{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZNESZTNKFGY2QAMUEL4MJP7BJW","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":"cb780fe54b6cecbe87ce97faaca6755fe508f71a0ebfeaa4b8bcb9f3aca02235","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-04T11:13:16Z","title_canon_sha256":"5f22230833ffc62280a59919f1ec798895eaa089c181d18a0fa70653179f7582"},"schema_version":"1.0","source":{"id":"1410.1038","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1038","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1038v1","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1038","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZNESZTNKFGY2","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZNESZTNKFGY2QAMU","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZNESZTNK","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:22c26e09c261fef03fbcdc24cd945cb92065a1392c46cc4b6f1d27581dbf6ab1","target":"graph","created_at":"2026-05-18T01:06:23Z","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":"The current paper deals with the enumeration and classification of the set $\\mathcal{SOR}_{r,n}$ of self-orthogonal $r\\times r$ partial Latin rectangles based on $n$ symbols. These combinatorial objects are identified with the independent sets of a Hamming graph and with the zeros of a radical zero-dimensional ideal of polynomials, whose reduced Gr\\\"obner basis and Hilbert series can be computed to determine explicitly the set $\\mathcal{SOR}_{r,n}$. In particular, the cardinality of this set is shown for $r\\leq 4$ and $n\\leq 9$ and several formulas on the cardinality of $\\mathcal{SOR}_{r,n}$ a","authors_text":"Ra\\'ul M. Falc\\'on","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-04T11:13:16Z","title":"Enumeration and classification of self-orthogonal partial Latin rectangles by using the polynomial method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1038","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:c4bc301b9a46181b50ebd42392cb77c0dbc08789686ed5803647dfc33ef6e863","target":"record","created_at":"2026-05-18T01:06:23Z","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":"cb780fe54b6cecbe87ce97faaca6755fe508f71a0ebfeaa4b8bcb9f3aca02235","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-04T11:13:16Z","title_canon_sha256":"5f22230833ffc62280a59919f1ec798895eaa089c181d18a0fa70653179f7582"},"schema_version":"1.0","source":{"id":"1410.1038","kind":"arxiv","version":1}},"canonical_sha256":"cb492ccdaa29b1a8019422f8c4bfe14da774185200e91bcb1bc9b59a5cccc634","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb492ccdaa29b1a8019422f8c4bfe14da774185200e91bcb1bc9b59a5cccc634","first_computed_at":"2026-05-18T01:06:23.113047Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:23.113047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L+IrZ783ZL9OFcZGGPfcPAWEbkqogaZsnKQR98r/WB3lJM3hMoRHvSMSCIxabkPD40divELGAQGXHqSws/1UCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:23.113762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.1038","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4bc301b9a46181b50ebd42392cb77c0dbc08789686ed5803647dfc33ef6e863","sha256:22c26e09c261fef03fbcdc24cd945cb92065a1392c46cc4b6f1d27581dbf6ab1"],"state_sha256":"ae27e681cf6cbbd9f2b59f050b1a942b4547549c8a2c6e0084bb5e6577299db1"}