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We show that the same holds with $K_n$ replaced by the binomial random graph $G_{n,p}$ whenever $H$ is also strictly $2$-balanced and $p \\ge (\\theta_H+o(1)) n^{-\\frac{1}{m_2(H)}} (\\log n)^{\\frac{1}{e_H-1}}$ for some explicit constant $\\theta_H$, which we believe to be optimal. This (partially) resolves a conjecture of DeMarco and Kahn."},"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":"2308.13455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-08-25T16:02:56Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"3e2a479700f6f85afac1d21ab503aebc5ab27cfd2b0a950d9e5a53d36f5cdef7","abstract_canon_sha256":"712fdd41c93af2053e0bffc858d79e0d26804e40d454e610ebbbfb01c817b5df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:44:44.288348Z","signature_b64":"sVhfj14CK53GUPRh1ML6rqVdTrm/8BjgUXhCCp/jbi5F4iOPQKsmO/n3O9L3RO4KIyhlba9+Meeu+VXMOVsoCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff3951e26445a9c56c23514482079368398f380018e3ccbfdbc3612ef0dcf43e","last_reissued_at":"2026-07-05T06:44:44.287825Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:44:44.287825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simonovits's theorem in random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Ilay Hoshen, Wojciech Samotij","submitted_at":"2023-08-25T16:02:56Z","abstract_excerpt":"Let $H$ be a graph with $\\chi(H) = r+1$. 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