{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BDBX52X3CNAIGTN6RHYFG6N72Z","short_pith_number":"pith:BDBX52X3","canonical_record":{"source":{"id":"1810.12639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-30T10:32:00Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"6f717cdaaac43cc09eab0f5f89f48c0cdebb3ad2d059141136b985a4a64f2ee2","abstract_canon_sha256":"88788f8a2b45e19968f77c50f69b072c32144ec59e54db00828e5a1a5a867912"},"schema_version":"1.0"},"canonical_sha256":"08c37eeafb1340834dbe89f05379bfd6647e205c7e656111cab95c5f0e2d9019","source":{"kind":"arxiv","id":"1810.12639","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12639","created_at":"2026-05-18T00:01:56Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12639v1","created_at":"2026-05-18T00:01:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12639","created_at":"2026-05-18T00:01:56Z"},{"alias_kind":"pith_short_12","alias_value":"BDBX52X3CNAI","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"BDBX52X3CNAIGTN6","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"BDBX52X3","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BDBX52X3CNAIGTN6RHYFG6N72Z","target":"record","payload":{"canonical_record":{"source":{"id":"1810.12639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-30T10:32:00Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"6f717cdaaac43cc09eab0f5f89f48c0cdebb3ad2d059141136b985a4a64f2ee2","abstract_canon_sha256":"88788f8a2b45e19968f77c50f69b072c32144ec59e54db00828e5a1a5a867912"},"schema_version":"1.0"},"canonical_sha256":"08c37eeafb1340834dbe89f05379bfd6647e205c7e656111cab95c5f0e2d9019","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:56.437515Z","signature_b64":"dvBwqopTsdKkFwN0k90wfyreZPzWFxL2+oJFri0fPeMuTS9JJ2gFtWdcF7W59VzzPwN6V2EslefrZ55AhxBSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08c37eeafb1340834dbe89f05379bfd6647e205c7e656111cab95c5f0e2d9019","last_reissued_at":"2026-05-18T00:01:56.437064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:56.437064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.12639","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":"2026-05-18T00:01:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VWCxk0vLpOMlsYjGGHVO710q21Vx/G4vNNkFfEaDWPf4HcuGc3NcKDZ6kSBl3tjaeQLZeJtsvSXW2IkMK0I8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:28:18.730042Z"},"content_sha256":"bc0905696f94ef0ca33a756531fe195294b10ea5d0525ff94dbec504f779960e","schema_version":"1.0","event_id":"sha256:bc0905696f94ef0ca33a756531fe195294b10ea5d0525ff94dbec504f779960e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BDBX52X3CNAIGTN6RHYFG6N72Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Triples of Orthogonal Latin and Youden Rectangles For Small Orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Denys Shcherbak, Gerold J\\\"ager, Klas Markstr\\\"om, Lars-Daniel \\\"Ohman","submitted_at":"2018-10-30T10:32:00Z","abstract_excerpt":"We have performed a complete enumeration of non-isotopic triples of mutually orthogonal $k\\times n$ Latin rectangles for $k\\leq n \\leq 7$. Here we will present a census of such triples, classified by various properties, including the order of the autotopism group of the triple. As part of this we have also achieved the first enumeration of pairwise orthogonal triples of Youden rectangles. We have also studied orthogonal triples of $k \\times 8$ rectangles which are formed by extending mutually orthogonal triples with non-trivial autotopisms one row at a time, and requiring that the autotopism g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12639","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":"2026-05-18T00:01:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rKbmr3i/TPVBJJD16NiGtQ7YNyVgLa81bbzQGxlGYuZQJlU8Pk1sKTbO99uYYGdO8PvK91zIYHquC6awBFkhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:28:18.730806Z"},"content_sha256":"43a0e45db41883ac51de4d7c191768deac6d60ac8bf231ad1c1e4b6ad98652ed","schema_version":"1.0","event_id":"sha256:43a0e45db41883ac51de4d7c191768deac6d60ac8bf231ad1c1e4b6ad98652ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDBX52X3CNAIGTN6RHYFG6N72Z/bundle.json","state_url":"https://pith.science/pith/BDBX52X3CNAIGTN6RHYFG6N72Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDBX52X3CNAIGTN6RHYFG6N72Z/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":"2026-06-06T08:28:18Z","links":{"resolver":"https://pith.science/pith/BDBX52X3CNAIGTN6RHYFG6N72Z","bundle":"https://pith.science/pith/BDBX52X3CNAIGTN6RHYFG6N72Z/bundle.json","state":"https://pith.science/pith/BDBX52X3CNAIGTN6RHYFG6N72Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDBX52X3CNAIGTN6RHYFG6N72Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BDBX52X3CNAIGTN6RHYFG6N72Z","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":"88788f8a2b45e19968f77c50f69b072c32144ec59e54db00828e5a1a5a867912","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-30T10:32:00Z","title_canon_sha256":"6f717cdaaac43cc09eab0f5f89f48c0cdebb3ad2d059141136b985a4a64f2ee2"},"schema_version":"1.0","source":{"id":"1810.12639","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12639","created_at":"2026-05-18T00:01:56Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12639v1","created_at":"2026-05-18T00:01:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12639","created_at":"2026-05-18T00:01:56Z"},{"alias_kind":"pith_short_12","alias_value":"BDBX52X3CNAI","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"BDBX52X3CNAIGTN6","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"BDBX52X3","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:43a0e45db41883ac51de4d7c191768deac6d60ac8bf231ad1c1e4b6ad98652ed","target":"graph","created_at":"2026-05-18T00:01:56Z","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":"We have performed a complete enumeration of non-isotopic triples of mutually orthogonal $k\\times n$ Latin rectangles for $k\\leq n \\leq 7$. Here we will present a census of such triples, classified by various properties, including the order of the autotopism group of the triple. As part of this we have also achieved the first enumeration of pairwise orthogonal triples of Youden rectangles. We have also studied orthogonal triples of $k \\times 8$ rectangles which are formed by extending mutually orthogonal triples with non-trivial autotopisms one row at a time, and requiring that the autotopism g","authors_text":"Denys Shcherbak, Gerold J\\\"ager, Klas Markstr\\\"om, Lars-Daniel \\\"Ohman","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-30T10:32:00Z","title":"Triples of Orthogonal Latin and Youden Rectangles For Small Orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12639","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:bc0905696f94ef0ca33a756531fe195294b10ea5d0525ff94dbec504f779960e","target":"record","created_at":"2026-05-18T00:01:56Z","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":"88788f8a2b45e19968f77c50f69b072c32144ec59e54db00828e5a1a5a867912","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-30T10:32:00Z","title_canon_sha256":"6f717cdaaac43cc09eab0f5f89f48c0cdebb3ad2d059141136b985a4a64f2ee2"},"schema_version":"1.0","source":{"id":"1810.12639","kind":"arxiv","version":1}},"canonical_sha256":"08c37eeafb1340834dbe89f05379bfd6647e205c7e656111cab95c5f0e2d9019","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08c37eeafb1340834dbe89f05379bfd6647e205c7e656111cab95c5f0e2d9019","first_computed_at":"2026-05-18T00:01:56.437064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:56.437064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dvBwqopTsdKkFwN0k90wfyreZPzWFxL2+oJFri0fPeMuTS9JJ2gFtWdcF7W59VzzPwN6V2EslefrZ55AhxBSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:56.437515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12639","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc0905696f94ef0ca33a756531fe195294b10ea5d0525ff94dbec504f779960e","sha256:43a0e45db41883ac51de4d7c191768deac6d60ac8bf231ad1c1e4b6ad98652ed"],"state_sha256":"10466ac50dc8ee9c312f02b133e531c98d6cffb46d1abc3d6cce922986afd9b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N1u/hMF2joJkATa8Rtlsc5g8X0bj9UB5ApF9XbREtn+ATys8r7ugB4pTIDX+N7lpTvhxmIwfUdfHX2yO6WmODA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T08:28:18.734750Z","bundle_sha256":"fca1d5a1fef6be0203321de83d2065802c33f6799344a461a4c5b8e3493c65b1"}}