{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:75FMW44QHUD2RLMF2YX7SDE6QJ","short_pith_number":"pith:75FMW44Q","schema_version":"1.0","canonical_sha256":"ff4acb73903d07a8ad85d62ff90c9e8244461b97199fe2db8fc08d3d9ed1381b","source":{"kind":"arxiv","id":"1407.2861","version":4},"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":"2014-07-10T16:50:29Z","abstract_excerpt":"In the paper, we study the asymptotic distribution of real algebraic integers of fixed degree as their naive height tends to infinity. Let $I \\subset \\mathbb{R}$ be an arbitrary bounded interval, and $Q$ be a sufficiently large number. We obtain an asymptotic formula for the count of algebraic integers $\\alpha$ of fixed degree $n$ and naive height $H(\\alpha)\\le Q$ lying in $I$. In this formula, we estimate the order of the error term from above and below. We show that algebraic integers of degree $n$ are distributed asymptotically like algebraic numbers of degree $(n-1)$ as the upper bound $Q$"},"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":"1407.2861","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-10T16:50:29Z","cross_cats_sorted":[],"title_canon_sha256":"db2deb2a379bb95812e6108151c453ea8ec9401b5a17d83718f72211721922d5","abstract_canon_sha256":"d64f67cc090a625ac1ff943f2a5b95a72bd0e001bcd3e267218f3e2318e7bce3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:30.985619Z","signature_b64":"Y8Yg0njHn8+0FMbgJhd6zgIREALXj4Xz0Kj1njDi7wP6HYmTUIGfVgwblanaDLc/n7P1uiSZrfVWi6S+V132BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff4acb73903d07a8ad85d62ff90c9e8244461b97199fe2db8fc08d3d9ed1381b","last_reissued_at":"2026-05-18T01:12:30.985194Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:30.985194Z","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":"2014-07-10T16:50:29Z","abstract_excerpt":"In the paper, we study the asymptotic distribution of real algebraic integers of fixed degree as their naive height tends to infinity. Let $I \\subset \\mathbb{R}$ be an arbitrary bounded interval, and $Q$ be a sufficiently large number. We obtain an asymptotic formula for the count of algebraic integers $\\alpha$ of fixed degree $n$ and naive height $H(\\alpha)\\le Q$ lying in $I$. In this formula, we estimate the order of the error term from above and below. We show that algebraic integers of degree $n$ are distributed asymptotically like algebraic numbers of degree $(n-1)$ as the upper bound $Q$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2861","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":""},"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":"1407.2861","created_at":"2026-05-18T01:12:30.985247+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.2861v4","created_at":"2026-05-18T01:12:30.985247+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2861","created_at":"2026-05-18T01:12:30.985247+00:00"},{"alias_kind":"pith_short_12","alias_value":"75FMW44QHUD2","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"75FMW44QHUD2RLMF","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"75FMW44Q","created_at":"2026-05-18T12:28:16.859392+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/75FMW44QHUD2RLMF2YX7SDE6QJ","json":"https://pith.science/pith/75FMW44QHUD2RLMF2YX7SDE6QJ.json","graph_json":"https://pith.science/api/pith-number/75FMW44QHUD2RLMF2YX7SDE6QJ/graph.json","events_json":"https://pith.science/api/pith-number/75FMW44QHUD2RLMF2YX7SDE6QJ/events.json","paper":"https://pith.science/paper/75FMW44Q"},"agent_actions":{"view_html":"https://pith.science/pith/75FMW44QHUD2RLMF2YX7SDE6QJ","download_json":"https://pith.science/pith/75FMW44QHUD2RLMF2YX7SDE6QJ.json","view_paper":"https://pith.science/paper/75FMW44Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.2861&json=true","fetch_graph":"https://pith.science/api/pith-number/75FMW44QHUD2RLMF2YX7SDE6QJ/graph.json","fetch_events":"https://pith.science/api/pith-number/75FMW44QHUD2RLMF2YX7SDE6QJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/75FMW44QHUD2RLMF2YX7SDE6QJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/75FMW44QHUD2RLMF2YX7SDE6QJ/action/storage_attestation","attest_author":"https://pith.science/pith/75FMW44QHUD2RLMF2YX7SDE6QJ/action/author_attestation","sign_citation":"https://pith.science/pith/75FMW44QHUD2RLMF2YX7SDE6QJ/action/citation_signature","submit_replication":"https://pith.science/pith/75FMW44QHUD2RLMF2YX7SDE6QJ/action/replication_record"}},"created_at":"2026-05-18T01:12:30.985247+00:00","updated_at":"2026-05-18T01:12:30.985247+00:00"}