{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IRL72LJZZA6JHSEZX5EVU2XT52","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":"4e69ba396c75bd750f3b0eb06e1a29ef0e1be7bc4d86183acf9ff386780c60fa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-09-09T14:27:19Z","title_canon_sha256":"ce49007cb546acf2a8a1b8af4eadb7fc7c010666d9b7b4d2af099bd1d24f9933"},"schema_version":"1.0","source":{"id":"2509.07792","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.07792","created_at":"2026-07-05T12:07:28Z"},{"alias_kind":"arxiv_version","alias_value":"2509.07792v1","created_at":"2026-07-05T12:07:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07792","created_at":"2026-07-05T12:07:28Z"},{"alias_kind":"pith_short_12","alias_value":"IRL72LJZZA6J","created_at":"2026-07-05T12:07:28Z"},{"alias_kind":"pith_short_16","alias_value":"IRL72LJZZA6JHSEZ","created_at":"2026-07-05T12:07:28Z"},{"alias_kind":"pith_short_8","alias_value":"IRL72LJZ","created_at":"2026-07-05T12:07:28Z"}],"graph_snapshots":[{"event_id":"sha256:c6f24d3ea81ef344a1a503a508087bef1b35b009c80c66e777e3bcfd77e321bb","target":"graph","created_at":"2026-07-05T12:07:28Z","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/2509.07792/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We conjecture the full asymptotic expansion of a product of Riemann zeta functions, evaluated at the non-trivial zeros of the zeta function, with shifts added in each argument. By taking derivatives with respect to these shifts, we form a conjecture for the integer moments of mixed derivatives of the zeta function. This generalises a result of the authors where they took complex moments of the first derivative of the zeta function, evaluated at the non-trivial zeros. We approach this problem in two different ways: the first uses a random matrix theory approach, and the second by the Ratios Con","authors_text":"Andrew Pearce-Crump, Christopher Hughes","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-09-09T14:27:19Z","title":"Integer moments of the derivatives of the Riemann zeta function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07792","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":"sha256:37217011bc204eaa4259837b0cad9acee601c1f306803c1faa6054967269488a","target":"record","created_at":"2026-07-05T12:07:28Z","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":"4e69ba396c75bd750f3b0eb06e1a29ef0e1be7bc4d86183acf9ff386780c60fa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-09-09T14:27:19Z","title_canon_sha256":"ce49007cb546acf2a8a1b8af4eadb7fc7c010666d9b7b4d2af099bd1d24f9933"},"schema_version":"1.0","source":{"id":"2509.07792","kind":"arxiv","version":1}},"canonical_sha256":"4457fd2d39c83c93c899bf495a6af3eeaa1ba94d44ed4d411eacfd461be5a77b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4457fd2d39c83c93c899bf495a6af3eeaa1ba94d44ed4d411eacfd461be5a77b","first_computed_at":"2026-07-05T12:07:28.436525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:07:28.436525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hAC/sAXocoUguaggXLm2PRmomqYmfiWMoPyDUOc2OeZx1m2stYOLC7WTfzXM/iKa0oGuHirCvQ9LqRBHueQ9Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T12:07:28.437074Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.07792","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37217011bc204eaa4259837b0cad9acee601c1f306803c1faa6054967269488a","sha256:c6f24d3ea81ef344a1a503a508087bef1b35b009c80c66e777e3bcfd77e321bb"],"state_sha256":"150dea4618803127e7b53e3357742abaef2103e34266c29608d77f1e0ca00240"}