{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:XPD5NW7ELWDD3EINQ5WUOBKYQX","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":"4e3e41bc37d3003bab8a275d975173a60b80f69543d6c8619b57e14f567dfdba","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2003-12-16T07:44:37Z","title_canon_sha256":"7db352a0cc6789c96b563c4c91e92acfad3a56445515ea6480f8ec1756dc948b"},"schema_version":"1.0","source":{"id":"math/0312303","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0312303","created_at":"2026-07-04T14:38:05Z"},{"alias_kind":"arxiv_version","alias_value":"math/0312303v1","created_at":"2026-07-04T14:38:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0312303","created_at":"2026-07-04T14:38:05Z"},{"alias_kind":"pith_short_12","alias_value":"XPD5NW7ELWDD","created_at":"2026-07-04T14:38:05Z"},{"alias_kind":"pith_short_16","alias_value":"XPD5NW7ELWDD3EIN","created_at":"2026-07-04T14:38:05Z"},{"alias_kind":"pith_short_8","alias_value":"XPD5NW7E","created_at":"2026-07-04T14:38:05Z"}],"graph_snapshots":[{"event_id":"sha256:e60ae94cfccea14b4df731f8c2982919226ca5b015c82f4b44c88683c75640cf","target":"graph","created_at":"2026-07-04T14:38:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0312303/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\gamma$ denote imaginary parts of complex zeros of the Riemann zeta-function $\\zeta(s)$. Certain sums over the $\\gamma$'s are evaluated, by using the function $G(s) = \\sum_{\\gamma>0}\\gamma^{-s}$ and other techniques. Some integrals involving the function $S(T) = (1/\\pi)\\arg\\zeta(1/2+iT)$ are also considered.","authors_text":"Aleksandar Ivi\\'c","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2003-12-16T07:44:37Z","title":"On certain sums over ordinates of zeta zeros"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0312303","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":"sha256:509f890b81ee3ccf56c51e4ed8662031625675d72f2865a725046f63ed76e141","target":"record","created_at":"2026-07-04T14:38:05Z","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":"4e3e41bc37d3003bab8a275d975173a60b80f69543d6c8619b57e14f567dfdba","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2003-12-16T07:44:37Z","title_canon_sha256":"7db352a0cc6789c96b563c4c91e92acfad3a56445515ea6480f8ec1756dc948b"},"schema_version":"1.0","source":{"id":"math/0312303","kind":"arxiv","version":1}},"canonical_sha256":"bbc7d6dbe45d863d910d876d47055885e63251fff66747779af1e8e02f54760c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbc7d6dbe45d863d910d876d47055885e63251fff66747779af1e8e02f54760c","first_computed_at":"2026-07-04T14:38:05.851005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:38:05.851005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dMjzcRS7ehwWhAcQ0t9HQJVLgBzFvrjTpNz8HmpY1QExMHMBdZCQMy9wiGzAj/FHr1y/2kIDVH8nJqtCg2MnCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:38:05.851381Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0312303","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:509f890b81ee3ccf56c51e4ed8662031625675d72f2865a725046f63ed76e141","sha256:e60ae94cfccea14b4df731f8c2982919226ca5b015c82f4b44c88683c75640cf"],"state_sha256":"94918edeb23e9e3f8928bbbf68d4decce7a92ee6065c087d024f8b3821f82484"}