{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DBDTSVO5VW2S3GASO7VOIXNUIY","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":"bface2a17f37f70981356321b09e46dde4ab75786af4234d77ce204739666f84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-17T17:09:22Z","title_canon_sha256":"075d9dfa0808f8b7efc23a28d424f6099b3e5446c101d3ff57510f361621ed15"},"schema_version":"1.0","source":{"id":"1605.05240","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05240","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05240v1","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05240","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"DBDTSVO5VW2S","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"DBDTSVO5VW2S3GAS","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"DBDTSVO5","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:ab239ffe1459beb4b59c77e7b1d939726eeb6ef43ac1572dca540ae1751bab40","target":"graph","created_at":"2026-05-18T01:14:36Z","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":"In this paper, we use the method developed previously by Hong, Qin and Zhao to obtain several results on the permutational behavior of the reversed Dickson polynomial $D_{n,k}(1,x)$ of the $(k+1)$-th kind over the finite field ${\\mathbb F}_{q}$. Particularly, we present the explicit evaluation of the first moment $\\sum_{a\\in {\\mathbb F}_{q}}D_{n,k}(1,a)$. Our results extend the known results from the case $0\\le k\\le 3$ to the general $k\\ge 0$ case.","authors_text":"Kaimin Cheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-17T17:09:22Z","title":"Permutational behavior of reversed Dickson polynomials over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05240","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:a72d6576aba53d12765389209fc4039b3d0aeca813e4090edbb7e9427901d214","target":"record","created_at":"2026-05-18T01:14:36Z","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":"bface2a17f37f70981356321b09e46dde4ab75786af4234d77ce204739666f84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-17T17:09:22Z","title_canon_sha256":"075d9dfa0808f8b7efc23a28d424f6099b3e5446c101d3ff57510f361621ed15"},"schema_version":"1.0","source":{"id":"1605.05240","kind":"arxiv","version":1}},"canonical_sha256":"18473955ddadb52d981277eae45db446369566cb172b578d71cecceb9a35ff54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18473955ddadb52d981277eae45db446369566cb172b578d71cecceb9a35ff54","first_computed_at":"2026-05-18T01:14:36.965936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:36.965936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L/cIGbH5UqKBvDjhhudC7f5xBdGhVN/8pq3N+1DB1RYKcLbGwhSprGJF827Dyk9cEd9zFOaTB9f+iGT9LaXaDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:36.966573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.05240","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a72d6576aba53d12765389209fc4039b3d0aeca813e4090edbb7e9427901d214","sha256:ab239ffe1459beb4b59c77e7b1d939726eeb6ef43ac1572dca540ae1751bab40"],"state_sha256":"088cbfe82c6dc48d71110dcab186c50f342375512647036dc1a26a21b05c2bb2"}