{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SG63FWEVWJ5C7HSLFTVEUUHXCG","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":"6916d05a1af0ceb6f4b98fdcdc0664b5c99f5bf5b5b57b4fd6d1fc3ffc4c1236","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-11T11:59:36Z","title_canon_sha256":"1126d41fbe6334ff154f36b3d32aa90539621106b321258ecb6b50b97fc8afba"},"schema_version":"1.0","source":{"id":"1804.03949","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03949","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03949v1","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03949","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"pith_short_12","alias_value":"SG63FWEVWJ5C","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SG63FWEVWJ5C7HSL","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SG63FWEV","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:7d3ea0eaaa0dfafae8c77facf99d2e3c1fdeddd2a6e454625ab4edfea485f9df","target":"graph","created_at":"2026-05-18T00:18:42Z","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":"In the paper, the authors present several new relations and applications for the combinatorial sequence that counts the possible partitions of a finite set with the restriction that the size of each block is contained in a given set. One of the main applications is in the study of lonesum matrices.","authors_text":"Be\\'ata B\\'enyi, Jos\\'e L. Ram\\'irez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-11T11:59:36Z","title":"Some Applications of $S$-restricted Set Partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03949","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":"sha256:9ed956e5e440af84f2e265e39e1310ef4a9b7b9f768f3c0b970ac5d3fddc716a","target":"record","created_at":"2026-05-18T00:18:42Z","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":"6916d05a1af0ceb6f4b98fdcdc0664b5c99f5bf5b5b57b4fd6d1fc3ffc4c1236","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-11T11:59:36Z","title_canon_sha256":"1126d41fbe6334ff154f36b3d32aa90539621106b321258ecb6b50b97fc8afba"},"schema_version":"1.0","source":{"id":"1804.03949","kind":"arxiv","version":1}},"canonical_sha256":"91bdb2d895b27a2f9e4b2cea4a50f711a91c142f4ba6727a42439276a260b119","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91bdb2d895b27a2f9e4b2cea4a50f711a91c142f4ba6727a42439276a260b119","first_computed_at":"2026-05-18T00:18:42.595397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:42.595397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+fCc1PTZ2K29KSq3mBSTntnToz8rVE71/Z9fJXf+FG/7lfUA3kNkSdP38fPNeYMeEpGWxfcwEK0cicnF1osWDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:42.596104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03949","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ed956e5e440af84f2e265e39e1310ef4a9b7b9f768f3c0b970ac5d3fddc716a","sha256:7d3ea0eaaa0dfafae8c77facf99d2e3c1fdeddd2a6e454625ab4edfea485f9df"],"state_sha256":"704853eb9fefb589e893859364d655e75b3ac83a94c8149d50e9c1a87aea768e"}