{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SRRIFIVJOGOG5K7ZRPUAZKKGB3","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":"4b5616f0542a53bde2a2bcc2eae4e82c5de902cb21bcfd4f025c2d88ad3c20b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-12-09T00:38:36Z","title_canon_sha256":"498f26ca70ce67aa9fce80311bccd2f34d67394f9fc29e11d8520ad493958afc"},"schema_version":"1.0","source":{"id":"1612.04365","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04365","created_at":"2026-05-18T00:55:04Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04365v1","created_at":"2026-05-18T00:55:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04365","created_at":"2026-05-18T00:55:04Z"},{"alias_kind":"pith_short_12","alias_value":"SRRIFIVJOGOG","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SRRIFIVJOGOG5K7Z","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SRRIFIVJ","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:6074421fe17db2e64dad037c222672fde7bfc6982bcc5d5f7d36e5169fcf4fa0","target":"graph","created_at":"2026-05-18T00:55:04Z","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 note we compare two formulas for the higher order derivatives of the function 1/(exp(x) -1). We also provide an integral representation for these derivatives and obtain a classical formula relating zeta values and Bernoulli numbers.","authors_text":"Ada, Khristo N. Boyadzhiev (Department of Mathematics, OH), Ohio Northern University, Statistics","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-12-09T00:38:36Z","title":"A note on the higher derivatives of the function 1/(exp(x) - 1)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04365","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":"sha256:575ce20e173f56115055211e64aa7ad192a7c818113464d09e9a595c70fc1e57","target":"record","created_at":"2026-05-18T00:55:04Z","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":"4b5616f0542a53bde2a2bcc2eae4e82c5de902cb21bcfd4f025c2d88ad3c20b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-12-09T00:38:36Z","title_canon_sha256":"498f26ca70ce67aa9fce80311bccd2f34d67394f9fc29e11d8520ad493958afc"},"schema_version":"1.0","source":{"id":"1612.04365","kind":"arxiv","version":1}},"canonical_sha256":"946282a2a9719c6eabf98be80ca9460ed5a077f18869c440b854949f255ee9ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"946282a2a9719c6eabf98be80ca9460ed5a077f18869c440b854949f255ee9ee","first_computed_at":"2026-05-18T00:55:04.715168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:04.715168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XSuchFWQxTP3kCP0nMWINlhbdOm6vXzqba150ASW7p+2aheleMz3jBGnwzi62mr23DB2mK6GcGjhFZzOHMgKBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:04.715670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04365","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:575ce20e173f56115055211e64aa7ad192a7c818113464d09e9a595c70fc1e57","sha256:6074421fe17db2e64dad037c222672fde7bfc6982bcc5d5f7d36e5169fcf4fa0"],"state_sha256":"becbd3f4c263396cb53112d633ab93ef62f67039ae4df71b58f4302fbad0bbab"}