{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:I3S34ZOE5LV3SH2FXPNHQV4BA6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5488fb29b14fcbe799e6e4b1131966aa52fa1c12128e4eb4b877abf09a5c69c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-02-13T04:16:11Z","title_canon_sha256":"a4ed407dcd1bde52ed8f023ea2ea7017729010bbc372f30faa111991c0538836"},"schema_version":"1.0","source":{"id":"1902.04736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.04736","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"arxiv_version","alias_value":"1902.04736v1","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.04736","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"pith_short_12","alias_value":"I3S34ZOE5LV3","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"I3S34ZOE5LV3SH2F","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"I3S34ZOE","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:b8b8649dd323dde857e36619e5039ee78d18b3446e9dfdf304f0655187645216","target":"graph","created_at":"2026-05-17T23:54:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $\\mathbb{F}_{q^n}$ be the extension of the field $\\mathbb{F}_q$ of degree n, where $q$ is power of prime $p$, i.e $q=p^k$, where k is a positive integer. In this paper, we provide sufficient condition for the existence of a primitive normal element $\\alpha\\in\\mathbb{F}_{q^n} $ such that $\\alpha^2+\\alpha+1$ is also primitive normal element over $\\mathbb{F}_{q^n}$.","authors_text":"Dhiren Kumar Basnet, Himangshu Hazarika","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-02-13T04:16:11Z","title":"Sufficient condition for existence of special type of primitive normal elements over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04736","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:874127a11cd408c7702dc48264b711f751672320a17104a92508346dbe348aab","target":"record","created_at":"2026-05-17T23:54:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5488fb29b14fcbe799e6e4b1131966aa52fa1c12128e4eb4b877abf09a5c69c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-02-13T04:16:11Z","title_canon_sha256":"a4ed407dcd1bde52ed8f023ea2ea7017729010bbc372f30faa111991c0538836"},"schema_version":"1.0","source":{"id":"1902.04736","kind":"arxiv","version":1}},"canonical_sha256":"46e5be65c4eaebb91f45bbda785781079130bd6202514528f75f29832ad066d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46e5be65c4eaebb91f45bbda785781079130bd6202514528f75f29832ad066d3","first_computed_at":"2026-05-17T23:54:06.132246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:06.132246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zU7XnGlo2xjyUS2guF3N+kgwP3qTrLkd0hLdkCUZSrjKVhCXIYB8uPt/56josL7whiyzPVwfSw9cxZC96rBeCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:06.133021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.04736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:874127a11cd408c7702dc48264b711f751672320a17104a92508346dbe348aab","sha256:b8b8649dd323dde857e36619e5039ee78d18b3446e9dfdf304f0655187645216"],"state_sha256":"dbaf097b27d7c5ed91044c7841dec78107c7dee74f42e53d7f1555e90b22eda2"}