{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ESW2DVFQNBMAOEFLGA4RZIH7TC","short_pith_number":"pith:ESW2DVFQ","schema_version":"1.0","canonical_sha256":"24ada1d4b068580710ab30391ca0ff98b8a126d6e752ea8f3f7a2a15ccc8e713","source":{"kind":"arxiv","id":"1706.10296","version":2},"attestation_state":"computed","paper":{"title":"Distribution of real algebraic integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dzianis Kaliada","submitted_at":"2017-06-30T17:58:49Z","abstract_excerpt":"In the paper, we study the asymptotic distribution of real algebraic integers of fixed degree as their na\\\"{\\i}ve height tends to infinity. For an arbitrary interval $I \\subset \\mathbb{R}$ and sufficiently large $Q>0$, we obtain an asymptotic formula for the number of algebraic integers $\\alpha\\in I$ of fixed degree $n$ and na\\\"{\\i}ve height $H(\\alpha)\\le Q$. In particular, we show that the real algebraic integers of degree $n$, with their height growing, tend to be distributed like the real algebraic numbers of degree $n-1$. However, we reveal two symmetric \"plateaux\", where the distribution "},"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":"1706.10296","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-30T17:58:49Z","cross_cats_sorted":[],"title_canon_sha256":"db2deb2a379bb95812e6108151c453ea8ec9401b5a17d83718f72211721922d5","abstract_canon_sha256":"6569eb45d79f57f18a0440db67ea7760b4965fe00da9bc3d7c226c7ee83e8c55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:07.570964Z","signature_b64":"7HYRJOAwjjvrqvmqjFrlLk4m47iQjwQISJoigvoevPlZnglWw692N6DR9XLQq67/n5rzwNHnAXOky3owsxHyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24ada1d4b068580710ab30391ca0ff98b8a126d6e752ea8f3f7a2a15ccc8e713","last_reissued_at":"2026-05-18T00:13:07.570272Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:07.570272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distribution of real algebraic integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dzianis Kaliada","submitted_at":"2017-06-30T17:58:49Z","abstract_excerpt":"In the paper, we study the asymptotic distribution of real algebraic integers of fixed degree as their na\\\"{\\i}ve height tends to infinity. For an arbitrary interval $I \\subset \\mathbb{R}$ and sufficiently large $Q>0$, we obtain an asymptotic formula for the number of algebraic integers $\\alpha\\in I$ of fixed degree $n$ and na\\\"{\\i}ve height $H(\\alpha)\\le Q$. In particular, we show that the real algebraic integers of degree $n$, with their height growing, tend to be distributed like the real algebraic numbers of degree $n-1$. However, we reveal two symmetric \"plateaux\", where the distribution "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10296","kind":"arxiv","version":2},"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":"1706.10296","created_at":"2026-05-18T00:13:07.570386+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.10296v2","created_at":"2026-05-18T00:13:07.570386+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.10296","created_at":"2026-05-18T00:13:07.570386+00:00"},{"alias_kind":"pith_short_12","alias_value":"ESW2DVFQNBMA","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"ESW2DVFQNBMAOEFL","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"ESW2DVFQ","created_at":"2026-05-18T12:31:12.930513+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/ESW2DVFQNBMAOEFLGA4RZIH7TC","json":"https://pith.science/pith/ESW2DVFQNBMAOEFLGA4RZIH7TC.json","graph_json":"https://pith.science/api/pith-number/ESW2DVFQNBMAOEFLGA4RZIH7TC/graph.json","events_json":"https://pith.science/api/pith-number/ESW2DVFQNBMAOEFLGA4RZIH7TC/events.json","paper":"https://pith.science/paper/ESW2DVFQ"},"agent_actions":{"view_html":"https://pith.science/pith/ESW2DVFQNBMAOEFLGA4RZIH7TC","download_json":"https://pith.science/pith/ESW2DVFQNBMAOEFLGA4RZIH7TC.json","view_paper":"https://pith.science/paper/ESW2DVFQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.10296&json=true","fetch_graph":"https://pith.science/api/pith-number/ESW2DVFQNBMAOEFLGA4RZIH7TC/graph.json","fetch_events":"https://pith.science/api/pith-number/ESW2DVFQNBMAOEFLGA4RZIH7TC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ESW2DVFQNBMAOEFLGA4RZIH7TC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ESW2DVFQNBMAOEFLGA4RZIH7TC/action/storage_attestation","attest_author":"https://pith.science/pith/ESW2DVFQNBMAOEFLGA4RZIH7TC/action/author_attestation","sign_citation":"https://pith.science/pith/ESW2DVFQNBMAOEFLGA4RZIH7TC/action/citation_signature","submit_replication":"https://pith.science/pith/ESW2DVFQNBMAOEFLGA4RZIH7TC/action/replication_record"}},"created_at":"2026-05-18T00:13:07.570386+00:00","updated_at":"2026-05-18T00:13:07.570386+00:00"}