{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:D7NMOBBYLMB6RVWWTNNAU2IJO4","short_pith_number":"pith:D7NMOBBY","canonical_record":{"source":{"id":"1401.7889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-30T15:47:21Z","cross_cats_sorted":[],"title_canon_sha256":"4193ac5161ceb16bb113d722ab278bdc455a30272bf87223dbbb54642b3466b6","abstract_canon_sha256":"c644bcd67f4aae11a04887a1f3c7985b67e46ad59672eef49671ec693146d0f2"},"schema_version":"1.0"},"canonical_sha256":"1fdac704385b03e8d6d69b5a0a6909770708181517c126818006761b645d56c4","source":{"kind":"arxiv","id":"1401.7889","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7889","created_at":"2026-05-18T03:00:38Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7889v1","created_at":"2026-05-18T03:00:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7889","created_at":"2026-05-18T03:00:38Z"},{"alias_kind":"pith_short_12","alias_value":"D7NMOBBYLMB6","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D7NMOBBYLMB6RVWW","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D7NMOBBY","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:D7NMOBBYLMB6RVWWTNNAU2IJO4","target":"record","payload":{"canonical_record":{"source":{"id":"1401.7889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-30T15:47:21Z","cross_cats_sorted":[],"title_canon_sha256":"4193ac5161ceb16bb113d722ab278bdc455a30272bf87223dbbb54642b3466b6","abstract_canon_sha256":"c644bcd67f4aae11a04887a1f3c7985b67e46ad59672eef49671ec693146d0f2"},"schema_version":"1.0"},"canonical_sha256":"1fdac704385b03e8d6d69b5a0a6909770708181517c126818006761b645d56c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:38.044282Z","signature_b64":"qn/nggfTWMeNG0MRHO0hcWqYTJpShHrroAWN/3ogJe1kiIloRVMcMl4YC4A9bAbvsOQQxaVUOPZvJgv21/QsBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fdac704385b03e8d6d69b5a0a6909770708181517c126818006761b645d56c4","last_reissued_at":"2026-05-18T03:00:38.043535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:38.043535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.7889","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:00:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D4aDnehxa6DOhAdl1OmT+7D3Ky5bUGCAMK6c9Q3ZGlvUjY0YwKOqt93UwRfduhN+yPLWy1e7m8RIWJYHyt2WBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:34:21.649732Z"},"content_sha256":"2d7256eeceac2e3d0844b731a2ac831b7d6b37762b840a0131bae3f078014a75","schema_version":"1.0","event_id":"sha256:2d7256eeceac2e3d0844b731a2ac831b7d6b37762b840a0131bae3f078014a75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:D7NMOBBYLMB6RVWWTNNAU2IJO4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Direct constructions for general families of cyclic mutually nearly orthogonal Latin squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abdollah Khodkar, Diane Donovan, Fatih Demirkale","submitted_at":"2014-01-30T15:47:21Z","abstract_excerpt":"Two Latin squares $L=[l(i,j)]$ and $M=[m(i,j)]$, of even order $n$ with entries $\\{0,1,2,\\ldots,n-1\\}$, are said to be nearly orthogonal if the superimposition of $L$ on $M$ yields an $n\\times n$ array $A=[(l(i,j),m(i,j))]$ in which each ordered pair $(x,y)$, $0\\leq x,y\\leq n-1$ and $x\\neq y$, occurs at least once and the ordered pair $(x,x+n/2)$ occurs exactly twice. In this paper, we present direct constructions for the existence of general families of three cyclic mutually orthogonal Latin squares of orders $48k+14$, $48k+22$, $48k+38$ and $48k+46$. The techniques employed are based on the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7889","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:00:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"caYR1HOG6s++/mh40JYLVPwcTEzroZD5enxBZYdJZCCxfPYO9hPbD9GsOn1AJOdbidKLLl0vxnUqTdDyvsi7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:34:21.650087Z"},"content_sha256":"b88b7d7cc428e1466692fd1e8e998207400ce04e8de046733fc2d18acc1ce2b9","schema_version":"1.0","event_id":"sha256:b88b7d7cc428e1466692fd1e8e998207400ce04e8de046733fc2d18acc1ce2b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D7NMOBBYLMB6RVWWTNNAU2IJO4/bundle.json","state_url":"https://pith.science/pith/D7NMOBBYLMB6RVWWTNNAU2IJO4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D7NMOBBYLMB6RVWWTNNAU2IJO4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T01:34:21Z","links":{"resolver":"https://pith.science/pith/D7NMOBBYLMB6RVWWTNNAU2IJO4","bundle":"https://pith.science/pith/D7NMOBBYLMB6RVWWTNNAU2IJO4/bundle.json","state":"https://pith.science/pith/D7NMOBBYLMB6RVWWTNNAU2IJO4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D7NMOBBYLMB6RVWWTNNAU2IJO4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:D7NMOBBYLMB6RVWWTNNAU2IJO4","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":"c644bcd67f4aae11a04887a1f3c7985b67e46ad59672eef49671ec693146d0f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-30T15:47:21Z","title_canon_sha256":"4193ac5161ceb16bb113d722ab278bdc455a30272bf87223dbbb54642b3466b6"},"schema_version":"1.0","source":{"id":"1401.7889","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7889","created_at":"2026-05-18T03:00:38Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7889v1","created_at":"2026-05-18T03:00:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7889","created_at":"2026-05-18T03:00:38Z"},{"alias_kind":"pith_short_12","alias_value":"D7NMOBBYLMB6","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D7NMOBBYLMB6RVWW","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D7NMOBBY","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:b88b7d7cc428e1466692fd1e8e998207400ce04e8de046733fc2d18acc1ce2b9","target":"graph","created_at":"2026-05-18T03:00:38Z","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 $L=[l(i,j)]$ and $M=[m(i,j)]$, of even order $n$ with entries $\\{0,1,2,\\ldots,n-1\\}$, are said to be nearly orthogonal if the superimposition of $L$ on $M$ yields an $n\\times n$ array $A=[(l(i,j),m(i,j))]$ in which each ordered pair $(x,y)$, $0\\leq x,y\\leq n-1$ and $x\\neq y$, occurs at least once and the ordered pair $(x,x+n/2)$ occurs exactly twice. In this paper, we present direct constructions for the existence of general families of three cyclic mutually orthogonal Latin squares of orders $48k+14$, $48k+22$, $48k+38$ and $48k+46$. The techniques employed are based on the ","authors_text":"Abdollah Khodkar, Diane Donovan, Fatih Demirkale","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-30T15:47:21Z","title":"Direct constructions for general families of cyclic mutually nearly orthogonal Latin squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7889","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":"sha256:2d7256eeceac2e3d0844b731a2ac831b7d6b37762b840a0131bae3f078014a75","target":"record","created_at":"2026-05-18T03:00:38Z","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":"c644bcd67f4aae11a04887a1f3c7985b67e46ad59672eef49671ec693146d0f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-30T15:47:21Z","title_canon_sha256":"4193ac5161ceb16bb113d722ab278bdc455a30272bf87223dbbb54642b3466b6"},"schema_version":"1.0","source":{"id":"1401.7889","kind":"arxiv","version":1}},"canonical_sha256":"1fdac704385b03e8d6d69b5a0a6909770708181517c126818006761b645d56c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fdac704385b03e8d6d69b5a0a6909770708181517c126818006761b645d56c4","first_computed_at":"2026-05-18T03:00:38.043535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:38.043535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qn/nggfTWMeNG0MRHO0hcWqYTJpShHrroAWN/3ogJe1kiIloRVMcMl4YC4A9bAbvsOQQxaVUOPZvJgv21/QsBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:38.044282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7889","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d7256eeceac2e3d0844b731a2ac831b7d6b37762b840a0131bae3f078014a75","sha256:b88b7d7cc428e1466692fd1e8e998207400ce04e8de046733fc2d18acc1ce2b9"],"state_sha256":"d85f490a5fe1efcebf00e42372a763de06bc125a48d4cba23f8dc48e887d3e2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iwJBZDA44XOW/9vu5aGS83JdUl5Wa6EY7IsPAKYjG57m+i2KZZcIf/RQsZwQKGX5QLUXzk09ByDMVIIIFoxcBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:34:21.652497Z","bundle_sha256":"fa3eaac42419a4b0325c5707f15e427de026dc9acd9535c22a54054f13f03088"}}