{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ZMI44WPSX2TVOMWO33NH6A5HME","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":"17b34595c605ea523334baf29e01f65343cd91a17fb6e409a9b2cdb7f4d722c3","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-01-17T06:21:22Z","title_canon_sha256":"ace24101f4b8f5fe26232d2cc90b2969764a89fde06b271bbd416d731d64d9b3"},"schema_version":"1.0","source":{"id":"2401.08997","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.08997","created_at":"2026-07-05T08:03:47Z"},{"alias_kind":"arxiv_version","alias_value":"2401.08997v4","created_at":"2026-07-05T08:03:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.08997","created_at":"2026-07-05T08:03:47Z"},{"alias_kind":"pith_short_12","alias_value":"ZMI44WPSX2TV","created_at":"2026-07-05T08:03:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZMI44WPSX2TVOMWO","created_at":"2026-07-05T08:03:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZMI44WPS","created_at":"2026-07-05T08:03:47Z"}],"graph_snapshots":[{"event_id":"sha256:b8ddd70e623bf087ef4f0b2713dc0666c12d67c059db21af8c60229f86c90261","target":"graph","created_at":"2026-07-05T08:03:47Z","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/2401.08997/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work derives 5 methods to evaluate families of odd zeta values by combining a power of $\\pi$ with Lambert series whose ratios of successive terms tend to $e^{-\\pi\\sqrt{a}}$ with integers $a\\ge7$, outperforming Ramanujan's results with merit $a=4$. Families with $a=7$ and $a=8$ evaluate $\\zeta(2n+1)$. Families with $a=9$ and $a=16$ evaluate $\\zeta(4n+1)$ with faster convergence. A fifth family with $a=12$ evaluates $\\zeta(6n+1)$ and gives the fastest convergence for $\\zeta(6n+7)$. Members of three of the families were discovered empirically by Simon Plouffe. An intensive new search strongl","authors_text":"David Broadhurst","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-01-17T06:21:22Z","title":"Five families of rapidly convergent evaluations of zeta values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.08997","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":"sha256:8b44ef861331788fba5380b651c9b5c4a46c5621b4e443a8037d9bfe36d0400d","target":"record","created_at":"2026-07-05T08:03:47Z","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":"17b34595c605ea523334baf29e01f65343cd91a17fb6e409a9b2cdb7f4d722c3","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-01-17T06:21:22Z","title_canon_sha256":"ace24101f4b8f5fe26232d2cc90b2969764a89fde06b271bbd416d731d64d9b3"},"schema_version":"1.0","source":{"id":"2401.08997","kind":"arxiv","version":4}},"canonical_sha256":"cb11ce59f2bea75732cededa7f03a7610950329d9a4c6a7774f6b355ddf95a6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb11ce59f2bea75732cededa7f03a7610950329d9a4c6a7774f6b355ddf95a6f","first_computed_at":"2026-07-05T08:03:47.979186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:03:47.979186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0CtwJYhy9kWO3+14LI3JmYC1HWtX0KN8tn6B2YAR20mimXVCDKiUtBC0tdPERjkr/5gEMw0mQXf1QMvYkav+DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:03:47.979722Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.08997","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b44ef861331788fba5380b651c9b5c4a46c5621b4e443a8037d9bfe36d0400d","sha256:b8ddd70e623bf087ef4f0b2713dc0666c12d67c059db21af8c60229f86c90261"],"state_sha256":"316780d0aa70387c103165461c4efdff7b04dd340c23ba04b11a291608d17f29"}