{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MTDRSMHAQNKJP6FOHTXVUX2N3J","short_pith_number":"pith:MTDRSMHA","schema_version":"1.0","canonical_sha256":"64c71930e0835497f8ae3cef5a5f4dda6023b547b7d148a2887da3d7707ab3ad","source":{"kind":"arxiv","id":"2606.01037","version":1},"attestation_state":"computed","paper":{"title":"A further study of polynomial $g_{n,q}$ over finite fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bhitali Kousik, Neranga Fernando","submitted_at":"2026-05-31T06:04:17Z","abstract_excerpt":"Let $n\\geq 0$ be an integer and $q$ a prime power. The polynomial $g_{n,q}$ was introduced in [10] with the purpose of finding new classes of permutation polynomials over finite fields. We investigate the permutation behaviour of the polynomial $g_{n,q}(X)$ over finite fields of even characteristic. We introduce the multivariate case of the polynomial $g_{n,q}$, and study the permutation polynomials in several variables and local permutation polynomials resulting from the polynomials $g_{n,q}(X_1,X_2,\\ldots , X_k)$. We also present several new identities of $g_{n,q}(X)$, and present some open "},"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":"2606.01037","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-31T06:04:17Z","cross_cats_sorted":[],"title_canon_sha256":"e6e2a8c0cb7296d9ea8dbdeba1275a58d98b0161061ad4cb24a8d3531d72c423","abstract_canon_sha256":"6da2301a86eff8d11f73a4d045ddde089742da5f074069484471d0f814ff713a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:04:19.179651Z","signature_b64":"JHh/YL1PWW83yvQ3q/WobGj8oLGtlXj3mPKSh/tkkQW18Y3UjHcuZpe4ybn31GBzEF0ZDV1EmvU5dXpWgAE3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64c71930e0835497f8ae3cef5a5f4dda6023b547b7d148a2887da3d7707ab3ad","last_reissued_at":"2026-06-02T01:04:19.179224Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:04:19.179224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A further study of polynomial $g_{n,q}$ over finite fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bhitali Kousik, Neranga Fernando","submitted_at":"2026-05-31T06:04:17Z","abstract_excerpt":"Let $n\\geq 0$ be an integer and $q$ a prime power. The polynomial $g_{n,q}$ was introduced in [10] with the purpose of finding new classes of permutation polynomials over finite fields. We investigate the permutation behaviour of the polynomial $g_{n,q}(X)$ over finite fields of even characteristic. We introduce the multivariate case of the polynomial $g_{n,q}$, and study the permutation polynomials in several variables and local permutation polynomials resulting from the polynomials $g_{n,q}(X_1,X_2,\\ldots , X_k)$. We also present several new identities of $g_{n,q}(X)$, and present some open "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01037","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.01037/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.01037","created_at":"2026-06-02T01:04:19.179286+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.01037v1","created_at":"2026-06-02T01:04:19.179286+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01037","created_at":"2026-06-02T01:04:19.179286+00:00"},{"alias_kind":"pith_short_12","alias_value":"MTDRSMHAQNKJ","created_at":"2026-06-02T01:04:19.179286+00:00"},{"alias_kind":"pith_short_16","alias_value":"MTDRSMHAQNKJP6FO","created_at":"2026-06-02T01:04:19.179286+00:00"},{"alias_kind":"pith_short_8","alias_value":"MTDRSMHA","created_at":"2026-06-02T01:04:19.179286+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/MTDRSMHAQNKJP6FOHTXVUX2N3J","json":"https://pith.science/pith/MTDRSMHAQNKJP6FOHTXVUX2N3J.json","graph_json":"https://pith.science/api/pith-number/MTDRSMHAQNKJP6FOHTXVUX2N3J/graph.json","events_json":"https://pith.science/api/pith-number/MTDRSMHAQNKJP6FOHTXVUX2N3J/events.json","paper":"https://pith.science/paper/MTDRSMHA"},"agent_actions":{"view_html":"https://pith.science/pith/MTDRSMHAQNKJP6FOHTXVUX2N3J","download_json":"https://pith.science/pith/MTDRSMHAQNKJP6FOHTXVUX2N3J.json","view_paper":"https://pith.science/paper/MTDRSMHA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.01037&json=true","fetch_graph":"https://pith.science/api/pith-number/MTDRSMHAQNKJP6FOHTXVUX2N3J/graph.json","fetch_events":"https://pith.science/api/pith-number/MTDRSMHAQNKJP6FOHTXVUX2N3J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MTDRSMHAQNKJP6FOHTXVUX2N3J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MTDRSMHAQNKJP6FOHTXVUX2N3J/action/storage_attestation","attest_author":"https://pith.science/pith/MTDRSMHAQNKJP6FOHTXVUX2N3J/action/author_attestation","sign_citation":"https://pith.science/pith/MTDRSMHAQNKJP6FOHTXVUX2N3J/action/citation_signature","submit_replication":"https://pith.science/pith/MTDRSMHAQNKJP6FOHTXVUX2N3J/action/replication_record"}},"created_at":"2026-06-02T01:04:19.179286+00:00","updated_at":"2026-06-02T01:04:19.179286+00:00"}