{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4KGKWTQHK6IX2FM64KSUH7EVD3","short_pith_number":"pith:4KGKWTQH","schema_version":"1.0","canonical_sha256":"e28cab4e0757917d159ee2a543fc951ec041cdffa66fffb764eb097a8fee29ee","source":{"kind":"arxiv","id":"1403.3473","version":1},"attestation_state":"computed","paper":{"title":"On the Infinitude of Prime Ideals in Dedekind Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.NT","authors_text":"Jose A. Velez-Marulanda","submitted_at":"2014-03-14T01:50:13Z","abstract_excerpt":"Let $R$ be an infinite Dedekind domain with at most finitely many units, and let $K$ denote its field of fractions. We prove the following statement. If $L/K$ is a finite Galois extension of fields and $\\mathcal{O}$ is the integral closure of $R$ in $L$, then $\\mathcal{O}$ contains infinitely many prime ideals. In particular, if $\\mathcal{O}$ is further a unique factorization domain, then $\\mathcal{O}$ contains infinitely many non-associate prime elements."},"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":"1403.3473","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-14T01:50:13Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"9f0c233e992cec0fc0648caab00e8c4627cc9de5cdecdb56e6011ee16617e553","abstract_canon_sha256":"c01baf60e8f2efeec23f070cce07b1c8bc2887d7f8e6a3d11b299d443df47614"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:39.093510Z","signature_b64":"OpfsZqd6dE2XJ3pjVw9kQgBvoPBN6wi3Sc4a33DgOl+uT+PdlTE99f6nEMX4ot/FYYl8pQwJ8CucBgOAWEofCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e28cab4e0757917d159ee2a543fc951ec041cdffa66fffb764eb097a8fee29ee","last_reissued_at":"2026-05-17T23:50:39.092940Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:39.092940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Infinitude of Prime Ideals in Dedekind Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.NT","authors_text":"Jose A. Velez-Marulanda","submitted_at":"2014-03-14T01:50:13Z","abstract_excerpt":"Let $R$ be an infinite Dedekind domain with at most finitely many units, and let $K$ denote its field of fractions. We prove the following statement. If $L/K$ is a finite Galois extension of fields and $\\mathcal{O}$ is the integral closure of $R$ in $L$, then $\\mathcal{O}$ contains infinitely many prime ideals. In particular, if $\\mathcal{O}$ is further a unique factorization domain, then $\\mathcal{O}$ contains infinitely many non-associate prime elements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3473","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":""},"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":"1403.3473","created_at":"2026-05-17T23:50:39.093053+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.3473v1","created_at":"2026-05-17T23:50:39.093053+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3473","created_at":"2026-05-17T23:50:39.093053+00:00"},{"alias_kind":"pith_short_12","alias_value":"4KGKWTQHK6IX","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4KGKWTQHK6IX2FM6","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4KGKWTQH","created_at":"2026-05-18T12:28:14.216126+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/4KGKWTQHK6IX2FM64KSUH7EVD3","json":"https://pith.science/pith/4KGKWTQHK6IX2FM64KSUH7EVD3.json","graph_json":"https://pith.science/api/pith-number/4KGKWTQHK6IX2FM64KSUH7EVD3/graph.json","events_json":"https://pith.science/api/pith-number/4KGKWTQHK6IX2FM64KSUH7EVD3/events.json","paper":"https://pith.science/paper/4KGKWTQH"},"agent_actions":{"view_html":"https://pith.science/pith/4KGKWTQHK6IX2FM64KSUH7EVD3","download_json":"https://pith.science/pith/4KGKWTQHK6IX2FM64KSUH7EVD3.json","view_paper":"https://pith.science/paper/4KGKWTQH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.3473&json=true","fetch_graph":"https://pith.science/api/pith-number/4KGKWTQHK6IX2FM64KSUH7EVD3/graph.json","fetch_events":"https://pith.science/api/pith-number/4KGKWTQHK6IX2FM64KSUH7EVD3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4KGKWTQHK6IX2FM64KSUH7EVD3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4KGKWTQHK6IX2FM64KSUH7EVD3/action/storage_attestation","attest_author":"https://pith.science/pith/4KGKWTQHK6IX2FM64KSUH7EVD3/action/author_attestation","sign_citation":"https://pith.science/pith/4KGKWTQHK6IX2FM64KSUH7EVD3/action/citation_signature","submit_replication":"https://pith.science/pith/4KGKWTQHK6IX2FM64KSUH7EVD3/action/replication_record"}},"created_at":"2026-05-17T23:50:39.093053+00:00","updated_at":"2026-05-17T23:50:39.093053+00:00"}