{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:BZ63OTM6XGUVHHV62UNP4ABI7Y","short_pith_number":"pith:BZ63OTM6","schema_version":"1.0","canonical_sha256":"0e7db74d9eb9a9539ebed51afe0028fe14e8190ea77018f52adc9aa6ff1799db","source":{"kind":"arxiv","id":"0910.5182","version":3},"attestation_state":"computed","paper":{"title":"An equivalent of Kronecker's Theorem for powers of an Algebraic Number and Structure of Linear Recurrences of fixed length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Maurizio Monge, Nevio Dubbini","submitted_at":"2009-10-27T17:21:47Z","abstract_excerpt":"After defining a notion of $\\epsilon$-density, we provide for any real algebraic number $\\alpha$ an estimate of the smallest $\\epsilon$ such that for each $m>1$ the set of vectors of the form $(t,t\\alpha,...,t\\alpha^{m-1})$ for $t\\in\\R$ is $\\epsilon$-dense modulo 1, in terms of the multiplicative Mahler measure $M(A(x))$ of the minimal integral polynomial $A(x)$ of $\\alpha$, and independently of $m$. In particular, we show that if $\\alpha$ has degree $d$ it is possible to take $\\epsilon = 2^{[d/2]}/M(A(x))$.\n  On the other hand using asymptotic estimates for Toeplitz determinants we show that "},"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":"0910.5182","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-10-27T17:21:47Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"6763b4a2bc88e452797fd15ff99a86efda30d7f38a3934411794fb8025d5428a","abstract_canon_sha256":"c704408829c812d6f8ec1c14aba3c947909626064143dde7be74115495e691b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:57.317068Z","signature_b64":"5cEA3ir+ai5Co1Xq5AVpMqYLKP/7I+YVop752I+eczVApMttSGLjHDQE4jaeNGAu8BuDsoX/h2eIxLggG1UlBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e7db74d9eb9a9539ebed51afe0028fe14e8190ea77018f52adc9aa6ff1799db","last_reissued_at":"2026-05-18T04:10:57.316532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:57.316532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An equivalent of Kronecker's Theorem for powers of an Algebraic Number and Structure of Linear Recurrences of fixed length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Maurizio Monge, Nevio Dubbini","submitted_at":"2009-10-27T17:21:47Z","abstract_excerpt":"After defining a notion of $\\epsilon$-density, we provide for any real algebraic number $\\alpha$ an estimate of the smallest $\\epsilon$ such that for each $m>1$ the set of vectors of the form $(t,t\\alpha,...,t\\alpha^{m-1})$ for $t\\in\\R$ is $\\epsilon$-dense modulo 1, in terms of the multiplicative Mahler measure $M(A(x))$ of the minimal integral polynomial $A(x)$ of $\\alpha$, and independently of $m$. In particular, we show that if $\\alpha$ has degree $d$ it is possible to take $\\epsilon = 2^{[d/2]}/M(A(x))$.\n  On the other hand using asymptotic estimates for Toeplitz determinants we show that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5182","kind":"arxiv","version":3},"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":"0910.5182","created_at":"2026-05-18T04:10:57.316601+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.5182v3","created_at":"2026-05-18T04:10:57.316601+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.5182","created_at":"2026-05-18T04:10:57.316601+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZ63OTM6XGUV","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZ63OTM6XGUVHHV6","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZ63OTM6","created_at":"2026-05-18T12:25:58.837520+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/BZ63OTM6XGUVHHV62UNP4ABI7Y","json":"https://pith.science/pith/BZ63OTM6XGUVHHV62UNP4ABI7Y.json","graph_json":"https://pith.science/api/pith-number/BZ63OTM6XGUVHHV62UNP4ABI7Y/graph.json","events_json":"https://pith.science/api/pith-number/BZ63OTM6XGUVHHV62UNP4ABI7Y/events.json","paper":"https://pith.science/paper/BZ63OTM6"},"agent_actions":{"view_html":"https://pith.science/pith/BZ63OTM6XGUVHHV62UNP4ABI7Y","download_json":"https://pith.science/pith/BZ63OTM6XGUVHHV62UNP4ABI7Y.json","view_paper":"https://pith.science/paper/BZ63OTM6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.5182&json=true","fetch_graph":"https://pith.science/api/pith-number/BZ63OTM6XGUVHHV62UNP4ABI7Y/graph.json","fetch_events":"https://pith.science/api/pith-number/BZ63OTM6XGUVHHV62UNP4ABI7Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZ63OTM6XGUVHHV62UNP4ABI7Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZ63OTM6XGUVHHV62UNP4ABI7Y/action/storage_attestation","attest_author":"https://pith.science/pith/BZ63OTM6XGUVHHV62UNP4ABI7Y/action/author_attestation","sign_citation":"https://pith.science/pith/BZ63OTM6XGUVHHV62UNP4ABI7Y/action/citation_signature","submit_replication":"https://pith.science/pith/BZ63OTM6XGUVHHV62UNP4ABI7Y/action/replication_record"}},"created_at":"2026-05-18T04:10:57.316601+00:00","updated_at":"2026-05-18T04:10:57.316601+00:00"}