{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6GK5FYRUV5O3RC7CTFVNLFMVSQ","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":"cb17e2cea8cf9d45cfdd80ee56e4c60910ad658bc16fe3f22abfd8165b39efc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-13T00:47:26Z","title_canon_sha256":"4ebbb542c312eade07a49d5927ca1c6c209418e5eef11792bcde0d760ca88ab7"},"schema_version":"1.0","source":{"id":"1903.05270","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.05270","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1903.05270v1","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05270","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"6GK5FYRUV5O3","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6GK5FYRUV5O3RC7C","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6GK5FYRU","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:fc452245b0225e684107c28ef1cdac64b872bc6b8735b35300a2cdb656efc6f4","target":"graph","created_at":"2026-05-17T23:51:24Z","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 present a symbolic representation for the poly-Bernoulli numbers. This allows us to prove several new iterated integral representations for the poly-Bernoulli numbers, including an integral transform of the Bernoulli-Barnes numbers. We also deduce some new recurrences for the poly-Bernoulli numbers. Finally, we use these results to present a new iterated integral representation for the Arakawa-Kaneko zeta function, including a nonlinear integral transform of the Barnes zeta function.","authors_text":"C. Vignat, T. Wakhare","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-13T00:47:26Z","title":"A symbolic approach to the poly-Bernoulli numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05270","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":"sha256:88c30d1af96520830127bc7685686f4da510e3f4fb343b073133023e84afbb0b","target":"record","created_at":"2026-05-17T23:51:24Z","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":"cb17e2cea8cf9d45cfdd80ee56e4c60910ad658bc16fe3f22abfd8165b39efc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-13T00:47:26Z","title_canon_sha256":"4ebbb542c312eade07a49d5927ca1c6c209418e5eef11792bcde0d760ca88ab7"},"schema_version":"1.0","source":{"id":"1903.05270","kind":"arxiv","version":1}},"canonical_sha256":"f195d2e234af5db88be2996ad59595942329c67c3b65572236404cce95fe071a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f195d2e234af5db88be2996ad59595942329c67c3b65572236404cce95fe071a","first_computed_at":"2026-05-17T23:51:24.841871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:24.841871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mcOMotcvECGqQBhkFFtQrjCbD0dfXXPslvCJM+dBnd2iQxwi0/K+D3jBbpLrRAlJSa9sOYRBT+jGtLAHGbPcBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:24.842477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.05270","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88c30d1af96520830127bc7685686f4da510e3f4fb343b073133023e84afbb0b","sha256:fc452245b0225e684107c28ef1cdac64b872bc6b8735b35300a2cdb656efc6f4"],"state_sha256":"92aa00574daf51b4cea15246ac44638b4da0448481ecde678d1c281f435bf679"}