LRYI7UU4I5O","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O2QY4LRY","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:e4590052d74612ed577f699c7911d94ee9888bd12023a9137adbc57406c9e7e4","target":"graph","created_at":"2026-05-17T23:47:12Z","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":"In this paper, we study Ramsey-type problems for directed graphs. We first consider the $k$-colour oriented Ramsey number of $H$, denoted by $\\overrightarrow{R}(H,k)$, which is the least $n$ for which every $k$-edge-coloured tournament on $n$ vertices contains a monochromatic copy of $H$. We prove that $ \\overrightarrow{R}(T,k) \\le c_k|T|^k$ for any oriented tree $T$. This is a generalisation of a similar result for directed paths by Chv\\'atal and by Gy\\'arf\\'as and Lehel, and answers a question of Yuster. In general, it is tight up to a constant factor.\n  We also consider the $k$-colour direc","authors_text":"Benny Sudakov, Matija Bucic, Shoham Letzter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T14:14:50Z","title":"Directed Ramsey number for trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04504","kind":"arxiv","version":2},"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:c1a45c7f8dda40d6c8ee48f2ac40907517a0dd496a3b117bc61705dfd8d9bf36","target":"record","created_at":"2026-05-17T23:47:12Z","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":"31f5a4f314923f224c92dd36ecf5cf6ab5670d6dfae4b7ca8b77d8e3c5f3b9bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T14:14:50Z","title_canon_sha256":"8ab6bb7b2a2765a3c414aa44f228dfcd5cf161fc8e8d740ed0124597c53baa71"},"schema_version":"1.0","source":{"id":"1708.04504","kind":"arxiv","version":2}},"canonical_sha256":"76a18e2e3847e94e23aec1a04f3c2dce3e591481c2d72a6002ad2e6aa41a7452","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76a18e2e3847e94e23aec1a04f3c2dce3e591481c2d72a6002ad2e6aa41a7452","first_computed_at":"2026-05-17T23:47:12.824555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:12.824555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1/Zgu7XykK9xSjW/o3ggZnxk4Zn0VumWNMpdO8BqVl8ss22PaJ382tEKRXu/TDoJwbA86a/nGw8YMrxRsmxuDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:12.824963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.04504","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1a45c7f8dda40d6c8ee48f2ac40907517a0dd496a3b117bc61705dfd8d9bf36","sha256:e4590052d74612ed577f699c7911d94ee9888bd12023a9137adbc57406c9e7e4"],"state_sha256":"42e1c5a09a5f23cb5ed4581884702cfdcc709c59a3e89d34580793856318a997"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EN/LbBh/vL1n1O5uLUNLbZ+YV6xUV+15BKdEzTSQ+5AYwU8hY3IV/sbioRnvEIgKUraAJkdb/+A/211t34knAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T09:53:21.393891Z","bundle_sha256":"2c3f76554b1745c97e92fcc7b627175965dd111c61091199b16a0283dcc3267f"}}