{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZYISWCSPDAMEKZ77TOJQSE33E4","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":"9e21a9d515cdc20a7ddd620ba8415b7e33586d56eb14dedfc7c7365f0a1989bd","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-03T16:56:42Z","title_canon_sha256":"474b76a3ac1723e69c7d3e81db5540e1fdf980e66f164b28070d7091e37c88a3"},"schema_version":"1.0","source":{"id":"1603.01175","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01175","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01175v1","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01175","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZYISWCSPDAME","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZYISWCSPDAMEKZ77","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZYISWCSP","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:00a747b078057ea352186e2166e66357947e6d7e47ad4ee12aa148a0f2dbf6e8","target":"graph","created_at":"2026-05-18T01:19:39Z","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":"Let F_{q^n} be the field of order q^n, and let Tr be the trace map from F_{q^n} to its q-element subfield. We exhibit nine sequences of polynomials of the form f(x):=x+c*Tr(x^k), with c in F_{q^n}, such that for each polynomial the function F_{q^n}-->F_{q^n} given by c-->f(c) is a permutation of F_{q^n}. We also computed all permutation polynomials of this form over finite fields of size less than 5000, and found that our examples comprise all examples with n>1 except for some simple cases where the polynomial induces a homomorphism of the additive group of F_{q^n}, along with a few sporadic e","authors_text":"Gohar Kyureghyan, Michael Zieve","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-03T16:56:42Z","title":"Permutation polynomials of the form x+c*Tr(x^k)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01175","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":"sha256:6852db5ba31a37aef78c094ae96fd57531440aabf5d35d80c5759f75c3caa139","target":"record","created_at":"2026-05-18T01:19:39Z","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":"9e21a9d515cdc20a7ddd620ba8415b7e33586d56eb14dedfc7c7365f0a1989bd","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-03T16:56:42Z","title_canon_sha256":"474b76a3ac1723e69c7d3e81db5540e1fdf980e66f164b28070d7091e37c88a3"},"schema_version":"1.0","source":{"id":"1603.01175","kind":"arxiv","version":1}},"canonical_sha256":"ce112b0a4f18184567ff9b9309137b270509c7b6d49f744b9586bb18dc003957","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce112b0a4f18184567ff9b9309137b270509c7b6d49f744b9586bb18dc003957","first_computed_at":"2026-05-18T01:19:39.499572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:39.499572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0enZ3yMP1B9gXpF5FnfD39/rHUfRQ2YUEn/gBQkFvM4uLYTheLtRqvhuAbHJIQD8IHve8tYVjvOZZ2iOwI9fAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:39.500135Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01175","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6852db5ba31a37aef78c094ae96fd57531440aabf5d35d80c5759f75c3caa139","sha256:00a747b078057ea352186e2166e66357947e6d7e47ad4ee12aa148a0f2dbf6e8"],"state_sha256":"6d75a54e46507cf401143858ac886a25d58fdd778108383c7135ccf15731c6bc"}