{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:T2KGY3XM3FS5FBQYH57STRLPSY","short_pith_number":"pith:T2KGY3XM","schema_version":"1.0","canonical_sha256":"9e946c6eecd965d286183f7f29c56f962397dcc8534cc59f33c79611dd12ca7f","source":{"kind":"arxiv","id":"1302.6094","version":1},"attestation_state":"computed","paper":{"title":"On the Number of Eisenstein Polynomials of Bounded Height","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Igor E. Shparlinski, Randell Heyman","submitted_at":"2013-02-25T14:08:51Z","abstract_excerpt":"We obtain a more precise version of an asymptotic formula of A. Dubickas for the number of monic Eisenstein polynomials of fixed degree $d$ and of height at most $H$, as $H\\to \\infty$. In particular, we give an explicit bound for the error term. We also obtain an asymptotic formula for arbitrary Eisenstein polynomials of height at most $H$."},"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":"1302.6094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T14:08:51Z","cross_cats_sorted":[],"title_canon_sha256":"18fa047f67fe9bc4aedd58501f4870017d69e8d82df590495e7938ba3e7f8c6f","abstract_canon_sha256":"5c81a7d39157553e3c2be0f4e9eab305756b3b2ad334a0b9694ae0906d4116d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:35.246554Z","signature_b64":"SbfKx7O14P5/d1+qif73nIPMAJf90mZrJY+Ao4SxMb1Dueb1uVeZWY+SatmmVmbVZFunb5BP0L2AHRZZ/HMHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e946c6eecd965d286183f7f29c56f962397dcc8534cc59f33c79611dd12ca7f","last_reissued_at":"2026-05-18T00:40:35.245991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:35.245991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Number of Eisenstein Polynomials of Bounded Height","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Igor E. Shparlinski, Randell Heyman","submitted_at":"2013-02-25T14:08:51Z","abstract_excerpt":"We obtain a more precise version of an asymptotic formula of A. Dubickas for the number of monic Eisenstein polynomials of fixed degree $d$ and of height at most $H$, as $H\\to \\infty$. In particular, we give an explicit bound for the error term. We also obtain an asymptotic formula for arbitrary Eisenstein polynomials of height at most $H$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6094","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":"1302.6094","created_at":"2026-05-18T00:40:35.246068+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.6094v1","created_at":"2026-05-18T00:40:35.246068+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6094","created_at":"2026-05-18T00:40:35.246068+00:00"},{"alias_kind":"pith_short_12","alias_value":"T2KGY3XM3FS5","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"T2KGY3XM3FS5FBQY","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"T2KGY3XM","created_at":"2026-05-18T12:27:59.945178+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/T2KGY3XM3FS5FBQYH57STRLPSY","json":"https://pith.science/pith/T2KGY3XM3FS5FBQYH57STRLPSY.json","graph_json":"https://pith.science/api/pith-number/T2KGY3XM3FS5FBQYH57STRLPSY/graph.json","events_json":"https://pith.science/api/pith-number/T2KGY3XM3FS5FBQYH57STRLPSY/events.json","paper":"https://pith.science/paper/T2KGY3XM"},"agent_actions":{"view_html":"https://pith.science/pith/T2KGY3XM3FS5FBQYH57STRLPSY","download_json":"https://pith.science/pith/T2KGY3XM3FS5FBQYH57STRLPSY.json","view_paper":"https://pith.science/paper/T2KGY3XM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.6094&json=true","fetch_graph":"https://pith.science/api/pith-number/T2KGY3XM3FS5FBQYH57STRLPSY/graph.json","fetch_events":"https://pith.science/api/pith-number/T2KGY3XM3FS5FBQYH57STRLPSY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T2KGY3XM3FS5FBQYH57STRLPSY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T2KGY3XM3FS5FBQYH57STRLPSY/action/storage_attestation","attest_author":"https://pith.science/pith/T2KGY3XM3FS5FBQYH57STRLPSY/action/author_attestation","sign_citation":"https://pith.science/pith/T2KGY3XM3FS5FBQYH57STRLPSY/action/citation_signature","submit_replication":"https://pith.science/pith/T2KGY3XM3FS5FBQYH57STRLPSY/action/replication_record"}},"created_at":"2026-05-18T00:40:35.246068+00:00","updated_at":"2026-05-18T00:40:35.246068+00:00"}