{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GGT5HH2AWJPFPNDUNPL2UKIFJ2","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":"5748a536b754e0f9ca87a9af6f8256dd6ffcbdcac3b609c8a772ccd10987952f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-22T11:36:24Z","title_canon_sha256":"e075cd371dd56063df4e90d1dfef649e5d6175a22c1216958581e3ed841c2061"},"schema_version":"1.0","source":{"id":"2607.20041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.20041","created_at":"2026-07-23T01:24:56Z"},{"alias_kind":"arxiv_version","alias_value":"2607.20041v1","created_at":"2026-07-23T01:24:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.20041","created_at":"2026-07-23T01:24:56Z"},{"alias_kind":"pith_short_12","alias_value":"GGT5HH2AWJPF","created_at":"2026-07-23T01:24:56Z"},{"alias_kind":"pith_short_16","alias_value":"GGT5HH2AWJPFPNDU","created_at":"2026-07-23T01:24:56Z"},{"alias_kind":"pith_short_8","alias_value":"GGT5HH2A","created_at":"2026-07-23T01:24:56Z"}],"graph_snapshots":[{"event_id":"sha256:095edd933480b1cc02777f8e79604becf062c4db2b338c3d24db90a2fb1bf784","target":"graph","created_at":"2026-07-23T01:24:56Z","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/2607.20041/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the value distribution of the Riemann zeta-function under general shifts. We establish discrepancy estimates for the Bohr--Jessen limit theorem for a broad class of shifts. We also prove a universality theorem for logarithmic-power shifts, which are not covered by previous universality results for general shifts. Furthermore, we obtain a quantitative Bohr--Jessen limit theorem for logarithmic-power shifts.","authors_text":"Keita Nakai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-22T11:36:24Z","title":"On the value distribution of the Riemann zeta-function with general shifts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20041","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:e435e63e7f7490a88c45e3247163ee402d25ea68010b8e0f03b24bb08a3b84cc","target":"record","created_at":"2026-07-23T01:24:56Z","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":"5748a536b754e0f9ca87a9af6f8256dd6ffcbdcac3b609c8a772ccd10987952f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-22T11:36:24Z","title_canon_sha256":"e075cd371dd56063df4e90d1dfef649e5d6175a22c1216958581e3ed841c2061"},"schema_version":"1.0","source":{"id":"2607.20041","kind":"arxiv","version":1}},"canonical_sha256":"31a7d39f40b25e57b4746bd7aa29054ea3c37b0311cdbd9184f6eb5a211b5554","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31a7d39f40b25e57b4746bd7aa29054ea3c37b0311cdbd9184f6eb5a211b5554","first_computed_at":"2026-07-23T01:24:56.986376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-23T01:24:56.986376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qsQiNbRTtuOPqD1zdCGTRriy6LBbJuAmfCwqCn3B+Q00LUtFTLfj4hpxNNPQkEmNj+dFjvef7+Xlj/QEz7LmDQ==","signature_status":"signed_v1","signed_at":"2026-07-23T01:24:56.987211Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.20041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e435e63e7f7490a88c45e3247163ee402d25ea68010b8e0f03b24bb08a3b84cc","sha256:095edd933480b1cc02777f8e79604becf062c4db2b338c3d24db90a2fb1bf784"],"state_sha256":"011c54c612b4819fa57aeb422ea314eecfb8aa9d6cc56da4b83c8e670502d1cb"}