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The Alon-Tarsi conjecture states that $L^{\\textrm{even}}(n)\\neq L^{\\textrm{odd}}(n)$ when $n$ is even (when $n$ is odd the two are equal for very simple reasons). In this short note we prove that $|L^{\\textrm{even}}(n) - L^{\\textrm{odd}}(n)|\\leq L(n)^{\\frac{1}{2} + o(1)},$ thus establishing the conjecture that the number of even and odd Latin squares, while conjecturally not equa"},"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":"1412.7574","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-23T23:46:51Z","cross_cats_sorted":[],"title_canon_sha256":"95ebc4a7e24d35ee331b33be58650ff9a5a922f41548777c05c7c8124916d809","abstract_canon_sha256":"398330a65f2d525f18d01304b7392a040dd46ef88a13bde2f3f6f114f49d288f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:33.491798Z","signature_b64":"8UusS1Q2HiDqfqgfLRHdgukMXpwOBVPe3IlJCzk+0o77ch0p/psmvcn4tkVCyA1LXtVCLJsSqEvWlx4ZzF5RBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8756f05357af71774dc2fd20d61d22dd623c64e3122c9b3ad453ab66b4159fa","last_reissued_at":"2026-05-18T02:30:33.491210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:33.491210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Square-root cancellation for the signs of Latin squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Levent Alpoge","submitted_at":"2014-12-23T23:46:51Z","abstract_excerpt":"Let $L(n)$ be the number of Latin squares of order $n$, and let $L^{\\textrm{even}}(n)$ and $L^{\\textrm{odd}}(n)$ be the number of even and odd such squares, so that $L(n) = L^{\\textrm{even}}(n) + L^{\\textrm{odd}}(n)$. The Alon-Tarsi conjecture states that $L^{\\textrm{even}}(n)\\neq L^{\\textrm{odd}}(n)$ when $n$ is even (when $n$ is odd the two are equal for very simple reasons). In this short note we prove that $|L^{\\textrm{even}}(n) - L^{\\textrm{odd}}(n)|\\leq L(n)^{\\frac{1}{2} + o(1)},$ thus establishing the conjecture that the number of even and odd Latin squares, while conjecturally not equa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7574","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":"1412.7574","created_at":"2026-05-18T02:30:33.491294+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.7574v1","created_at":"2026-05-18T02:30:33.491294+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7574","created_at":"2026-05-18T02:30:33.491294+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZB2W6BJVPL3R","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZB2W6BJVPL3RO5G4","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZB2W6BJV","created_at":"2026-05-18T12:28:59.999130+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/ZB2W6BJVPL3RO5G4F7JA2YOSFX","json":"https://pith.science/pith/ZB2W6BJVPL3RO5G4F7JA2YOSFX.json","graph_json":"https://pith.science/api/pith-number/ZB2W6BJVPL3RO5G4F7JA2YOSFX/graph.json","events_json":"https://pith.science/api/pith-number/ZB2W6BJVPL3RO5G4F7JA2YOSFX/events.json","paper":"https://pith.science/paper/ZB2W6BJV"},"agent_actions":{"view_html":"https://pith.science/pith/ZB2W6BJVPL3RO5G4F7JA2YOSFX","download_json":"https://pith.science/pith/ZB2W6BJVPL3RO5G4F7JA2YOSFX.json","view_paper":"https://pith.science/paper/ZB2W6BJV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.7574&json=true","fetch_graph":"https://pith.science/api/pith-number/ZB2W6BJVPL3RO5G4F7JA2YOSFX/graph.json","fetch_events":"https://pith.science/api/pith-number/ZB2W6BJVPL3RO5G4F7JA2YOSFX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZB2W6BJVPL3RO5G4F7JA2YOSFX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZB2W6BJVPL3RO5G4F7JA2YOSFX/action/storage_attestation","attest_author":"https://pith.science/pith/ZB2W6BJVPL3RO5G4F7JA2YOSFX/action/author_attestation","sign_citation":"https://pith.science/pith/ZB2W6BJVPL3RO5G4F7JA2YOSFX/action/citation_signature","submit_replication":"https://pith.science/pith/ZB2W6BJVPL3RO5G4F7JA2YOSFX/action/replication_record"}},"created_at":"2026-05-18T02:30:33.491294+00:00","updated_at":"2026-05-18T02:30:33.491294+00:00"}