{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:AJCV4UYWVKDQVSJLF4DLWVTGVT","short_pith_number":"pith:AJCV4UYW","canonical_record":{"source":{"id":"1910.02753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-10-07T12:35:44Z","cross_cats_sorted":[],"title_canon_sha256":"fb0d9b147131d1a0703991a7ee04b28c28057550199d6b09b5eaf99f6f20ac08","abstract_canon_sha256":"63e1e0b919ecb937db7e24649c2a518e21b8f5439e0dda76009bd644d2059ccc"},"schema_version":"1.0"},"canonical_sha256":"02455e5316aa870ac92b2f06bb5666acdd07c29257cc9bbab50d17de2df035f0","source":{"kind":"arxiv","id":"1910.02753","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.02753","created_at":"2026-07-05T00:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1910.02753v1","created_at":"2026-07-05T00:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.02753","created_at":"2026-07-05T00:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"AJCV4UYWVKDQ","created_at":"2026-07-05T00:10:11Z"},{"alias_kind":"pith_short_16","alias_value":"AJCV4UYWVKDQVSJL","created_at":"2026-07-05T00:10:11Z"},{"alias_kind":"pith_short_8","alias_value":"AJCV4UYW","created_at":"2026-07-05T00:10:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:AJCV4UYWVKDQVSJLF4DLWVTGVT","target":"record","payload":{"canonical_record":{"source":{"id":"1910.02753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-10-07T12:35:44Z","cross_cats_sorted":[],"title_canon_sha256":"fb0d9b147131d1a0703991a7ee04b28c28057550199d6b09b5eaf99f6f20ac08","abstract_canon_sha256":"63e1e0b919ecb937db7e24649c2a518e21b8f5439e0dda76009bd644d2059ccc"},"schema_version":"1.0"},"canonical_sha256":"02455e5316aa870ac92b2f06bb5666acdd07c29257cc9bbab50d17de2df035f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:10:11.245569Z","signature_b64":"qtmxq7/2TetMvyyEebDMkcNZE6Og0N1VFlRIY4pHRRwZ3tGHe5FnZsDftTHVxmSs3Xf/VAbRBl3519LNX1F/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02455e5316aa870ac92b2f06bb5666acdd07c29257cc9bbab50d17de2df035f0","last_reissued_at":"2026-07-05T00:10:11.245190Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:10:11.245190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1910.02753","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":"2026-07-05T00:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rKj9zR6Y1TtqimkesZy+Jtgr5dC2cm1nrS3lBLocdcIdoNUvTUoB33538g9uy43/1nVaJDHyg0tuN9rcj5M1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T07:39:27.752102Z"},"content_sha256":"12572d76daca3f3bfe5bf9e4cefaaafca7010cb531ea3fc556642f80bec82819","schema_version":"1.0","event_id":"sha256:12572d76daca3f3bfe5bf9e4cefaaafca7010cb531ea3fc556642f80bec82819"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:AJCV4UYWVKDQVSJLF4DLWVTGVT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enumerating extensions of mutually orthogonal Latin squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shagnik Das, Simona Boyadzhiyska, Tibor Szab\\'o","submitted_at":"2019-10-07T12:35:44Z","abstract_excerpt":"Two $n \\times n$ Latin squares $L_1, L_2$ are said to be orthogonal if, for every ordered pair $(x,y)$ of symbols, there are coordinates $(i,j)$ such that $L_1(i,j) = x$ and $L_2(i,j) = y$. A $k$-MOLS is a sequence of $k$ pairwise-orthogonal Latin squares, and the existence and enumeration of these objects has attracted a great deal of attention.\n  Recent work of Keevash and Luria provides, for all fixed $k$, log-asymptotically tight bounds on the number of $k$-MOLS. To study the situation when $k$ grows with $n$, we bound the number of ways a $k$-MOLS can be extended to a $(k+1)$-MOLS. These "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.02753","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.02753/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pZ3RNCANKJTWyWslq0U8RwCItNEv92KEUld2YWLS47//Wn5gqrX+jqJ3IJaUdAbaPjEk5RSSp1mNwtd0KjoNAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T07:39:27.752637Z"},"content_sha256":"60ff0de5560d1eb5f4a5897ed8cf2833be5e4fea73c43c117141fccd5c55ee17","schema_version":"1.0","event_id":"sha256:60ff0de5560d1eb5f4a5897ed8cf2833be5e4fea73c43c117141fccd5c55ee17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AJCV4UYWVKDQVSJLF4DLWVTGVT/bundle.json","state_url":"https://pith.science/pith/AJCV4UYWVKDQVSJLF4DLWVTGVT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AJCV4UYWVKDQVSJLF4DLWVTGVT/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":"2026-08-05T07:39:27Z","links":{"resolver":"https://pith.science/pith/AJCV4UYWVKDQVSJLF4DLWVTGVT","bundle":"https://pith.science/pith/AJCV4UYWVKDQVSJLF4DLWVTGVT/bundle.json","state":"https://pith.science/pith/AJCV4UYWVKDQVSJLF4DLWVTGVT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AJCV4UYWVKDQVSJLF4DLWVTGVT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AJCV4UYWVKDQVSJLF4DLWVTGVT","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":"63e1e0b919ecb937db7e24649c2a518e21b8f5439e0dda76009bd644d2059ccc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-10-07T12:35:44Z","title_canon_sha256":"fb0d9b147131d1a0703991a7ee04b28c28057550199d6b09b5eaf99f6f20ac08"},"schema_version":"1.0","source":{"id":"1910.02753","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.02753","created_at":"2026-07-05T00:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1910.02753v1","created_at":"2026-07-05T00:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.02753","created_at":"2026-07-05T00:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"AJCV4UYWVKDQ","created_at":"2026-07-05T00:10:11Z"},{"alias_kind":"pith_short_16","alias_value":"AJCV4UYWVKDQVSJL","created_at":"2026-07-05T00:10:11Z"},{"alias_kind":"pith_short_8","alias_value":"AJCV4UYW","created_at":"2026-07-05T00:10:11Z"}],"graph_snapshots":[{"event_id":"sha256:60ff0de5560d1eb5f4a5897ed8cf2833be5e4fea73c43c117141fccd5c55ee17","target":"graph","created_at":"2026-07-05T00:10:11Z","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/1910.02753/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Two $n \\times n$ Latin squares $L_1, L_2$ are said to be orthogonal if, for every ordered pair $(x,y)$ of symbols, there are coordinates $(i,j)$ such that $L_1(i,j) = x$ and $L_2(i,j) = y$. A $k$-MOLS is a sequence of $k$ pairwise-orthogonal Latin squares, and the existence and enumeration of these objects has attracted a great deal of attention.\n  Recent work of Keevash and Luria provides, for all fixed $k$, log-asymptotically tight bounds on the number of $k$-MOLS. To study the situation when $k$ grows with $n$, we bound the number of ways a $k$-MOLS can be extended to a $(k+1)$-MOLS. These ","authors_text":"Shagnik Das, Simona Boyadzhiyska, Tibor Szab\\'o","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-10-07T12:35:44Z","title":"Enumerating extensions of mutually orthogonal Latin squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.02753","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":"sha256:12572d76daca3f3bfe5bf9e4cefaaafca7010cb531ea3fc556642f80bec82819","target":"record","created_at":"2026-07-05T00:10:11Z","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":"63e1e0b919ecb937db7e24649c2a518e21b8f5439e0dda76009bd644d2059ccc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-10-07T12:35:44Z","title_canon_sha256":"fb0d9b147131d1a0703991a7ee04b28c28057550199d6b09b5eaf99f6f20ac08"},"schema_version":"1.0","source":{"id":"1910.02753","kind":"arxiv","version":1}},"canonical_sha256":"02455e5316aa870ac92b2f06bb5666acdd07c29257cc9bbab50d17de2df035f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02455e5316aa870ac92b2f06bb5666acdd07c29257cc9bbab50d17de2df035f0","first_computed_at":"2026-07-05T00:10:11.245190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:10:11.245190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qtmxq7/2TetMvyyEebDMkcNZE6Og0N1VFlRIY4pHRRwZ3tGHe5FnZsDftTHVxmSs3Xf/VAbRBl3519LNX1F/BA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:10:11.245569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.02753","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12572d76daca3f3bfe5bf9e4cefaaafca7010cb531ea3fc556642f80bec82819","sha256:60ff0de5560d1eb5f4a5897ed8cf2833be5e4fea73c43c117141fccd5c55ee17"],"state_sha256":"fe3fe3ff95441abc7e4fd0b48a71868518faf2d5907d6008ccfc9529e5ffad06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fgcLjNWO/Y8GY5wrwqvWtub4EJO8yF8Eieu4XsXYHh/3LVcwdVkPcjJSdni9/nofflVoCQGR/dQE87NsXKVbCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T07:39:27.758065Z","bundle_sha256":"dfd72bc40056b299bd5766e2d3180ea5e3edd47558a09e65864347b0015b06f0"}}