{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XWIQRPNLEKN2BCXHBB3G472X2Z","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":"677a2536723bdcd4ccdb6b238408eea6a5be945b005ac4293c3ccca0543776d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-10T00:53:00Z","title_canon_sha256":"27b63a59dba60de6fd207c8a4f68599eb2f0749deca660d24a2b8f41cb80fff8"},"schema_version":"1.0","source":{"id":"1908.03658","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03658","created_at":"2026-07-05T00:01:03Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03658v2","created_at":"2026-07-05T00:01:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03658","created_at":"2026-07-05T00:01:03Z"},{"alias_kind":"pith_short_12","alias_value":"XWIQRPNLEKN2","created_at":"2026-07-05T00:01:03Z"},{"alias_kind":"pith_short_16","alias_value":"XWIQRPNLEKN2BCXH","created_at":"2026-07-05T00:01:03Z"},{"alias_kind":"pith_short_8","alias_value":"XWIQRPNL","created_at":"2026-07-05T00:01:03Z"}],"graph_snapshots":[{"event_id":"sha256:da06ccc3003faa40310f4ed9e3562c16f200bd8c3f5c7c9e1853dcd9ca92424a","target":"graph","created_at":"2026-07-05T00:01:03Z","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/1908.03658/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we show that the Riemann hypothesis for the Dedekind zeta--function $\\zeta_{\\mathrm{K}}(s)$ of an algebraic number field $\\mathrm{K}$ is equivalent to a problem of the rate of convergence of certain discrete measures defined arithmetically on the multiplicative group of positive real numbers to the measure $\\zeta_{\\mathrm{K}}(2)^{-1}\\kappa q dq $, where $\\kappa$ denotes the residue of $\\zeta_{\\mathrm{K}}(s)$ at $s=1$ and $dq$ the Lebesgue measure.","authors_text":"Samuel Estala-Arias","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-10T00:53:00Z","title":"Discrete Measures and the Extended Riemann Hypothesis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03658","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":"sha256:2c1ebe1527aab741a5d894c5dd1ef8118b7ed56ce3b24bfd78aa09f6bf63ea75","target":"record","created_at":"2026-07-05T00:01:03Z","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":"677a2536723bdcd4ccdb6b238408eea6a5be945b005ac4293c3ccca0543776d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-08-10T00:53:00Z","title_canon_sha256":"27b63a59dba60de6fd207c8a4f68599eb2f0749deca660d24a2b8f41cb80fff8"},"schema_version":"1.0","source":{"id":"1908.03658","kind":"arxiv","version":2}},"canonical_sha256":"bd9108bdab229ba08ae708766e7f57d65075ba00b8a1e2c9c3c60ec7b4ef4078","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd9108bdab229ba08ae708766e7f57d65075ba00b8a1e2c9c3c60ec7b4ef4078","first_computed_at":"2026-07-05T00:01:03.181802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:01:03.181802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7rXmu4ZS7ZiJXxgrt/SNrM+4oIa+yaMyMFdjI6gzU3qA9sVt6FozJPfyEx7YnR/bIs74I0cs5t/dexh0/3IKDw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:01:03.182152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03658","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c1ebe1527aab741a5d894c5dd1ef8118b7ed56ce3b24bfd78aa09f6bf63ea75","sha256:da06ccc3003faa40310f4ed9e3562c16f200bd8c3f5c7c9e1853dcd9ca92424a"],"state_sha256":"ec793b0a50c3353f7fb5fbb133313d8e624af7020d48d771a53740755bed1e7b"}