{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:V6PNZQPIALYERAJ4VYPWRY4R2R","short_pith_number":"pith:V6PNZQPI","schema_version":"1.0","canonical_sha256":"af9edcc1e802f048813cae1f68e391d479349aa2e01e5862159f630ff6d5b573","source":{"kind":"arxiv","id":"0904.1331","version":2},"attestation_state":"computed","paper":{"title":"Primitive Polynomials, Singer Cycles, and Word-Oriented Linear Feedback Shift Registers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Meena Kumari, Sartaj Ul Hasan, Sudhir R. Ghorpade","submitted_at":"2009-04-08T13:06:59Z","abstract_excerpt":"Using the structure of Singer cycles in general linear groups, we prove that a conjecture of Zeng, Han and He (2007) holds in the affirmative in a special case, and outline a plausible approach to prove it in the general case. This conjecture is about the number of primitive $\\sigma$-LFSRs of a given order over a finite field, and it generalizes a known formula for the number of primitive LFSRs, which, in turn, is the number of primitive polynomials of a given degree over a finite field. Moreover, this conjecture is intimately related to an open question of Niederreiter (1995) on the enumerati"},"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":"0904.1331","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-04-08T13:06:59Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"432afaffc55bcccb84a250f3e008539ab79c2d042be5470e9718d990847fb8ad","abstract_canon_sha256":"857f1e0226de55d52081d455a40aeeb568e8e73425c1860ffe7d82e9a1377dc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:44.680054Z","signature_b64":"fisbM4jnMW8aCdkSXysAMmTivqWKoOgoLkbM2NvRkxRKf2IXczY418aX09rCTYyWfSFZsxtJRniE9nP/MBYLDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af9edcc1e802f048813cae1f68e391d479349aa2e01e5862159f630ff6d5b573","last_reissued_at":"2026-05-18T04:29:44.679588Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:44.679588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Primitive Polynomials, Singer Cycles, and Word-Oriented Linear Feedback Shift Registers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Meena Kumari, Sartaj Ul Hasan, Sudhir R. Ghorpade","submitted_at":"2009-04-08T13:06:59Z","abstract_excerpt":"Using the structure of Singer cycles in general linear groups, we prove that a conjecture of Zeng, Han and He (2007) holds in the affirmative in a special case, and outline a plausible approach to prove it in the general case. This conjecture is about the number of primitive $\\sigma$-LFSRs of a given order over a finite field, and it generalizes a known formula for the number of primitive LFSRs, which, in turn, is the number of primitive polynomials of a given degree over a finite field. Moreover, this conjecture is intimately related to an open question of Niederreiter (1995) on the enumerati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.1331","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":"0904.1331","created_at":"2026-05-18T04:29:44.679658+00:00"},{"alias_kind":"arxiv_version","alias_value":"0904.1331v2","created_at":"2026-05-18T04:29:44.679658+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.1331","created_at":"2026-05-18T04:29:44.679658+00:00"},{"alias_kind":"pith_short_12","alias_value":"V6PNZQPIALYE","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"V6PNZQPIALYERAJ4","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"V6PNZQPI","created_at":"2026-05-18T12:26:02.257875+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/V6PNZQPIALYERAJ4VYPWRY4R2R","json":"https://pith.science/pith/V6PNZQPIALYERAJ4VYPWRY4R2R.json","graph_json":"https://pith.science/api/pith-number/V6PNZQPIALYERAJ4VYPWRY4R2R/graph.json","events_json":"https://pith.science/api/pith-number/V6PNZQPIALYERAJ4VYPWRY4R2R/events.json","paper":"https://pith.science/paper/V6PNZQPI"},"agent_actions":{"view_html":"https://pith.science/pith/V6PNZQPIALYERAJ4VYPWRY4R2R","download_json":"https://pith.science/pith/V6PNZQPIALYERAJ4VYPWRY4R2R.json","view_paper":"https://pith.science/paper/V6PNZQPI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0904.1331&json=true","fetch_graph":"https://pith.science/api/pith-number/V6PNZQPIALYERAJ4VYPWRY4R2R/graph.json","fetch_events":"https://pith.science/api/pith-number/V6PNZQPIALYERAJ4VYPWRY4R2R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V6PNZQPIALYERAJ4VYPWRY4R2R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V6PNZQPIALYERAJ4VYPWRY4R2R/action/storage_attestation","attest_author":"https://pith.science/pith/V6PNZQPIALYERAJ4VYPWRY4R2R/action/author_attestation","sign_citation":"https://pith.science/pith/V6PNZQPIALYERAJ4VYPWRY4R2R/action/citation_signature","submit_replication":"https://pith.science/pith/V6PNZQPIALYERAJ4VYPWRY4R2R/action/replication_record"}},"created_at":"2026-05-18T04:29:44.679658+00:00","updated_at":"2026-05-18T04:29:44.679658+00:00"}