{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CN3HDJHPC5ULOJSOKOZGTZAWEE","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":"bb56ab7e5964ba0af4febabe3842bb1e1d7b50c35c7ec482307fe8668d821694","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-30T13:36:52Z","title_canon_sha256":"83cb2bf8051b98ecb19a8af52bbc4b5ff6ab2a0a31b1f75e3474e601fa2b2fdb"},"schema_version":"1.0","source":{"id":"2412.00480","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.00480","created_at":"2026-07-05T09:42:42Z"},{"alias_kind":"arxiv_version","alias_value":"2412.00480v1","created_at":"2026-07-05T09:42:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.00480","created_at":"2026-07-05T09:42:42Z"},{"alias_kind":"pith_short_12","alias_value":"CN3HDJHPC5UL","created_at":"2026-07-05T09:42:42Z"},{"alias_kind":"pith_short_16","alias_value":"CN3HDJHPC5ULOJSO","created_at":"2026-07-05T09:42:42Z"},{"alias_kind":"pith_short_8","alias_value":"CN3HDJHP","created_at":"2026-07-05T09:42:42Z"}],"graph_snapshots":[{"event_id":"sha256:42a00817191f476ac1aff212bdd7c20b7fd1efb10d1f1b9ecae983dad86e57dd","target":"graph","created_at":"2026-07-05T09:42:42Z","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/2412.00480/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We will show that there are at least 8, 10 and 9 mutually orthogonal Latin squares (MOLS) of orders $n=54$, $96$ and $108$. The cases $n=54$ and $96$ are obtained by constructing separable permutation codes consisting of $8 \\times 54$ and $10 \\times 96$ codeword respectively; in addition, these codes respectively have lengths $54$, $96$ and minimum distances $53$, $95$. Here we will follow exactly the procedure given in \\cite{JS2019}. The case $n=108$ is obtained by constructing a $(108,10,1)$ difference matrix. Also, an error in \\cite{ACD} for $n=45$ will be corrected.","authors_text":"Ingo Janiszczak, Reiner Staszewski, R. Julian R. Abel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-30T13:36:52Z","title":"Improvements for lower bounds of mutually orthogonal Latin squares of sizes $54$, $96$ and $108$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.00480","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:bee8eddceddf96ba084747c52748f193399db3c4e28f793d6543c701ad3896c9","target":"record","created_at":"2026-07-05T09:42:42Z","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":"bb56ab7e5964ba0af4febabe3842bb1e1d7b50c35c7ec482307fe8668d821694","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-30T13:36:52Z","title_canon_sha256":"83cb2bf8051b98ecb19a8af52bbc4b5ff6ab2a0a31b1f75e3474e601fa2b2fdb"},"schema_version":"1.0","source":{"id":"2412.00480","kind":"arxiv","version":1}},"canonical_sha256":"137671a4ef1768b7264e53b269e416213a69967bf728f3e093de6c63958e9dbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"137671a4ef1768b7264e53b269e416213a69967bf728f3e093de6c63958e9dbd","first_computed_at":"2026-07-05T09:42:42.146703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:42:42.146703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s3fpC9jjQnXGgyelJbQapMQM6Cr3NhKk15Oy6lvO3DoK3tVikCNafurV71IxSVqdwIgGhgvq4e7ZAU/OJJNsCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:42:42.147128Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.00480","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bee8eddceddf96ba084747c52748f193399db3c4e28f793d6543c701ad3896c9","sha256:42a00817191f476ac1aff212bdd7c20b7fd1efb10d1f1b9ecae983dad86e57dd"],"state_sha256":"3b8f09a139d1f89bd378c014922f4e2c3be2fd6215e77971e86b3d4a829d7d67"}