{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:NWA32TS7TNRPMPV43S2UE6JQMF","short_pith_number":"pith:NWA32TS7","schema_version":"1.0","canonical_sha256":"6d81bd4e5f9b62f63ebcdcb5427930614cdd429694daeaf1c3360e1475151bd6","source":{"kind":"arxiv","id":"2510.27444","version":4},"attestation_state":"computed","paper":{"title":"Estimating the number of zeros of Dedekind zeta-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Victor Amberger","submitted_at":"2025-10-31T12:52:31Z","abstract_excerpt":"In this article, I derive a new approach to estimate the number of non-trivial zeros of a given Dedekind zeta function with absolute height at most $T\\geq1$ counted with multiplicity. The error term in corresponding asymptotic formula improves all previous results, even in the case of the Riemann zeta function."},"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":"2510.27444","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-10-31T12:52:31Z","cross_cats_sorted":[],"title_canon_sha256":"07139772989144cf4f9a0a1cdfcf97a9474a21bd387f7842ad008308c420de84","abstract_canon_sha256":"6c2cec53db1a9283bba82933399e3e8e3c8ce6eb343ec7897a991cd1730180f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T02:04:44.103777Z","signature_b64":"fxBA4YICdEpuAgpQH0BjpG3MtNOvOt6VpAARVAuaHYInpahUZTKZrRT79qlQfQg9qqT0YuBGZUhkb2r7A+LkCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d81bd4e5f9b62f63ebcdcb5427930614cdd429694daeaf1c3360e1475151bd6","last_reissued_at":"2026-05-28T02:04:44.103238Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T02:04:44.103238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimating the number of zeros of Dedekind zeta-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Victor Amberger","submitted_at":"2025-10-31T12:52:31Z","abstract_excerpt":"In this article, I derive a new approach to estimate the number of non-trivial zeros of a given Dedekind zeta function with absolute height at most $T\\geq1$ counted with multiplicity. The error term in corresponding asymptotic formula improves all previous results, even in the case of the Riemann zeta function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.27444","kind":"arxiv","version":4},"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/2510.27444/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":"2510.27444","created_at":"2026-05-28T02:04:44.103302+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.27444v4","created_at":"2026-05-28T02:04:44.103302+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.27444","created_at":"2026-05-28T02:04:44.103302+00:00"},{"alias_kind":"pith_short_12","alias_value":"NWA32TS7TNRP","created_at":"2026-05-28T02:04:44.103302+00:00"},{"alias_kind":"pith_short_16","alias_value":"NWA32TS7TNRPMPV4","created_at":"2026-05-28T02:04:44.103302+00:00"},{"alias_kind":"pith_short_8","alias_value":"NWA32TS7","created_at":"2026-05-28T02:04:44.103302+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.31441","citing_title":"Counting zeros of Artin $L$-functions","ref_index":52,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NWA32TS7TNRPMPV43S2UE6JQMF","json":"https://pith.science/pith/NWA32TS7TNRPMPV43S2UE6JQMF.json","graph_json":"https://pith.science/api/pith-number/NWA32TS7TNRPMPV43S2UE6JQMF/graph.json","events_json":"https://pith.science/api/pith-number/NWA32TS7TNRPMPV43S2UE6JQMF/events.json","paper":"https://pith.science/paper/NWA32TS7"},"agent_actions":{"view_html":"https://pith.science/pith/NWA32TS7TNRPMPV43S2UE6JQMF","download_json":"https://pith.science/pith/NWA32TS7TNRPMPV43S2UE6JQMF.json","view_paper":"https://pith.science/paper/NWA32TS7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.27444&json=true","fetch_graph":"https://pith.science/api/pith-number/NWA32TS7TNRPMPV43S2UE6JQMF/graph.json","fetch_events":"https://pith.science/api/pith-number/NWA32TS7TNRPMPV43S2UE6JQMF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NWA32TS7TNRPMPV43S2UE6JQMF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NWA32TS7TNRPMPV43S2UE6JQMF/action/storage_attestation","attest_author":"https://pith.science/pith/NWA32TS7TNRPMPV43S2UE6JQMF/action/author_attestation","sign_citation":"https://pith.science/pith/NWA32TS7TNRPMPV43S2UE6JQMF/action/citation_signature","submit_replication":"https://pith.science/pith/NWA32TS7TNRPMPV43S2UE6JQMF/action/replication_record"}},"created_at":"2026-05-28T02:04:44.103302+00:00","updated_at":"2026-05-28T02:04:44.103302+00:00"}