{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XV337QQNCO6WHYF62QMTQB6YHD","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":"0e799e2d91dc8122d20aeec2813f7c5d5cbb13a54911c1ac5d091b5b61ee768a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-08-06T08:22:27Z","title_canon_sha256":"3475a871dd03e8c73d1e444e49b99bbf967139b5ab97278b9876903a05ce0723"},"schema_version":"1.0","source":{"id":"1808.01763","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01763","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01763v1","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01763","created_at":"2026-05-18T00:08:49Z"},{"alias_kind":"pith_short_12","alias_value":"XV337QQNCO6W","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XV337QQNCO6WHYF6","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XV337QQN","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:6609da632418da6023a90b0267cdf81e2ded47bc6241fa464283f82d2a0587f3","target":"graph","created_at":"2026-05-18T00:08:49Z","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":"Let $\\gamma$ denote the imaginary parts of complex zeros $\\rho = \\beta+i\\gamma$ of $\\zeta(s)$. The problem of analytic continuation of the function $G(s) := \\sum\\limits_{\\gamma > 0}\\gamma^{-s}$ to the left of the line $\\Re s = -1$ is investigated, and its Laurent expansion at the pole $s=1$ is obtained. Estimates for the second moment on the critical line $\\int_1^T|G(1/2+it)|^2\\,dt$ are revisited. This paper is a continuation of work begun by the second author in 2001.","authors_text":"Aleksandar Ivi\\'c, Andriy Bondarenko, Eero Saksman, Kristian Seip","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-08-06T08:22:27Z","title":"On certain sums over ordinates of zeta-zeros II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01763","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:d97ffd9fd0a9459ec0a48bd3b58f405a2aea1d4d740fd0445b542aa1b833d2d7","target":"record","created_at":"2026-05-18T00:08:49Z","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":"0e799e2d91dc8122d20aeec2813f7c5d5cbb13a54911c1ac5d091b5b61ee768a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-08-06T08:22:27Z","title_canon_sha256":"3475a871dd03e8c73d1e444e49b99bbf967139b5ab97278b9876903a05ce0723"},"schema_version":"1.0","source":{"id":"1808.01763","kind":"arxiv","version":1}},"canonical_sha256":"bd77bfc20d13bd63e0bed4193807d838ecf9b6ab553c9cf42a0a3f4e649ed137","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd77bfc20d13bd63e0bed4193807d838ecf9b6ab553c9cf42a0a3f4e649ed137","first_computed_at":"2026-05-18T00:08:49.704942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:49.704942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F/z+FV5Lc+jGrP6hhvQDQ67iIQrpJv1N24yy6knE2u0BguBKq7c8INqxjdOTgGcrTJtikxvJCE+vTTFq6ebgDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:49.705650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.01763","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d97ffd9fd0a9459ec0a48bd3b58f405a2aea1d4d740fd0445b542aa1b833d2d7","sha256:6609da632418da6023a90b0267cdf81e2ded47bc6241fa464283f82d2a0587f3"],"state_sha256":"075830d7bfc61c35701a1d6c05da8c2dd26a2e10916d675f9ae48631abfde0d0"}