{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:G66E7DW5ZFRGPSWTV2AL2BADWY","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":"536acb237296a8f6752896671dc224bc87509437f2f8d1258c517593160aba18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-11-20T05:21:11Z","title_canon_sha256":"79d7566eaf4be0638b451ac926dd95b41bdcf6264433cc5ec44be552dc9aa3ed"},"schema_version":"1.0","source":{"id":"0911.3969","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.3969","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"arxiv_version","alias_value":"0911.3969v2","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.3969","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"pith_short_12","alias_value":"G66E7DW5ZFRG","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"G66E7DW5ZFRGPSWT","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"G66E7DW5","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:6aba80a8b2166291f71e97b904bb3d20ae39202dba5b674158ef67a30c64789b","target":"graph","created_at":"2026-05-18T04:35:14Z","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":"It is an intriguing question to see what kind of information on the structure of an oriented graph $D$ one can obtain if $D$ does not contain a fixed oriented graph $H$ as a subgraph. The related question in the unoriented case has been an active area of research, and is relatively well-understood in the theory of quasi-random graphs and extremal combinatorics. In this paper, we consider the simplest cases of such a general question for oriented graphs, and provide some results on the global behavior of the orientation of $D$. For the case that $H$ is an oriented four-cycle we prove: in every ","authors_text":"Florian Huc, Omid Amini, Simon Griffiths","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-11-20T05:21:11Z","title":"Subgraphs of weakly quasi-random oriented graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3969","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:dd070203608d620764636c2ad5acdcd20453e646acce3ede6e4b9fae20871182","target":"record","created_at":"2026-05-18T04:35:14Z","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":"536acb237296a8f6752896671dc224bc87509437f2f8d1258c517593160aba18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-11-20T05:21:11Z","title_canon_sha256":"79d7566eaf4be0638b451ac926dd95b41bdcf6264433cc5ec44be552dc9aa3ed"},"schema_version":"1.0","source":{"id":"0911.3969","kind":"arxiv","version":2}},"canonical_sha256":"37bc4f8eddc96267cad3ae80bd0403b60c374347a74ff7ba6d48af5c253eda43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37bc4f8eddc96267cad3ae80bd0403b60c374347a74ff7ba6d48af5c253eda43","first_computed_at":"2026-05-18T04:35:14.899820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:14.899820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f5aEcuy8TFA3J1NCA1I4XooqLitHpTFWl2OkiFbsXhp1yUjwUfZdQAH4EoJ+tk3w+9IFFNfxUPxFRwbM8cTfDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:14.900543Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.3969","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd070203608d620764636c2ad5acdcd20453e646acce3ede6e4b9fae20871182","sha256:6aba80a8b2166291f71e97b904bb3d20ae39202dba5b674158ef67a30c64789b"],"state_sha256":"67e107732fbd8c0de2c5f9957cefb6c6cb99a6a00087afd86827f4ed30eb4c25"}