{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:TNI3WN7FPYZPUCTSY5Y3ZR5BUP","short_pith_number":"pith:TNI3WN7F","schema_version":"1.0","canonical_sha256":"9b51bb37e57e32fa0a72c771bcc7a1a3e078369a3b05d0d2eb75aa2585163307","source":{"kind":"arxiv","id":"1401.6588","version":1},"attestation_state":"computed","paper":{"title":"Combinatorial proofs of some Bell number formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mark Shattuck","submitted_at":"2014-01-25T22:27:33Z","abstract_excerpt":"In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further interpretation for a related difference of Catalan numbers in terms of the inclusion-exclusion principle."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.6588","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-25T22:27:33Z","cross_cats_sorted":[],"title_canon_sha256":"8c26da23c3d33745007544dd6cabd0895ee11f7c3ec82b9e7d9a5ab0c0222a89","abstract_canon_sha256":"6247e17cb4158fc9d268b4bdaeae16882f5a4e235231e26ac7d69fbf8ab12d44"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:01.258733Z","signature_b64":"XPxfjESqxqttduW24EFhGl015UMRyKE8YtBwWDzgHrUT3xzi7ZtywqYdcdApPNDDphrdRNml4CJ/N1/AmCLUDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b51bb37e57e32fa0a72c771bcc7a1a3e078369a3b05d0d2eb75aa2585163307","last_reissued_at":"2026-05-18T03:01:01.258055Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:01.258055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial proofs of some Bell number formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mark Shattuck","submitted_at":"2014-01-25T22:27:33Z","abstract_excerpt":"In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further interpretation for a related difference of Catalan numbers in terms of the inclusion-exclusion principle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6588","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1401.6588","created_at":"2026-05-18T03:01:01.258163+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.6588v1","created_at":"2026-05-18T03:01:01.258163+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6588","created_at":"2026-05-18T03:01:01.258163+00:00"},{"alias_kind":"pith_short_12","alias_value":"TNI3WN7FPYZP","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"TNI3WN7FPYZPUCTS","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"TNI3WN7F","created_at":"2026-05-18T12:28:49.207871+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TNI3WN7FPYZPUCTSY5Y3ZR5BUP","json":"https://pith.science/pith/TNI3WN7FPYZPUCTSY5Y3ZR5BUP.json","graph_json":"https://pith.science/api/pith-number/TNI3WN7FPYZPUCTSY5Y3ZR5BUP/graph.json","events_json":"https://pith.science/api/pith-number/TNI3WN7FPYZPUCTSY5Y3ZR5BUP/events.json","paper":"https://pith.science/paper/TNI3WN7F"},"agent_actions":{"view_html":"https://pith.science/pith/TNI3WN7FPYZPUCTSY5Y3ZR5BUP","download_json":"https://pith.science/pith/TNI3WN7FPYZPUCTSY5Y3ZR5BUP.json","view_paper":"https://pith.science/paper/TNI3WN7F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.6588&json=true","fetch_graph":"https://pith.science/api/pith-number/TNI3WN7FPYZPUCTSY5Y3ZR5BUP/graph.json","fetch_events":"https://pith.science/api/pith-number/TNI3WN7FPYZPUCTSY5Y3ZR5BUP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TNI3WN7FPYZPUCTSY5Y3ZR5BUP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TNI3WN7FPYZPUCTSY5Y3ZR5BUP/action/storage_attestation","attest_author":"https://pith.science/pith/TNI3WN7FPYZPUCTSY5Y3ZR5BUP/action/author_attestation","sign_citation":"https://pith.science/pith/TNI3WN7FPYZPUCTSY5Y3ZR5BUP/action/citation_signature","submit_replication":"https://pith.science/pith/TNI3WN7FPYZPUCTSY5Y3ZR5BUP/action/replication_record"}},"created_at":"2026-05-18T03:01:01.258163+00:00","updated_at":"2026-05-18T03:01:01.258163+00:00"}