{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DKVA6UWOER6XCP4MRIWVG3HUTD","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":"a029f84f5e5411e5f79c0fac9f23b0b1ecc848f20bd46963e2ba5ea033bad31f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-08T13:44:48Z","title_canon_sha256":"68842b72ce45c38a72739138f7939d44f317909d388d2ab701544fe904d82cb6"},"schema_version":"1.0","source":{"id":"1404.2127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2127","created_at":"2026-05-18T02:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2127v1","created_at":"2026-05-18T02:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2127","created_at":"2026-05-18T02:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"DKVA6UWOER6X","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DKVA6UWOER6XCP4M","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DKVA6UWO","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:eea019c1acd3f71ae83f8afabd157d4a8d3baf05e315d213ec95afd3be083e1c","target":"graph","created_at":"2026-05-18T02:54:38Z","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 present several necessary conditions for the reversed Dickson polynomial $E_{n}(1, x)$ of the second kind to be a permutation of $\\mathbb{F}_{q}$. In particular, we give explicit evaluation of the sum $\\sum_{a\\in \\mathbb{F}_{q}}E_{n}(1,a)$.","authors_text":"Shaofang Hong, Xiaoer Qin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-08T13:44:48Z","title":"Necessary conditions for reversed Dickson polynomials of the second kind to be permutational"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2127","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":"sha256:7a0d9486867396a086cdbe466951138aa5b099332eafb50cc8ead441eb7a9f5c","target":"record","created_at":"2026-05-18T02:54:38Z","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":"a029f84f5e5411e5f79c0fac9f23b0b1ecc848f20bd46963e2ba5ea033bad31f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-08T13:44:48Z","title_canon_sha256":"68842b72ce45c38a72739138f7939d44f317909d388d2ab701544fe904d82cb6"},"schema_version":"1.0","source":{"id":"1404.2127","kind":"arxiv","version":1}},"canonical_sha256":"1aaa0f52ce247d713f8c8a2d536cf498f977a507cc3f832e5656a4fd84bad87a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1aaa0f52ce247d713f8c8a2d536cf498f977a507cc3f832e5656a4fd84bad87a","first_computed_at":"2026-05-18T02:54:38.481245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:38.481245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BDjBE7hDdMpLkqZOfCZPyVGr9oB/N2E2CxkpkqiarkHXKtsCPo+m8eSTII8PeGzMhL7jFe2ZHtGHan2+kMJAAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:38.481788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.2127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a0d9486867396a086cdbe466951138aa5b099332eafb50cc8ead441eb7a9f5c","sha256:eea019c1acd3f71ae83f8afabd157d4a8d3baf05e315d213ec95afd3be083e1c"],"state_sha256":"23f0f2d272913f39467a83c340f7bcdfd0aa1c52aa54d4d15ffe25407fcc86d1"}