{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:CLQRHU67R5BTAE55AQBCFZY5CP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"24c44bd9fac9b5eb94aa37a8ee2d1a951b3e069f2c89ee10587fafaac41264d4","cross_cats_sorted":["cs.DM","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-12-12T18:32:04Z","title_canon_sha256":"ed3c8eb55b100ddc949a52f2a83e0f9153fa416e5a567242f624644da93e93dd"},"schema_version":"1.0","source":{"id":"2212.06109","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.06109","created_at":"2026-07-05T05:26:29Z"},{"alias_kind":"arxiv_version","alias_value":"2212.06109v2","created_at":"2026-07-05T05:26:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.06109","created_at":"2026-07-05T05:26:29Z"},{"alias_kind":"pith_short_12","alias_value":"CLQRHU67R5BT","created_at":"2026-07-05T05:26:29Z"},{"alias_kind":"pith_short_16","alias_value":"CLQRHU67R5BTAE55","created_at":"2026-07-05T05:26:29Z"},{"alias_kind":"pith_short_8","alias_value":"CLQRHU67","created_at":"2026-07-05T05:26:29Z"}],"graph_snapshots":[{"event_id":"sha256:c8fe5188363a7379a76c55a0100ea93af6942a191a31898edeadf663f2a66a52","target":"graph","created_at":"2026-07-05T05:26:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2212.06109/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the threshold for the binomial random $3$-partite, $3$-uniform hypergraph $G^{3}((n,n,n),p)$ to contain a Latin square is $\\Theta(\\log{n}/n)$. We also prove analogous results for Steiner triple systems and proper list edge-colorings of the complete (bipartite) graph with random lists. Our results answer several related questions of Johansson, Luria-Simkin, Casselgren-H\\\"aggkvist, Simkin, and Kang-Kelly-K\\\"uhn-Methuku-Osthus.","authors_text":"Huy Tuan Pham, Vishesh Jain","cross_cats":["cs.DM","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-12-12T18:32:04Z","title":"Optimal thresholds for Latin squares, Steiner Triple Systems, and edge colorings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.06109","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2ec2197c2d3279c5c17862bba2d9055ac97bdc06a2ab7ccfa7a57b1db2ff1356","target":"record","created_at":"2026-07-05T05:26:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"24c44bd9fac9b5eb94aa37a8ee2d1a951b3e069f2c89ee10587fafaac41264d4","cross_cats_sorted":["cs.DM","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-12-12T18:32:04Z","title_canon_sha256":"ed3c8eb55b100ddc949a52f2a83e0f9153fa416e5a567242f624644da93e93dd"},"schema_version":"1.0","source":{"id":"2212.06109","kind":"arxiv","version":2}},"canonical_sha256":"12e113d3df8f433013bd040222e71d13d776773678fb327797b3bc2ad1ecf816","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12e113d3df8f433013bd040222e71d13d776773678fb327797b3bc2ad1ecf816","first_computed_at":"2026-07-05T05:26:29.198792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:26:29.198792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ge8DpudxbuAhh+9t4a8SIkEohFvEnhM/iXEAToTGNKaha5monwREhh/uoYR8FxMdA+3zUAGBL0396xc4VcJWAg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:26:29.199195Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.06109","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ec2197c2d3279c5c17862bba2d9055ac97bdc06a2ab7ccfa7a57b1db2ff1356","sha256:c8fe5188363a7379a76c55a0100ea93af6942a191a31898edeadf663f2a66a52"],"state_sha256":"95cddf5e837e4d50dcc9145b10d5c3f88d79744069391e50f4daec0ee28b3bc8"}