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Equivalently, $\\mathbb{P}\\left[\\mathbf{N}=0\\right]\\ge e^{-n^{2}/4-o(n^{2})}=e^{-(1+o(1))\\mathbb{E}\\mathbf{N}}$, where $\\mathbf{N}$ is the number of intercalates "},"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":"2202.05088","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-02-10T15:16:04Z","cross_cats_sorted":[],"title_canon_sha256":"5c699c178e3b2793e73c69a32c3942b9e1974158b6b40a254599d9f529c3b552","abstract_canon_sha256":"2d47c144761b3ab2d3f28797cb23f1bb09c9f90a4c26dc1e4bcf4351b40f6928"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:45:57.857216Z","signature_b64":"Tkp684syON0Fu7YCr5N52jQGPwZb8vT8LN6jGpOPvMRNT8hXlVWqm5DsGWzy5p+2M4MOtb/KB6LdXWIzuL+3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0387991c477f2543d8fd621bdaf1851ef9df45924277dae8889e0f2ac0176e5d","last_reissued_at":"2026-07-05T04:45:57.856777Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:45:57.856777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Substructures in Latin squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ashwin Sah, Matthew Kwan, Mehtaab Sawhney, Michael Simkin","submitted_at":"2022-02-10T15:16:04Z","abstract_excerpt":"We prove several results about substructures in Latin squares. 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