{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7OF4XKSTPTVERXBTEELOLOCSUQ","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":"2c8f02c1704d395ed766924770a92466e9af07ff6e13fca1d65db485f5a36f65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-11T16:50:20Z","title_canon_sha256":"fce5c8cd9174d94da8f54774dd7a20d69799e80677b0600cf5347c8f1dfe2667"},"schema_version":"1.0","source":{"id":"1506.03741","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03741","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03741v1","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03741","created_at":"2026-05-18T01:11:05Z"},{"alias_kind":"pith_short_12","alias_value":"7OF4XKSTPTVE","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7OF4XKSTPTVERXBT","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7OF4XKST","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:104fc824ac966714f78ad2ef3effbe83d169ee5eb9a9455cdaf73b09b775e37d","target":"graph","created_at":"2026-05-18T01:11:05Z","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":"We establish the equivalence of conjectures concerning the pair correlation of zeros of $L$-functions in the Selberg class and the variances of sums of a related class of arithmetic functions over primes in short intervals. This extends the results of Goldston & Montgomery [7] and Montgomery & Soundararajan [11] for the Riemann zeta-function to other $L$-functions in the Selberg class. Our approach is based on the statistics of the zeros because the analogue of the Hardy-Littlewood conjecture for the auto-correlation of the arithmetic functions we consider is not available in general. One of o","authors_text":"D. J. Smith, H. M. Bui, J. P. Keating","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-11T16:50:20Z","title":"On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03741","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":"sha256:08a395a77a9e4f5c01cf0060010694d452b1c5294253f4ca07dc3cf1b11e46ad","target":"record","created_at":"2026-05-18T01:11:05Z","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":"2c8f02c1704d395ed766924770a92466e9af07ff6e13fca1d65db485f5a36f65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-11T16:50:20Z","title_canon_sha256":"fce5c8cd9174d94da8f54774dd7a20d69799e80677b0600cf5347c8f1dfe2667"},"schema_version":"1.0","source":{"id":"1506.03741","kind":"arxiv","version":1}},"canonical_sha256":"fb8bcbaa537cea48dc332116e5b852a4154475e3289dc62abf1d4496019b38f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb8bcbaa537cea48dc332116e5b852a4154475e3289dc62abf1d4496019b38f0","first_computed_at":"2026-05-18T01:11:05.229190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:05.229190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SMeKGfH5XrCdbUR9kvO68CUuMeYDr4FYVQ5UjZpCm7XY4qrhraPQnK2tvIWNuJnx8BXSxqFyrSNRd+u++KwcDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:05.229731Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03741","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08a395a77a9e4f5c01cf0060010694d452b1c5294253f4ca07dc3cf1b11e46ad","sha256:104fc824ac966714f78ad2ef3effbe83d169ee5eb9a9455cdaf73b09b775e37d"],"state_sha256":"a508958b2ed32a4cb5067d2e6b498bf9325f525c19645704fd6b322f3a2b1bdf"}