{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:S5GIP3KPQ7VGRMVGDH3OJC5NCV","short_pith_number":"pith:S5GIP3KP","schema_version":"1.0","canonical_sha256":"974c87ed4f87ea68b2a619f6e48bad156156d81aae947616e299825286bbc6ec","source":{"kind":"arxiv","id":"2212.12869","version":1},"attestation_state":"computed","paper":{"title":"A general construction of regular complete permutation polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NT"],"primary_cat":"cs.IT","authors_text":"Wei Lu, Xia Wu, Xiwang Cao, Yufei Wang","submitted_at":"2022-12-25T07:30:20Z","abstract_excerpt":"Let $r\\geq 3$ be a positive integer and $\\mathbb{F}_q$ the finite field with $q$ elements. In this paper, we consider the $r$-regular complete permutation property of maps with the form $f=\\tau\\circ\\sigma_M\\circ\\tau^{-1}$ where $\\tau$ is a PP over an extension field $\\mathbb{F}_{q^d}$ and $\\sigma_M$ is an invertible linear map over $\\mathbb{F}_{q^d}$. We give a general construction of $r$-regular PPs for any positive integer $r$. When $\\tau$ is additive, we give a general construction of $r$-regular CPPs for any positive integer $r$. When $\\tau$ is not additive, we give many examples of regula"},"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":"2212.12869","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-12-25T07:30:20Z","cross_cats_sorted":["math.IT","math.NT"],"title_canon_sha256":"2de9b489712e8f977cb16d268015cef0ff334bda75ec5297877c19410ac067e2","abstract_canon_sha256":"95292aac1fe57fe87f392b6dcaf984a254f8414b3d921c6a3246e69715455164"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:28:49.437915Z","signature_b64":"KQixAgL439z9XJoAQXiuu8jbN1eQP7mf6+1HN7QnDtnPq+8zibv9zaq7dlC4VMpf+sY8mD6ByLncSkCeCnE6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"974c87ed4f87ea68b2a619f6e48bad156156d81aae947616e299825286bbc6ec","last_reissued_at":"2026-07-05T05:28:49.437518Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:28:49.437518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A general construction of regular complete permutation polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NT"],"primary_cat":"cs.IT","authors_text":"Wei Lu, Xia Wu, Xiwang Cao, Yufei Wang","submitted_at":"2022-12-25T07:30:20Z","abstract_excerpt":"Let $r\\geq 3$ be a positive integer and $\\mathbb{F}_q$ the finite field with $q$ elements. In this paper, we consider the $r$-regular complete permutation property of maps with the form $f=\\tau\\circ\\sigma_M\\circ\\tau^{-1}$ where $\\tau$ is a PP over an extension field $\\mathbb{F}_{q^d}$ and $\\sigma_M$ is an invertible linear map over $\\mathbb{F}_{q^d}$. We give a general construction of $r$-regular PPs for any positive integer $r$. When $\\tau$ is additive, we give a general construction of $r$-regular CPPs for any positive integer $r$. When $\\tau$ is not additive, we give many examples of regula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.12869","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/2212.12869/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":"2212.12869","created_at":"2026-07-05T05:28:49.437581+00:00"},{"alias_kind":"arxiv_version","alias_value":"2212.12869v1","created_at":"2026-07-05T05:28:49.437581+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.12869","created_at":"2026-07-05T05:28:49.437581+00:00"},{"alias_kind":"pith_short_12","alias_value":"S5GIP3KPQ7VG","created_at":"2026-07-05T05:28:49.437581+00:00"},{"alias_kind":"pith_short_16","alias_value":"S5GIP3KPQ7VGRMVG","created_at":"2026-07-05T05:28:49.437581+00:00"},{"alias_kind":"pith_short_8","alias_value":"S5GIP3KP","created_at":"2026-07-05T05:28:49.437581+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/S5GIP3KPQ7VGRMVGDH3OJC5NCV","json":"https://pith.science/pith/S5GIP3KPQ7VGRMVGDH3OJC5NCV.json","graph_json":"https://pith.science/api/pith-number/S5GIP3KPQ7VGRMVGDH3OJC5NCV/graph.json","events_json":"https://pith.science/api/pith-number/S5GIP3KPQ7VGRMVGDH3OJC5NCV/events.json","paper":"https://pith.science/paper/S5GIP3KP"},"agent_actions":{"view_html":"https://pith.science/pith/S5GIP3KPQ7VGRMVGDH3OJC5NCV","download_json":"https://pith.science/pith/S5GIP3KPQ7VGRMVGDH3OJC5NCV.json","view_paper":"https://pith.science/paper/S5GIP3KP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2212.12869&json=true","fetch_graph":"https://pith.science/api/pith-number/S5GIP3KPQ7VGRMVGDH3OJC5NCV/graph.json","fetch_events":"https://pith.science/api/pith-number/S5GIP3KPQ7VGRMVGDH3OJC5NCV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S5GIP3KPQ7VGRMVGDH3OJC5NCV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S5GIP3KPQ7VGRMVGDH3OJC5NCV/action/storage_attestation","attest_author":"https://pith.science/pith/S5GIP3KPQ7VGRMVGDH3OJC5NCV/action/author_attestation","sign_citation":"https://pith.science/pith/S5GIP3KPQ7VGRMVGDH3OJC5NCV/action/citation_signature","submit_replication":"https://pith.science/pith/S5GIP3KPQ7VGRMVGDH3OJC5NCV/action/replication_record"}},"created_at":"2026-07-05T05:28:49.437581+00:00","updated_at":"2026-07-05T05:28:49.437581+00:00"}