{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:3SKLWKSCJ6QA6HGXQXKHOW3ICU","short_pith_number":"pith:3SKLWKSC","canonical_record":{"source":{"id":"1802.01244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-05T02:57:52Z","cross_cats_sorted":[],"title_canon_sha256":"a707664639f398a0349803f730e747367a7b11fb570727352218a55717856ace","abstract_canon_sha256":"468b1888b2f2c402cf853252a60d5df5dc0b88095264de5a2320e0511d3b1d9c"},"schema_version":"1.0"},"canonical_sha256":"dc94bb2a424fa00f1cd785d4775b681502ee59a62077daa8b35de1de8af49b9d","source":{"kind":"arxiv","id":"1802.01244","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.01244","created_at":"2026-05-18T00:24:26Z"},{"alias_kind":"arxiv_version","alias_value":"1802.01244v1","created_at":"2026-05-18T00:24:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01244","created_at":"2026-05-18T00:24:26Z"},{"alias_kind":"pith_short_12","alias_value":"3SKLWKSCJ6QA","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"3SKLWKSCJ6QA6HGX","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"3SKLWKSC","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:3SKLWKSCJ6QA6HGXQXKHOW3ICU","target":"record","payload":{"canonical_record":{"source":{"id":"1802.01244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-05T02:57:52Z","cross_cats_sorted":[],"title_canon_sha256":"a707664639f398a0349803f730e747367a7b11fb570727352218a55717856ace","abstract_canon_sha256":"468b1888b2f2c402cf853252a60d5df5dc0b88095264de5a2320e0511d3b1d9c"},"schema_version":"1.0"},"canonical_sha256":"dc94bb2a424fa00f1cd785d4775b681502ee59a62077daa8b35de1de8af49b9d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:26.959654Z","signature_b64":"pqkWIY0pCF6XkpMZt7Zq0Kvmf/eYfsFJ3WzK8+w7eSryCOMMuvNp1dVbdSbPI1vBHz0j2MLqKCx5VRhxJWvnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc94bb2a424fa00f1cd785d4775b681502ee59a62077daa8b35de1de8af49b9d","last_reissued_at":"2026-05-18T00:24:26.958923Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:26.958923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.01244","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":"2026-05-18T00:24:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7WjYnwvfUs9qqnOthtlcZmrmDWvJPecZKL+bTFIWV5mzLGRZbgE/39tcV1ep2UyBK5WlYLiHxJPgbt6pIGJDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:15:38.427414Z"},"content_sha256":"93fb82228e00cdd12dd13bf84c6a87fc333a848c3454aa9eb1d804a18da40ec6","schema_version":"1.0","event_id":"sha256:93fb82228e00cdd12dd13bf84c6a87fc333a848c3454aa9eb1d804a18da40ec6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:3SKLWKSCJ6QA6HGXQXKHOW3ICU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some identities involving special numbers and moments of random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dae San Kim, Hyuck-In Kwon, Taekyun Kim, Yonghong Yao","submitted_at":"2018-02-05T02:57:52Z","abstract_excerpt":"In this paper, we derive some identities involving special numbers and moments of random variables by using the generating functions of the moments of certain random variables. Here the related special numbers are Stirling numbers of the first and second kinds, degenerate Stirling numbers of the first and second kinds, derangement numbers, higher-order Bernoulli numbers and Bernoulli numbers of the second kind."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01244","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"21EwLDYoA3c2wzr/8ch2bMai/gw7vrKfR1RXwbkbqcNg6n6vc2Qhe1vw2bjeRvrBDxhLzOcMKmMwl/WEmDTKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:15:38.427755Z"},"content_sha256":"e67a1a3501439a04eaf6ebd5665fd916b1b9e1b23473f78d259e997e09054f21","schema_version":"1.0","event_id":"sha256:e67a1a3501439a04eaf6ebd5665fd916b1b9e1b23473f78d259e997e09054f21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3SKLWKSCJ6QA6HGXQXKHOW3ICU/bundle.json","state_url":"https://pith.science/pith/3SKLWKSCJ6QA6HGXQXKHOW3ICU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3SKLWKSCJ6QA6HGXQXKHOW3ICU/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":"2026-06-03T08:15:38Z","links":{"resolver":"https://pith.science/pith/3SKLWKSCJ6QA6HGXQXKHOW3ICU","bundle":"https://pith.science/pith/3SKLWKSCJ6QA6HGXQXKHOW3ICU/bundle.json","state":"https://pith.science/pith/3SKLWKSCJ6QA6HGXQXKHOW3ICU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3SKLWKSCJ6QA6HGXQXKHOW3ICU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3SKLWKSCJ6QA6HGXQXKHOW3ICU","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":"468b1888b2f2c402cf853252a60d5df5dc0b88095264de5a2320e0511d3b1d9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-05T02:57:52Z","title_canon_sha256":"a707664639f398a0349803f730e747367a7b11fb570727352218a55717856ace"},"schema_version":"1.0","source":{"id":"1802.01244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.01244","created_at":"2026-05-18T00:24:26Z"},{"alias_kind":"arxiv_version","alias_value":"1802.01244v1","created_at":"2026-05-18T00:24:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01244","created_at":"2026-05-18T00:24:26Z"},{"alias_kind":"pith_short_12","alias_value":"3SKLWKSCJ6QA","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"3SKLWKSCJ6QA6HGX","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"3SKLWKSC","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:e67a1a3501439a04eaf6ebd5665fd916b1b9e1b23473f78d259e997e09054f21","target":"graph","created_at":"2026-05-18T00:24:26Z","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 this paper, we derive some identities involving special numbers and moments of random variables by using the generating functions of the moments of certain random variables. Here the related special numbers are Stirling numbers of the first and second kinds, degenerate Stirling numbers of the first and second kinds, derangement numbers, higher-order Bernoulli numbers and Bernoulli numbers of the second kind.","authors_text":"Dae San Kim, Hyuck-In Kwon, Taekyun Kim, Yonghong Yao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-05T02:57:52Z","title":"Some identities involving special numbers and moments of random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01244","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":"sha256:93fb82228e00cdd12dd13bf84c6a87fc333a848c3454aa9eb1d804a18da40ec6","target":"record","created_at":"2026-05-18T00:24:26Z","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":"468b1888b2f2c402cf853252a60d5df5dc0b88095264de5a2320e0511d3b1d9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-02-05T02:57:52Z","title_canon_sha256":"a707664639f398a0349803f730e747367a7b11fb570727352218a55717856ace"},"schema_version":"1.0","source":{"id":"1802.01244","kind":"arxiv","version":1}},"canonical_sha256":"dc94bb2a424fa00f1cd785d4775b681502ee59a62077daa8b35de1de8af49b9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc94bb2a424fa00f1cd785d4775b681502ee59a62077daa8b35de1de8af49b9d","first_computed_at":"2026-05-18T00:24:26.958923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:26.958923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pqkWIY0pCF6XkpMZt7Zq0Kvmf/eYfsFJ3WzK8+w7eSryCOMMuvNp1dVbdSbPI1vBHz0j2MLqKCx5VRhxJWvnCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:26.959654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.01244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93fb82228e00cdd12dd13bf84c6a87fc333a848c3454aa9eb1d804a18da40ec6","sha256:e67a1a3501439a04eaf6ebd5665fd916b1b9e1b23473f78d259e997e09054f21"],"state_sha256":"05019da3b823289c9958fa8f0c1024a3763294b6c4d9546d13152acbcde34d07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oU9ZIB7MM/rc/EB8uyKBzBUONDdj0icxnYL7210xUNgmSkQU/y6Y7PdQopcG+Whw3V0jXez0hA3pcAmZu3IEDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:15:38.429964Z","bundle_sha256":"c15fa253a9786f44172d47e7a1e58d154ff5f8510b47e016c8283586a2c82c7a"}}