{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:XL7Q7DYB74MOVM6RNOV7DREDUY","short_pith_number":"pith:XL7Q7DYB","schema_version":"1.0","canonical_sha256":"baff0f8f01ff18eab3d16babf1c483a60fd5ac05cc298c1b800cea521917b2f1","source":{"kind":"arxiv","id":"2605.18458","version":1},"attestation_state":"computed","paper":{"title":"The typical structure of oriented graphs and digraphs with forbidden blow-up of transitive tournaments","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Jianxi Liu, Meili Liang, Ruiling Zheng, Yue Guan","submitted_at":"2026-05-18T14:21:44Z","abstract_excerpt":"For integers \\(r\\ge 2\\), \\(t\\ge 1\\) and a real number \\(a\\in(3/2,2]\\), we study the typical structure of oriented graphs and digraphs that do not contain a blow-up \\(T_{r+1}^t\\) of a transitive tournament. We prove that almost every \\(T_{r+1}^t\\)-free oriented graph on n vertices admits an r-partition \\(V_1\\cup\\cdots\\cup V_r\\) such that each induced subgraph \\(G[V_i]\\) is \\(T_2^t\\)-free, and the same holds for almost every \\(T_{r+1}^t\\)-free digraph.Consequently, the number \\(f(n,T_{r+1}^t)\\) of labelled \\(T_{r+1}^t\\)-free oriented graphs satisfies \\(f(n,T_{r+1}^t)=|\\mathcal{P}_{n,r,t}|(1+o(1)"},"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":"2605.18458","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-18T14:21:44Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"6ad5337c923766deda48243d27143ea7b74525c9d130e6d2a27e43ade9c8baa2","abstract_canon_sha256":"c8c4a5427f4f27440dd1e4a5a352bc7ec6debceb522bff7b779bd623f91c0a0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:06:02.287479Z","signature_b64":"ZgRRdD3KwLvInOtRZ1IdYRXwTTpHJcMvzEL+PxKLZH1KDms1jIexkrg2naSDVsSUODq3ELeIg6mEzybx7CeMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"baff0f8f01ff18eab3d16babf1c483a60fd5ac05cc298c1b800cea521917b2f1","last_reissued_at":"2026-05-20T00:06:02.286629Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:06:02.286629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The typical structure of oriented graphs and digraphs with forbidden blow-up of transitive tournaments","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Jianxi Liu, Meili Liang, Ruiling Zheng, Yue Guan","submitted_at":"2026-05-18T14:21:44Z","abstract_excerpt":"For integers \\(r\\ge 2\\), \\(t\\ge 1\\) and a real number \\(a\\in(3/2,2]\\), we study the typical structure of oriented graphs and digraphs that do not contain a blow-up \\(T_{r+1}^t\\) of a transitive tournament. We prove that almost every \\(T_{r+1}^t\\)-free oriented graph on n vertices admits an r-partition \\(V_1\\cup\\cdots\\cup V_r\\) such that each induced subgraph \\(G[V_i]\\) is \\(T_2^t\\)-free, and the same holds for almost every \\(T_{r+1}^t\\)-free digraph.Consequently, the number \\(f(n,T_{r+1}^t)\\) of labelled \\(T_{r+1}^t\\)-free oriented graphs satisfies \\(f(n,T_{r+1}^t)=|\\mathcal{P}_{n,r,t}|(1+o(1)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18458","kind":"arxiv","version":1},"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/2605.18458/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":"2605.18458","created_at":"2026-05-20T00:06:02.286772+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.18458v1","created_at":"2026-05-20T00:06:02.286772+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18458","created_at":"2026-05-20T00:06:02.286772+00:00"},{"alias_kind":"pith_short_12","alias_value":"XL7Q7DYB74MO","created_at":"2026-05-20T00:06:02.286772+00:00"},{"alias_kind":"pith_short_16","alias_value":"XL7Q7DYB74MOVM6R","created_at":"2026-05-20T00:06:02.286772+00:00"},{"alias_kind":"pith_short_8","alias_value":"XL7Q7DYB","created_at":"2026-05-20T00:06:02.286772+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XL7Q7DYB74MOVM6RNOV7DREDUY","json":"https://pith.science/pith/XL7Q7DYB74MOVM6RNOV7DREDUY.json","graph_json":"https://pith.science/api/pith-number/XL7Q7DYB74MOVM6RNOV7DREDUY/graph.json","events_json":"https://pith.science/api/pith-number/XL7Q7DYB74MOVM6RNOV7DREDUY/events.json","paper":"https://pith.science/paper/XL7Q7DYB"},"agent_actions":{"view_html":"https://pith.science/pith/XL7Q7DYB74MOVM6RNOV7DREDUY","download_json":"https://pith.science/pith/XL7Q7DYB74MOVM6RNOV7DREDUY.json","view_paper":"https://pith.science/paper/XL7Q7DYB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.18458&json=true","fetch_graph":"https://pith.science/api/pith-number/XL7Q7DYB74MOVM6RNOV7DREDUY/graph.json","fetch_events":"https://pith.science/api/pith-number/XL7Q7DYB74MOVM6RNOV7DREDUY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XL7Q7DYB74MOVM6RNOV7DREDUY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XL7Q7DYB74MOVM6RNOV7DREDUY/action/storage_attestation","attest_author":"https://pith.science/pith/XL7Q7DYB74MOVM6RNOV7DREDUY/action/author_attestation","sign_citation":"https://pith.science/pith/XL7Q7DYB74MOVM6RNOV7DREDUY/action/citation_signature","submit_replication":"https://pith.science/pith/XL7Q7DYB74MOVM6RNOV7DREDUY/action/replication_record"}},"created_at":"2026-05-20T00:06:02.286772+00:00","updated_at":"2026-05-20T00:06:02.286772+00:00"}