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Similarly, what is the least integer $t=t(T_n,H)$ so that adding $t$ edges to the $n$-vertex transitive tournament, results in a digraph containing a copy of $H$. Besides proving several results on these problems, our main contributions are the following:\n  (1) Pach and Tardos conjectured that if $M$ is an acyclic $0/1$ matrix, then any $n \\times n$ matrix with $n(\\log n)^{O(1)}$ "},"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":"1502.02433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-09T11:07:01Z","cross_cats_sorted":[],"title_canon_sha256":"98df1cd44276c571db8f0359e48f518f392f0a2bcf8d8ad462edd9dacc7c5aec","abstract_canon_sha256":"8503c31b555c39416dc7823ccfd98aef17c2225191fc36acd7d07690db8d1f87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:42.376501Z","signature_b64":"EYzAlSCoDWrenHfq7T9MCfub6hp5zPt18tVvE27vz7zfGWvc4dBZF/yexHmtlJoDsamQJS0jRMQhDUvT2F7+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdb3369356054b26d90e8fe2baddc882fc4e12b542206872703a0fe7edcd1a93","last_reissued_at":"2026-05-18T02:27:42.375615Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:42.375615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A tournament approach to pattern avoiding matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Asaf Shapira, Raphy Yuster","submitted_at":"2015-02-09T11:07:01Z","abstract_excerpt":"We consider the following Tur\\'an-type problem: given a fixed tournament $H$, what is the least integer $t=t(n,H)$ so that adding $t$ edges to any $n$-vertex tournament, results in a digraph containing a copy of $H$. 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Besides proving several results on these problems, our main contributions are the following:\n  (1) Pach and Tardos conjectured that if $M$ is an acyclic $0/1$ matrix, then any $n \\times n$ matrix with $n(\\log n)^{O(1)}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02433","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":""},"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":"1502.02433","created_at":"2026-05-18T02:27:42.375768+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.02433v1","created_at":"2026-05-18T02:27:42.375768+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02433","created_at":"2026-05-18T02:27:42.375768+00:00"},{"alias_kind":"pith_short_12","alias_value":"XWZTNE2WAVFS","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XWZTNE2WAVFSNWIO","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XWZTNE2W","created_at":"2026-05-18T12:29:50.041715+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/XWZTNE2WAVFSNWIOR7RLVXOIQL","json":"https://pith.science/pith/XWZTNE2WAVFSNWIOR7RLVXOIQL.json","graph_json":"https://pith.science/api/pith-number/XWZTNE2WAVFSNWIOR7RLVXOIQL/graph.json","events_json":"https://pith.science/api/pith-number/XWZTNE2WAVFSNWIOR7RLVXOIQL/events.json","paper":"https://pith.science/paper/XWZTNE2W"},"agent_actions":{"view_html":"https://pith.science/pith/XWZTNE2WAVFSNWIOR7RLVXOIQL","download_json":"https://pith.science/pith/XWZTNE2WAVFSNWIOR7RLVXOIQL.json","view_paper":"https://pith.science/paper/XWZTNE2W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.02433&json=true","fetch_graph":"https://pith.science/api/pith-number/XWZTNE2WAVFSNWIOR7RLVXOIQL/graph.json","fetch_events":"https://pith.science/api/pith-number/XWZTNE2WAVFSNWIOR7RLVXOIQL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XWZTNE2WAVFSNWIOR7RLVXOIQL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XWZTNE2WAVFSNWIOR7RLVXOIQL/action/storage_attestation","attest_author":"https://pith.science/pith/XWZTNE2WAVFSNWIOR7RLVXOIQL/action/author_attestation","sign_citation":"https://pith.science/pith/XWZTNE2WAVFSNWIOR7RLVXOIQL/action/citation_signature","submit_replication":"https://pith.science/pith/XWZTNE2WAVFSNWIOR7RLVXOIQL/action/replication_record"}},"created_at":"2026-05-18T02:27:42.375768+00:00","updated_at":"2026-05-18T02:27:42.375768+00:00"}