{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:WZ5UAQO765ZFTAKXQP3MWLWFCE","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":"646e2a13f2aac7ab6b439b985de02bd749b91726f17400d1d907dfd491c377e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-04-20T08:30:27Z","title_canon_sha256":"1f700198f625af1d9c1abb7a6d6442ad0bd2c47ec41e41571947ff2129e03cd7"},"schema_version":"1.0","source":{"id":"2004.10086","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.10086","created_at":"2026-07-05T00:56:57Z"},{"alias_kind":"arxiv_version","alias_value":"2004.10086v1","created_at":"2026-07-05T00:56:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.10086","created_at":"2026-07-05T00:56:57Z"},{"alias_kind":"pith_short_12","alias_value":"WZ5UAQO765ZF","created_at":"2026-07-05T00:56:57Z"},{"alias_kind":"pith_short_16","alias_value":"WZ5UAQO765ZFTAKX","created_at":"2026-07-05T00:56:57Z"},{"alias_kind":"pith_short_8","alias_value":"WZ5UAQO7","created_at":"2026-07-05T00:56:57Z"}],"graph_snapshots":[{"event_id":"sha256:e43de4f35107ca6c55c52370bcba5201f9cc5e6c529e58a0f500e3c44d896a5f","target":"graph","created_at":"2026-07-05T00:56:57Z","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/2004.10086/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a Vasyunin-type formula for an autocorrelation function arising from a Nyman-Beurling criterion generalized to a probabilistic framework. This formula can also be seen as a reciprocity formula for cotangent sums, related to the ones proven in [BC13], [ABB17].","authors_text":"Erwan Hillion, S\\'ebastien Darses","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-04-20T08:30:27Z","title":"An exponentially averaged Vasyunin formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.10086","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":"sha256:6af316130a262895f4f4e72da6f9836302e1f11cfdd606825a2bb91f4930bfb9","target":"record","created_at":"2026-07-05T00:56:57Z","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":"646e2a13f2aac7ab6b439b985de02bd749b91726f17400d1d907dfd491c377e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-04-20T08:30:27Z","title_canon_sha256":"1f700198f625af1d9c1abb7a6d6442ad0bd2c47ec41e41571947ff2129e03cd7"},"schema_version":"1.0","source":{"id":"2004.10086","kind":"arxiv","version":1}},"canonical_sha256":"b67b4041dff77259815783f6cb2ec51137892d31a3727daac8f1d34be572e054","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b67b4041dff77259815783f6cb2ec51137892d31a3727daac8f1d34be572e054","first_computed_at":"2026-07-05T00:56:57.424000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:56:57.424000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lAjLaQjoEBf0hKT5Q5W7X6NOkiyJiQLhC+6R09F2tE9LOaKeYLAZvAdsMAYjBabSo/E0slB3ZLLLQG5Ax0wQAA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:56:57.424466Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.10086","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6af316130a262895f4f4e72da6f9836302e1f11cfdd606825a2bb91f4930bfb9","sha256:e43de4f35107ca6c55c52370bcba5201f9cc5e6c529e58a0f500e3c44d896a5f"],"state_sha256":"2bb16ae9584706bd75117ae00fea8d5a225df7104efcd1c1bc3cf742c3e0acfd"}