{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:KYZO2NAADAVLMXUJDZR32TAV4B","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":"8fc1259be7ed1828732c1400ac3452b324b74a66c6333f7bf662dedbc5778f0b","cross_cats_sorted":["cs.NA","math.NA","math.NT"],"license":"","primary_cat":"math.CA","submitted_at":"2007-02-09T15:23:06Z","title_canon_sha256":"c6d812a53d8f571c7c9169a2a4d324d047f111809a62daa3a730a59a18be3de1"},"schema_version":"1.0","source":{"id":"math/0702243","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702243","created_at":"2026-06-03T22:06:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702243v4","created_at":"2026-06-03T22:06:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702243","created_at":"2026-06-03T22:06:22Z"},{"alias_kind":"pith_short_12","alias_value":"KYZO2NAADAVL","created_at":"2026-06-03T22:06:22Z"},{"alias_kind":"pith_short_16","alias_value":"KYZO2NAADAVLMXUJ","created_at":"2026-06-03T22:06:22Z"},{"alias_kind":"pith_short_8","alias_value":"KYZO2NAA","created_at":"2026-06-03T22:06:22Z"}],"graph_snapshots":[{"event_id":"sha256:51ce38866bad7eee7d173bb4989e1b36b53307fc6e68428d8d084c098e97eed8","target":"graph","created_at":"2026-06-03T22:06:22Z","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/0702243/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper sketches a technique for improving the rate of convergence of a general oscillatory sequence, and then applies this series acceleration algorithm to the polylogarithm and the Hurwitz zeta function. As such, it may be taken as an extension of the techniques given by Borwein's \"An efficient algorithm for computing the Riemann zeta function\", to more general series. The algorithm provides a rapid means of evaluating Li_s(z) for general values of complex s and the region of complex z values given by |z^2/(z-1)|<4.\n  Alternatively, the Hurwitz zeta can be very rapidly evaluated by means ","authors_text":"Linas Vepstas","cross_cats":["cs.NA","math.NA","math.NT"],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2007-02-09T15:23:06Z","title":"An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702243","kind":"arxiv","version":4},"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:bb2eefa9320ec3cc898c815bf578f506800863fb711dbd7cdcc6eaa93a97772b","target":"record","created_at":"2026-06-03T22:06:22Z","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":"8fc1259be7ed1828732c1400ac3452b324b74a66c6333f7bf662dedbc5778f0b","cross_cats_sorted":["cs.NA","math.NA","math.NT"],"license":"","primary_cat":"math.CA","submitted_at":"2007-02-09T15:23:06Z","title_canon_sha256":"c6d812a53d8f571c7c9169a2a4d324d047f111809a62daa3a730a59a18be3de1"},"schema_version":"1.0","source":{"id":"math/0702243","kind":"arxiv","version":4}},"canonical_sha256":"5632ed3400182ab65e891e63bd4c15e067c629604656d0ebe8705838cd4a5b59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5632ed3400182ab65e891e63bd4c15e067c629604656d0ebe8705838cd4a5b59","first_computed_at":"2026-06-03T22:06:22.022973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:22.022973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kmqkvvjM6YNlAr2aRPyZGDeLXETrB1bTqp0mKebU46OdwcFXGcZsGCIKBMVjvnW7PvDGp0eDfSQDizIIXYfsDA==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:22.023389Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0702243","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb2eefa9320ec3cc898c815bf578f506800863fb711dbd7cdcc6eaa93a97772b","sha256:51ce38866bad7eee7d173bb4989e1b36b53307fc6e68428d8d084c098e97eed8"],"state_sha256":"d5c4c7015f2f6781b531439a96e893b59e9190caa5543d336cfb1602f9de4197"}