{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BK7BF3TF2DLMK4RQIB4IVA5HVZ","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":"08b3a0a0bb1aad914aa425c8c2713b46085c3a069d7c92da1f7cb87d6c68782b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-25T20:01:08Z","title_canon_sha256":"cef21059b8e77530ea7b092d16e362dd9c8791048c99fbceec12d8966e8e0e62"},"schema_version":"1.0","source":{"id":"2606.27516","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27516","created_at":"2026-06-29T00:14:08Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27516v1","created_at":"2026-06-29T00:14:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27516","created_at":"2026-06-29T00:14:08Z"},{"alias_kind":"pith_short_12","alias_value":"BK7BF3TF2DLM","created_at":"2026-06-29T00:14:08Z"},{"alias_kind":"pith_short_16","alias_value":"BK7BF3TF2DLMK4RQ","created_at":"2026-06-29T00:14:08Z"},{"alias_kind":"pith_short_8","alias_value":"BK7BF3TF","created_at":"2026-06-29T00:14:08Z"}],"graph_snapshots":[{"event_id":"sha256:3b2ea039f685f37ba23f9d64b265f80408bc1281f582289c8bf52b781c450abf","target":"graph","created_at":"2026-06-29T00:14:08Z","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/2606.27516/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Assuming the Generalized Riemann Hypothesis, we establish upper bounds of conjectural order of magnitude for shifted moments of the Dedekind zeta function associated with a finite Galois extension. This improves results of Milinovich and Turnage-Butterbaugh and extends a recent result of Hagen.","authors_text":"Kamalakshya Mahatab, Nilmoni Karak","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-25T20:01:08Z","title":"Sharp Bounds for Moments of the Dedekind Zeta Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27516","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:e3984d02fac05ba14d31576ef51b175045d6e6a5c0a086e195983263dbb70171","target":"record","created_at":"2026-06-29T00:14:08Z","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":"08b3a0a0bb1aad914aa425c8c2713b46085c3a069d7c92da1f7cb87d6c68782b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-25T20:01:08Z","title_canon_sha256":"cef21059b8e77530ea7b092d16e362dd9c8791048c99fbceec12d8966e8e0e62"},"schema_version":"1.0","source":{"id":"2606.27516","kind":"arxiv","version":1}},"canonical_sha256":"0abe12ee65d0d6c5723040788a83a7ae6eb0af8bf786485cca4fd2919700d0e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0abe12ee65d0d6c5723040788a83a7ae6eb0af8bf786485cca4fd2919700d0e5","first_computed_at":"2026-06-29T00:14:08.788114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T00:14:08.788114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G5ErjgcMv3TEEWrcbCPwAFLbLkAFJ4RpbaiakP5erwR2MPlc6OtKI61o8FYANJNzsXMnMiX+GdKVRWdnycXbAw==","signature_status":"signed_v1","signed_at":"2026-06-29T00:14:08.788502Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.27516","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3984d02fac05ba14d31576ef51b175045d6e6a5c0a086e195983263dbb70171","sha256:3b2ea039f685f37ba23f9d64b265f80408bc1281f582289c8bf52b781c450abf"],"state_sha256":"79124b3358db1da43633ed69b24da0faef1d11290641fd0fe5311ab11cff89e5"}