{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:IRL72LJZZA6JHSEZX5EVU2XT52","short_pith_number":"pith:IRL72LJZ","schema_version":"1.0","canonical_sha256":"4457fd2d39c83c93c899bf495a6af3eeaa1ba94d44ed4d411eacfd461be5a77b","source":{"kind":"arxiv","id":"2509.07792","version":1},"attestation_state":"computed","paper":{"title":"Integer moments of the derivatives of the Riemann zeta function","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew Pearce-Crump, Christopher Hughes","submitted_at":"2025-09-09T14:27:19Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2509.07792","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-09-09T14:27:19Z","cross_cats_sorted":[],"title_canon_sha256":"ce49007cb546acf2a8a1b8af4eadb7fc7c010666d9b7b4d2af099bd1d24f9933","abstract_canon_sha256":"4e69ba396c75bd750f3b0eb06e1a29ef0e1be7bc4d86183acf9ff386780c60fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:07:28.437074Z","signature_b64":"hAC/sAXocoUguaggXLm2PRmomqYmfiWMoPyDUOc2OeZx1m2stYOLC7WTfzXM/iKa0oGuHirCvQ9LqRBHueQ9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4457fd2d39c83c93c899bf495a6af3eeaa1ba94d44ed4d411eacfd461be5a77b","last_reissued_at":"2026-07-05T12:07:28.436525Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:07:28.436525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integer moments of the derivatives of the Riemann zeta function","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew Pearce-Crump, Christopher Hughes","submitted_at":"2025-09-09T14:27:19Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07792","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/2509.07792/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2509.07792","created_at":"2026-07-05T12:07:28.436592+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.07792v1","created_at":"2026-07-05T12:07:28.436592+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07792","created_at":"2026-07-05T12:07:28.436592+00:00"},{"alias_kind":"pith_short_12","alias_value":"IRL72LJZZA6J","created_at":"2026-07-05T12:07:28.436592+00:00"},{"alias_kind":"pith_short_16","alias_value":"IRL72LJZZA6JHSEZ","created_at":"2026-07-05T12:07:28.436592+00:00"},{"alias_kind":"pith_short_8","alias_value":"IRL72LJZ","created_at":"2026-07-05T12:07:28.436592+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IRL72LJZZA6JHSEZX5EVU2XT52","json":"https://pith.science/pith/IRL72LJZZA6JHSEZX5EVU2XT52.json","graph_json":"https://pith.science/api/pith-number/IRL72LJZZA6JHSEZX5EVU2XT52/graph.json","events_json":"https://pith.science/api/pith-number/IRL72LJZZA6JHSEZX5EVU2XT52/events.json","paper":"https://pith.science/paper/IRL72LJZ"},"agent_actions":{"view_html":"https://pith.science/pith/IRL72LJZZA6JHSEZX5EVU2XT52","download_json":"https://pith.science/pith/IRL72LJZZA6JHSEZX5EVU2XT52.json","view_paper":"https://pith.science/paper/IRL72LJZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.07792&json=true","fetch_graph":"https://pith.science/api/pith-number/IRL72LJZZA6JHSEZX5EVU2XT52/graph.json","fetch_events":"https://pith.science/api/pith-number/IRL72LJZZA6JHSEZX5EVU2XT52/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IRL72LJZZA6JHSEZX5EVU2XT52/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IRL72LJZZA6JHSEZX5EVU2XT52/action/storage_attestation","attest_author":"https://pith.science/pith/IRL72LJZZA6JHSEZX5EVU2XT52/action/author_attestation","sign_citation":"https://pith.science/pith/IRL72LJZZA6JHSEZX5EVU2XT52/action/citation_signature","submit_replication":"https://pith.science/pith/IRL72LJZZA6JHSEZX5EVU2XT52/action/replication_record"}},"created_at":"2026-07-05T12:07:28.436592+00:00","updated_at":"2026-07-05T12:07:28.436592+00:00"}