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We prove that asymptotically the correlation is negative for small $p$, $p<\\frac{C_1}n$, where $C_1\\approx0.3617$, positive for $\\frac{C_1}n<p<\\frac2n$ and up to $p=p_2(n)$. Computer aided computations suggest that $p_2(n)=\\frac{C_2}n$, with $C_2\\approx7.5$. We conjecture that the correlation then stays negative for $p$ up to the previously known zero at $\\frac12$; for larger $p$ it is positive."},"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":"1304.2016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-07T16:19:27Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"866b0ac5c8abd2baefecd306b448d71b781c53ba6eff63291384a35b5f817da7","abstract_canon_sha256":"5b5808d829ec87ed2ceb5f4de38fa89822ac7925da329411c5c47897297b2eb6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:44.383517Z","signature_b64":"dbC84oEU4Z+Y43p3GLSiPCpcc4ubAyKnjVkiwo8aIfEX387z+nlldvp0KTGvYcT9WxyjlSHCtAyv0ogxtdBjCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c1114ab75e29c956716950d06145c64fbb8acf3fd727dc0ddb8c1276d3250fe","last_reissued_at":"2026-05-18T03:28:44.382712Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:44.382712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"First critical probability for a problem on random orientations in $G(n,p)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Svante Janson, Svante Linusson, Sven Erick Alm","submitted_at":"2013-04-07T16:19:27Z","abstract_excerpt":"We study the random graph $G(n,p)$ with a random orientation. 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