{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:DAV7D2H2LCTQ2X6SR5SCHUR5VJ","short_pith_number":"pith:DAV7D2H2","canonical_record":{"source":{"id":"2009.13791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-09-29T05:55:33Z","cross_cats_sorted":[],"title_canon_sha256":"7cdf83003cdb24eeb6a6f53278550b6f37f8edd89f0a39eaeb855650bd2a930a","abstract_canon_sha256":"67956e13f082eb1cbf3fd055311925b3fb14d6f653f2fecc214b6bbbd9c7b04b"},"schema_version":"1.0"},"canonical_sha256":"182bf1e8fa58a70d5fd28f6423d23daa77e025ae8ae5aee99d579984e9c926f1","source":{"kind":"arxiv","id":"2009.13791","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.13791","created_at":"2026-07-05T03:09:27Z"},{"alias_kind":"arxiv_version","alias_value":"2009.13791v1","created_at":"2026-07-05T03:09:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.13791","created_at":"2026-07-05T03:09:27Z"},{"alias_kind":"pith_short_12","alias_value":"DAV7D2H2LCTQ","created_at":"2026-07-05T03:09:27Z"},{"alias_kind":"pith_short_16","alias_value":"DAV7D2H2LCTQ2X6S","created_at":"2026-07-05T03:09:27Z"},{"alias_kind":"pith_short_8","alias_value":"DAV7D2H2","created_at":"2026-07-05T03:09:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:DAV7D2H2LCTQ2X6SR5SCHUR5VJ","target":"record","payload":{"canonical_record":{"source":{"id":"2009.13791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-09-29T05:55:33Z","cross_cats_sorted":[],"title_canon_sha256":"7cdf83003cdb24eeb6a6f53278550b6f37f8edd89f0a39eaeb855650bd2a930a","abstract_canon_sha256":"67956e13f082eb1cbf3fd055311925b3fb14d6f653f2fecc214b6bbbd9c7b04b"},"schema_version":"1.0"},"canonical_sha256":"182bf1e8fa58a70d5fd28f6423d23daa77e025ae8ae5aee99d579984e9c926f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:09:27.564844Z","signature_b64":"DVTx9GgW34H+DBywHN4zGIDu8FDQP7MRZL9PsmFOGONdF+HsvPLyePuZFPOAylzWh8VLN1fAyATHmWE+h2cSAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"182bf1e8fa58a70d5fd28f6423d23daa77e025ae8ae5aee99d579984e9c926f1","last_reissued_at":"2026-07-05T03:09:27.564366Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:09:27.564366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.13791","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:09:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"moBd5YKuSFQ5u/2F+x2qK4Xy06iweWbMtTcA+xauvoxkuhme60S0GBruc1WC9/lWIrp0luM1U+UT8nQ4SXx5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T15:28:04.393782Z"},"content_sha256":"c4007a82064faface500ab6ec2ae4bc1a7fb36ff70dc2fc28f7a845958359433","schema_version":"1.0","event_id":"sha256:c4007a82064faface500ab6ec2ae4bc1a7fb36ff70dc2fc28f7a845958359433"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:DAV7D2H2LCTQ2X6SR5SCHUR5VJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Accurate estimation of sums over zeros of the Riemann zeta-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David J. Platt, Richard P. Brent, Timothy S. Trudgian","submitted_at":"2020-09-29T05:55:33Z","abstract_excerpt":"We consider sums of the form $\\sum \\phi(\\gamma)$, where $\\phi$ is a given function, and $\\gamma$ ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in a given interval. We show how the numerical estimation of such sums can be accelerated by a simple device, and give examples involving both convergent and divergent infinite sums."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.13791","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.13791/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:09:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e6duvFAFSh4/LyLriIqSC5VpAQBMvcODn4iB7mMhkWcJ18Ftymcb+ME7M8Os+RreluuCwl0BzJ0LcdgvjbV/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T15:28:04.394871Z"},"content_sha256":"b72010a68382e71e5ed6e1def73ebf7690ef2bc5fa1aeff421b3d1de080159df","schema_version":"1.0","event_id":"sha256:b72010a68382e71e5ed6e1def73ebf7690ef2bc5fa1aeff421b3d1de080159df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DAV7D2H2LCTQ2X6SR5SCHUR5VJ/bundle.json","state_url":"https://pith.science/pith/DAV7D2H2LCTQ2X6SR5SCHUR5VJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DAV7D2H2LCTQ2X6SR5SCHUR5VJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-11T15:28:04Z","links":{"resolver":"https://pith.science/pith/DAV7D2H2LCTQ2X6SR5SCHUR5VJ","bundle":"https://pith.science/pith/DAV7D2H2LCTQ2X6SR5SCHUR5VJ/bundle.json","state":"https://pith.science/pith/DAV7D2H2LCTQ2X6SR5SCHUR5VJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DAV7D2H2LCTQ2X6SR5SCHUR5VJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:DAV7D2H2LCTQ2X6SR5SCHUR5VJ","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":"67956e13f082eb1cbf3fd055311925b3fb14d6f653f2fecc214b6bbbd9c7b04b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-09-29T05:55:33Z","title_canon_sha256":"7cdf83003cdb24eeb6a6f53278550b6f37f8edd89f0a39eaeb855650bd2a930a"},"schema_version":"1.0","source":{"id":"2009.13791","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.13791","created_at":"2026-07-05T03:09:27Z"},{"alias_kind":"arxiv_version","alias_value":"2009.13791v1","created_at":"2026-07-05T03:09:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.13791","created_at":"2026-07-05T03:09:27Z"},{"alias_kind":"pith_short_12","alias_value":"DAV7D2H2LCTQ","created_at":"2026-07-05T03:09:27Z"},{"alias_kind":"pith_short_16","alias_value":"DAV7D2H2LCTQ2X6S","created_at":"2026-07-05T03:09:27Z"},{"alias_kind":"pith_short_8","alias_value":"DAV7D2H2","created_at":"2026-07-05T03:09:27Z"}],"graph_snapshots":[{"event_id":"sha256:b72010a68382e71e5ed6e1def73ebf7690ef2bc5fa1aeff421b3d1de080159df","target":"graph","created_at":"2026-07-05T03:09:27Z","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/2009.13791/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider sums of the form $\\sum \\phi(\\gamma)$, where $\\phi$ is a given function, and $\\gamma$ ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in a given interval. We show how the numerical estimation of such sums can be accelerated by a simple device, and give examples involving both convergent and divergent infinite sums.","authors_text":"David J. Platt, Richard P. Brent, Timothy S. Trudgian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-09-29T05:55:33Z","title":"Accurate estimation of sums over zeros of the Riemann zeta-function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.13791","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:c4007a82064faface500ab6ec2ae4bc1a7fb36ff70dc2fc28f7a845958359433","target":"record","created_at":"2026-07-05T03:09:27Z","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":"67956e13f082eb1cbf3fd055311925b3fb14d6f653f2fecc214b6bbbd9c7b04b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-09-29T05:55:33Z","title_canon_sha256":"7cdf83003cdb24eeb6a6f53278550b6f37f8edd89f0a39eaeb855650bd2a930a"},"schema_version":"1.0","source":{"id":"2009.13791","kind":"arxiv","version":1}},"canonical_sha256":"182bf1e8fa58a70d5fd28f6423d23daa77e025ae8ae5aee99d579984e9c926f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"182bf1e8fa58a70d5fd28f6423d23daa77e025ae8ae5aee99d579984e9c926f1","first_computed_at":"2026-07-05T03:09:27.564366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:09:27.564366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DVTx9GgW34H+DBywHN4zGIDu8FDQP7MRZL9PsmFOGONdF+HsvPLyePuZFPOAylzWh8VLN1fAyATHmWE+h2cSAw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:09:27.564844Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.13791","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4007a82064faface500ab6ec2ae4bc1a7fb36ff70dc2fc28f7a845958359433","sha256:b72010a68382e71e5ed6e1def73ebf7690ef2bc5fa1aeff421b3d1de080159df"],"state_sha256":"fa2fec1f437ff1e288ee5d714321d1c67765f83b78e3e6e437e331143f03cf17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"344HrIYv/WasJdiQ3wgBZ/cT03d/LqApmCXZREDZQuXJKsfLVRaf5n7SLuh+hYFDeXld6KdHeHfyQWdS308BDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T15:28:04.402287Z","bundle_sha256":"c5fa5e4dcb81c600e26bd975bb939ac9d8c3167471bc8ba88b9e2cd328b6d897"}}