{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:L7VXGWSMGBPDYVY3FKTA2ZTXHB","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":"c067e21857a6b1f3bc2855ecbc414012bbbf0d8d455e11645e18f07afc8c106d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-14T23:14:30Z","title_canon_sha256":"d84047f2c16e51354821888cd08653755599aa60fae903ea5d00d763a73f851e"},"schema_version":"1.0","source":{"id":"1508.03673","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03673","created_at":"2026-05-18T00:47:15Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03673v2","created_at":"2026-05-18T00:47:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03673","created_at":"2026-05-18T00:47:15Z"},{"alias_kind":"pith_short_12","alias_value":"L7VXGWSMGBPD","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"L7VXGWSMGBPDYVY3","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"L7VXGWSM","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:35549a2992c297f6d4a88de89d36608ae4a580b8d1fbe87ee734d4063d6db1ce","target":"graph","created_at":"2026-05-18T00:47:15Z","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 consider a generalization of Eulerian numbers which count the number of placements of $cn$ \"rooks\" on an $n\\times n$ board where there are exactly $c$ rooks in each row and each column, and exactly $k$ rooks below the main diagonal. The standard Eulerian numbers correspond to the case $c=1$. We show that for any $c$ the resulting numbers are symmetric and give generating functions of these numbers for small values of $k$.","authors_text":"Christopher Cox, Esther Banaian, Jacob Landgraf, Jeffrey Davis, Scarlitte Ponce, Steve Butler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-14T23:14:30Z","title":"A generalization of Eulerian numbers via rook placements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03673","kind":"arxiv","version":2},"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":"sha256:902ad8ae9526cdc799278b2f779577570e6d4afc087da907b2968031ec684155","target":"record","created_at":"2026-05-18T00:47:15Z","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":"c067e21857a6b1f3bc2855ecbc414012bbbf0d8d455e11645e18f07afc8c106d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-14T23:14:30Z","title_canon_sha256":"d84047f2c16e51354821888cd08653755599aa60fae903ea5d00d763a73f851e"},"schema_version":"1.0","source":{"id":"1508.03673","kind":"arxiv","version":2}},"canonical_sha256":"5feb735a4c305e3c571b2aa60d6677385c959a9d42e04946bb9d3a2c0b0217dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5feb735a4c305e3c571b2aa60d6677385c959a9d42e04946bb9d3a2c0b0217dd","first_computed_at":"2026-05-18T00:47:15.833939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:15.833939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sS9VStJy1BKqGJ1H75JEYPU7Ox2er6ZwZuAoy40sPDgs1D+rtZlhXgDNsZDiBjzr+KF3gggH6ddfisqQIyqjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:15.834536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03673","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:902ad8ae9526cdc799278b2f779577570e6d4afc087da907b2968031ec684155","sha256:35549a2992c297f6d4a88de89d36608ae4a580b8d1fbe87ee734d4063d6db1ce"],"state_sha256":"86d0cde097aff163244358722aa185df2006569582cb174bd0920f296b57b2ed"}