{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OWLMFDBE4JP7XRPN3WTB4WKO4L","short_pith_number":"pith:OWLMFDBE","canonical_record":{"source":{"id":"1703.04764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-14T22:15:14Z","cross_cats_sorted":[],"title_canon_sha256":"c0b57e8d4b4f0f72bd647c90b1c44a78a16d3ef6723896289628f15e485e8603","abstract_canon_sha256":"d03cd14bf502c23c5789738421c16e8e65da85df3bbd76af72614655dbfb38bd"},"schema_version":"1.0"},"canonical_sha256":"7596c28c24e25ffbc5eddda61e594ee2de7cc6ce26a4fe496cdcb6371e60a180","source":{"kind":"arxiv","id":"1703.04764","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04764","created_at":"2026-05-18T00:26:30Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04764v1","created_at":"2026-05-18T00:26:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04764","created_at":"2026-05-18T00:26:30Z"},{"alias_kind":"pith_short_12","alias_value":"OWLMFDBE4JP7","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OWLMFDBE4JP7XRPN","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OWLMFDBE","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OWLMFDBE4JP7XRPN3WTB4WKO4L","target":"record","payload":{"canonical_record":{"source":{"id":"1703.04764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-14T22:15:14Z","cross_cats_sorted":[],"title_canon_sha256":"c0b57e8d4b4f0f72bd647c90b1c44a78a16d3ef6723896289628f15e485e8603","abstract_canon_sha256":"d03cd14bf502c23c5789738421c16e8e65da85df3bbd76af72614655dbfb38bd"},"schema_version":"1.0"},"canonical_sha256":"7596c28c24e25ffbc5eddda61e594ee2de7cc6ce26a4fe496cdcb6371e60a180","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:30.362033Z","signature_b64":"OS8vq3F44zhQ/3pXFmWfI/X9HLk2Yrcz3eii/4bmdXw/+mhiNUqTvmDTIOgOKfgtzPD06RHWtJDFvuoU9tDEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7596c28c24e25ffbc5eddda61e594ee2de7cc6ce26a4fe496cdcb6371e60a180","last_reissued_at":"2026-05-18T00:26:30.361420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:30.361420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.04764","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":"2026-05-18T00:26:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4SRCche9fLd5nFpvClxB2vfcMys6fQ9XtUX6uRi+ModfPQ29b32yUMidNRyLWBf0GvyB3dIBwQn0mgX8Po4zAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:06:08.137678Z"},"content_sha256":"059c5ef5ced2c754e2b786b496218045322aac1b51aaa728c475d33f17149ec3","schema_version":"1.0","event_id":"sha256:059c5ef5ced2c754e2b786b496218045322aac1b51aaa728c475d33f17149ec3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OWLMFDBE4JP7XRPN3WTB4WKO4L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parity of Sets of Mutually Orthogonal Latin Squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ian M. Wanless, Nevena Franceti\\'c, Sarada Herke","submitted_at":"2017-03-14T22:15:14Z","abstract_excerpt":"Every Latin square has three attributes that can be even or odd, but any two of these attributes determines the third. Hence the parity of a Latin square has an information content of 2 bits. We extend the definition of parity from Latin squares to sets of mutually orthogonal Latin squares (MOLS) and the corresponding orthogonal arrays (OA). Suppose the parity of an $\\mathrm{OA}(k,n)$ has an information content of $\\dim(k,n)$ bits. We show that $\\dim(k,n) \\leq {k \\choose 2}-1$. For the case corresponding to projective planes we prove a tighter bound, namely $\\dim(n+1,n) \\leq {n \\choose 2}$ whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04764","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":"2026-05-18T00:26:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EYpODmmY2W5fGxHlaQZAPJJYlj2pdV1qGP1NGCX5pbD701KRnSeo9TzMmkE3rvdfzOgzKz6YWniq8BLfdVl4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:06:08.138026Z"},"content_sha256":"17ce04342205f04a4200c5930b98e9fd357edb6891f9c594c6c742f0b398cccd","schema_version":"1.0","event_id":"sha256:17ce04342205f04a4200c5930b98e9fd357edb6891f9c594c6c742f0b398cccd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OWLMFDBE4JP7XRPN3WTB4WKO4L/bundle.json","state_url":"https://pith.science/pith/OWLMFDBE4JP7XRPN3WTB4WKO4L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OWLMFDBE4JP7XRPN3WTB4WKO4L/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":"2026-06-07T02:06:08Z","links":{"resolver":"https://pith.science/pith/OWLMFDBE4JP7XRPN3WTB4WKO4L","bundle":"https://pith.science/pith/OWLMFDBE4JP7XRPN3WTB4WKO4L/bundle.json","state":"https://pith.science/pith/OWLMFDBE4JP7XRPN3WTB4WKO4L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OWLMFDBE4JP7XRPN3WTB4WKO4L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OWLMFDBE4JP7XRPN3WTB4WKO4L","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":"d03cd14bf502c23c5789738421c16e8e65da85df3bbd76af72614655dbfb38bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-14T22:15:14Z","title_canon_sha256":"c0b57e8d4b4f0f72bd647c90b1c44a78a16d3ef6723896289628f15e485e8603"},"schema_version":"1.0","source":{"id":"1703.04764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04764","created_at":"2026-05-18T00:26:30Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04764v1","created_at":"2026-05-18T00:26:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04764","created_at":"2026-05-18T00:26:30Z"},{"alias_kind":"pith_short_12","alias_value":"OWLMFDBE4JP7","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OWLMFDBE4JP7XRPN","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OWLMFDBE","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:17ce04342205f04a4200c5930b98e9fd357edb6891f9c594c6c742f0b398cccd","target":"graph","created_at":"2026-05-18T00:26:30Z","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":"Every Latin square has three attributes that can be even or odd, but any two of these attributes determines the third. Hence the parity of a Latin square has an information content of 2 bits. We extend the definition of parity from Latin squares to sets of mutually orthogonal Latin squares (MOLS) and the corresponding orthogonal arrays (OA). Suppose the parity of an $\\mathrm{OA}(k,n)$ has an information content of $\\dim(k,n)$ bits. We show that $\\dim(k,n) \\leq {k \\choose 2}-1$. For the case corresponding to projective planes we prove a tighter bound, namely $\\dim(n+1,n) \\leq {n \\choose 2}$ whe","authors_text":"Ian M. Wanless, Nevena Franceti\\'c, Sarada Herke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-14T22:15:14Z","title":"Parity of Sets of Mutually Orthogonal Latin Squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04764","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":"sha256:059c5ef5ced2c754e2b786b496218045322aac1b51aaa728c475d33f17149ec3","target":"record","created_at":"2026-05-18T00:26:30Z","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":"d03cd14bf502c23c5789738421c16e8e65da85df3bbd76af72614655dbfb38bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-14T22:15:14Z","title_canon_sha256":"c0b57e8d4b4f0f72bd647c90b1c44a78a16d3ef6723896289628f15e485e8603"},"schema_version":"1.0","source":{"id":"1703.04764","kind":"arxiv","version":1}},"canonical_sha256":"7596c28c24e25ffbc5eddda61e594ee2de7cc6ce26a4fe496cdcb6371e60a180","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7596c28c24e25ffbc5eddda61e594ee2de7cc6ce26a4fe496cdcb6371e60a180","first_computed_at":"2026-05-18T00:26:30.361420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:30.361420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OS8vq3F44zhQ/3pXFmWfI/X9HLk2Yrcz3eii/4bmdXw/+mhiNUqTvmDTIOgOKfgtzPD06RHWtJDFvuoU9tDEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:30.362033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.04764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:059c5ef5ced2c754e2b786b496218045322aac1b51aaa728c475d33f17149ec3","sha256:17ce04342205f04a4200c5930b98e9fd357edb6891f9c594c6c742f0b398cccd"],"state_sha256":"8606505257e754d2645ff15df582a12720808d56de94244e263ed8bed3a6e311"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cK4ZWggd2sRaA5gvPmV+6Lhdb3WzHYJhjPWb27NtDI9pQIR46/4280O63rOmF2AR1c+IwMPpXmfs5fElp2nTBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:06:08.139952Z","bundle_sha256":"25fc4cee47f10800f00f355b8c059733fe37ee4ab4cd44c9d4a1c849533bcf26"}}