{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NMKDKHFIESSHBHUTODWNBIB7XB","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":"ed27afbbbb0ebc17d7c422c2389786eeaa89250066662d0d5aafc4bb8b37b098","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-24T17:12:55Z","title_canon_sha256":"60d05605eb17360209fc834d73d545eadefdddbd17944fc5e1641ee57e3f0e61"},"schema_version":"1.0","source":{"id":"1410.6743","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6743","created_at":"2026-05-18T02:39:24Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6743v1","created_at":"2026-05-18T02:39:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6743","created_at":"2026-05-18T02:39:24Z"},{"alias_kind":"pith_short_12","alias_value":"NMKDKHFIESSH","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NMKDKHFIESSHBHUT","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NMKDKHFI","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:1af8c46fac1c1c2c37f1d2553a84b075c3adeba3e854118e90f8d20e38bcf98a","target":"graph","created_at":"2026-05-18T02:39:24Z","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"},"paper":{"abstract_excerpt":"Two latin squares are orthogonal if, when they are superimposed, every ordered pair of symbols appears exactly once. This definition extends naturally to `incomplete' latin squares each having a hole on the same rows, columns, and symbols. If an incomplete latin square of order $n$ has a hole of order $m$, then it is an easy observation that $n \\ge 2m$. More generally, if a set of $t$ incomplete mutually orthogonal latin squares of order $n$ have a common hole of order $m$, then $n \\ge (t+1)m$. In this article, we prove such sets of incomplete squares exist for all $n,m \\gg 0$ satisfying $n \\g","authors_text":"Christopher M. van Bommel, Peter J. Dukes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-24T17:12:55Z","title":"Mutually orthogonal latin squares with large holes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6743","kind":"arxiv","version":1},"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":"sha256:3adabcabff9679fe07305225f0f5cd8e79f6266ce4d27fb21f936ba11c7abb8b","target":"record","created_at":"2026-05-18T02:39:24Z","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":"ed27afbbbb0ebc17d7c422c2389786eeaa89250066662d0d5aafc4bb8b37b098","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-24T17:12:55Z","title_canon_sha256":"60d05605eb17360209fc834d73d545eadefdddbd17944fc5e1641ee57e3f0e61"},"schema_version":"1.0","source":{"id":"1410.6743","kind":"arxiv","version":1}},"canonical_sha256":"6b14351ca824a4709e9370ecd0a03fb8634615f4a32e9969d3cc66deca8a6ac2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b14351ca824a4709e9370ecd0a03fb8634615f4a32e9969d3cc66deca8a6ac2","first_computed_at":"2026-05-18T02:39:24.645106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:24.645106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"43+rvHd6JdziZgYyTe4hUQBNEGJvKpXQfegfzBneLymbypyOKia5ZbFq/1wHocsyNF9aH0LTfBxv6uAcEA4uCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:24.645605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6743","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3adabcabff9679fe07305225f0f5cd8e79f6266ce4d27fb21f936ba11c7abb8b","sha256:1af8c46fac1c1c2c37f1d2553a84b075c3adeba3e854118e90f8d20e38bcf98a"],"state_sha256":"bd88d5dbbd39d9812d66e489ddf406eb4af55bf240a491d5fa45e31e308d42bd"}