{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:NLJEZ2XLUXC37XMXKAKJW4MS44","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":"4665f36e0cee3c18a181857e4672265ab120fa95df1fa82500cd7b8d54118e5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-11-26T21:46:04Z","title_canon_sha256":"a829241f03b8e8c76eb13c01c2a3589d1a90b74710b7f4ece361387f8d437763"},"schema_version":"1.0","source":{"id":"0811.4437","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.4437","created_at":"2026-05-18T01:02:59Z"},{"alias_kind":"arxiv_version","alias_value":"0811.4437v1","created_at":"2026-05-18T01:02:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.4437","created_at":"2026-05-18T01:02:59Z"},{"alias_kind":"pith_short_12","alias_value":"NLJEZ2XLUXC3","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"NLJEZ2XLUXC37XMX","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"NLJEZ2XL","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:78ef8ff9705ba7d9a1e5ca4e7e90c2d0d5ae9498fa20d7c736c2a5c3226049b9","target":"graph","created_at":"2026-05-18T01:02:59Z","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 study three special Dirichlet series, two of them alternating, related to the Riemann zeta function. These series are shown to have extensions to the entire complex plane and we find their values at the negative integers (or residues at poles). These values are given in terms of Bernoulli and Euler numbers.","authors_text":"H. Gopalkrishna Gadiyar, Khristo N. Boyadzhiev, R. Padma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-11-26T21:46:04Z","title":"Alternating Euler sums at the negative integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.4437","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":"sha256:9189a18743ca63ec3f4bee225b649841fac782eb1b729019b09c4c5e2fff6673","target":"record","created_at":"2026-05-18T01:02:59Z","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":"4665f36e0cee3c18a181857e4672265ab120fa95df1fa82500cd7b8d54118e5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-11-26T21:46:04Z","title_canon_sha256":"a829241f03b8e8c76eb13c01c2a3589d1a90b74710b7f4ece361387f8d437763"},"schema_version":"1.0","source":{"id":"0811.4437","kind":"arxiv","version":1}},"canonical_sha256":"6ad24ceaeba5c5bfdd9750149b7192e720ff80d2bc9bf07e3494727ca3220dca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ad24ceaeba5c5bfdd9750149b7192e720ff80d2bc9bf07e3494727ca3220dca","first_computed_at":"2026-05-18T01:02:59.748628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:59.748628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s5H6ZajnUNKCuJW3VA1MrSapxIie33bBvHTTe9m2tCVXRdroXmtcm7bu6tbafKzU3oK6x2XckgvnognoCl7gAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:59.749407Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.4437","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9189a18743ca63ec3f4bee225b649841fac782eb1b729019b09c4c5e2fff6673","sha256:78ef8ff9705ba7d9a1e5ca4e7e90c2d0d5ae9498fa20d7c736c2a5c3226049b9"],"state_sha256":"251779a54d4e647e46b79882f6dafb285b2172da985d2b1882e6c9cf2d4390d7"}