{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NUSLC3AI4BRYX4MO6KRHS57G7M","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":"74ae8a879923c2b6e5e220fa11ffdd479f016077aa687a7bdc6862442b4162e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-22T18:08:58Z","title_canon_sha256":"12160c6351e95db70e593b36d673e0478e3bdd9a2b8aa22be4269261dd640b3e"},"schema_version":"1.0","source":{"id":"1603.06893","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06893","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06893v2","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06893","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"pith_short_12","alias_value":"NUSLC3AI4BRY","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NUSLC3AI4BRYX4MO","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NUSLC3AI","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:7d27e0f3fb5e0f69f5dd382ca0c1466eb7d643f4707aee35fc00055161567246","target":"graph","created_at":"2026-05-18T01:07:53Z","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":"In this series we examine the calculation of the $2k$th moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper begins the general study of what we call Type II sums which utilize a circle method framework and a convolution of shifted convolution sums to obtain all of the lower order terms in the asymptotic formula for the mean square along $[T,2T]$ of a Dirichlet polynomial of length up to $T^3$ with divisor functions as coefficients.","authors_text":"Brian Conrey, Jonathan P. Keating","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-22T18:08:58Z","title":"Moments of zeta and correlations of divisor-sums: IV"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06893","kind":"arxiv","version":2},"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":"sha256:358bce080de7833143e0927c1e258b98771c11cb7f77252faf7d3765e7a05e97","target":"record","created_at":"2026-05-18T01:07:53Z","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":"74ae8a879923c2b6e5e220fa11ffdd479f016077aa687a7bdc6862442b4162e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-22T18:08:58Z","title_canon_sha256":"12160c6351e95db70e593b36d673e0478e3bdd9a2b8aa22be4269261dd640b3e"},"schema_version":"1.0","source":{"id":"1603.06893","kind":"arxiv","version":2}},"canonical_sha256":"6d24b16c08e0638bf18ef2a27977e6fb21ba47f2e84096bb04e6bd601095d096","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d24b16c08e0638bf18ef2a27977e6fb21ba47f2e84096bb04e6bd601095d096","first_computed_at":"2026-05-18T01:07:53.807587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:53.807587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ci5bobOpcb0WlfkDhmYDnEcTalKukImQ/sPt/98EfPqXqXE+8ROYD0EoyN8cYCIgTAd1N7lvF8LR3W/FE4oBDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:53.807975Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06893","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:358bce080de7833143e0927c1e258b98771c11cb7f77252faf7d3765e7a05e97","sha256:7d27e0f3fb5e0f69f5dd382ca0c1466eb7d643f4707aee35fc00055161567246"],"state_sha256":"8ea28b2cad8d4654ee1955494f0bdc59135d2734b2048c2c596f5999cbda844a"}