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It is known that $\\text{ex}_<(n,H) > n^{1+\\varepsilon}$ for some positive $\\varepsilon=\\varepsilon(H)$ unless $H$ is a forest that has a proper 2-coloring with one color class totally preceding the other one. Making progress towards a conjecture of Pach and Tardos, we prove that $\\text{ex}_<(n,H) =n^{1+o(1)}$ "},"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":"1711.07723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-21T11:25:46Z","cross_cats_sorted":[],"title_canon_sha256":"5127fcd52c682c6d84e40ee1d6691f9377e127709db7603733e5d2850f5b28a7","abstract_canon_sha256":"11c0412c5ffb9921b44ace9f9c4ce366cd2d6f0502948fcfe1c2cfd0ad5db8db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:56.643592Z","signature_b64":"g1yp90iNqQ7JD5Qfi2Zq+J7GuAVXy19rlGYO6Ppbpwe+YSiA/4pTR/qBuY4ZftAFuJiy6TbHUQ3MdeIFf2WVBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf4144b7651a6567ade3ad3c11f7a9a686ad9ce028d1292bd46642034049b3ea","last_reissued_at":"2026-05-18T00:29:56.642991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:56.642991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Tur\\'an number of ordered forests","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Craig Weidert, D\\'aniel Kor\\'andi, G\\'abor Tardos, Istv\\'an Tomon","submitted_at":"2017-11-21T11:25:46Z","abstract_excerpt":"An ordered graph $H$ is a simple graph with a linear order on its vertex set. 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