{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Y4OWMAHL25CWDOQWD2OA5VBMR3","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":"a778b2a1ad3dc6b524de21b79ea37a2e488a2d2bceeb3049db0c88192ab9e0ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-12T13:37:14Z","title_canon_sha256":"8e94bcc3b2e35b500b333e4643675992eed9e295f07a22915b428cc28d5a6d8b"},"schema_version":"1.0","source":{"id":"1609.03393","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03393","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03393v1","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03393","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"Y4OWMAHL25CW","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Y4OWMAHL25CWDOQW","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Y4OWMAHL","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:f048f4729ba5400c9dca3e922899d57c9c5f4435d81077c63c0daa3707035045","target":"graph","created_at":"2026-05-18T01:04:47Z","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":"An oriented tree $T$ on $n$ vertices is unavoidable if every tournament on $n$ vertices contains a copy of $T$. In this paper we give a sufficient condition for $T$ to be unavoidable, and use this to prove that almost all labelled oriented trees are unavoidable, verifying a conjecture of Bender and Wormald. We additionally prove that every tournament on $n + o(n)$ vertices contains a copy of every oriented tree $T$ on $n$ vertices with polylogarithmic maximum degree, improving a result of K\\\"uhn, Mycroft and Osthus.","authors_text":"Richard Mycroft, T\\'assio Naia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-12T13:37:14Z","title":"Unavoidable trees in tournaments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03393","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:d8270782ac800f2a7f0bced3bb31dcd5e73b547fbe2dce037e59a58f54f6b54b","target":"record","created_at":"2026-05-18T01:04:47Z","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":"a778b2a1ad3dc6b524de21b79ea37a2e488a2d2bceeb3049db0c88192ab9e0ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-12T13:37:14Z","title_canon_sha256":"8e94bcc3b2e35b500b333e4643675992eed9e295f07a22915b428cc28d5a6d8b"},"schema_version":"1.0","source":{"id":"1609.03393","kind":"arxiv","version":1}},"canonical_sha256":"c71d6600ebd74561ba161e9c0ed42c8ed62e99f6b512ceb86caa5595392ddb7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c71d6600ebd74561ba161e9c0ed42c8ed62e99f6b512ceb86caa5595392ddb7e","first_computed_at":"2026-05-18T01:04:47.050620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:47.050620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mUvW2maWkmyT9Jv47mV3SIymBGGM5MJMWoyM/gBQhTS8BZJOX4I/7vzkKYto/8SsJbNnarvxnABGY3nY1E8bCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:47.051161Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03393","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8270782ac800f2a7f0bced3bb31dcd5e73b547fbe2dce037e59a58f54f6b54b","sha256:f048f4729ba5400c9dca3e922899d57c9c5f4435d81077c63c0daa3707035045"],"state_sha256":"569ccec0512df4bb152488694276bae02d4345f573c77f88c6f2e0b8783fa991"}