{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:T24ZGUUTWZOSMHCQZBM5JWJTSM","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":"df66088af6ae0327585394af7bb54b99deb34995c55d28843aaf0982105a8f58","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-01-25T15:52:59Z","title_canon_sha256":"bab0c629dada20ff0f1101736ad85c956ba451409bad91760d7b664776f5ab4d"},"schema_version":"1.0","source":{"id":"1801.08460","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08460","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08460v1","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08460","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"pith_short_12","alias_value":"T24ZGUUTWZOS","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"T24ZGUUTWZOSMHCQ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"T24ZGUUT","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:4571b8ec35287f02916dc8f4848d3f9512f7e45d2d4b96b17e3a6664a9e4b108","target":"graph","created_at":"2026-05-18T00:25:06Z","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":"We show the existence of many infinite classes of permutations over finite fields and bent functions by extending the notion of linear translators, introduced by Kyureghyan [12]. We call these translators Frobenius translators since the derivatives of $f : F_{p^n} \\rightarrow F_{p^k}$, where $n = rk$, are of the form $f(x + u\\phi) - f(x) = u^{p^i}b$, for a fixed $b \\in F_{p^k}$ and all $u \\in F_{p^k}$, rather than considering the standard case corresponding to $i = 0$. This considerably extends a rather rare family {f} admitting linear translators of the above form. Furthermore, we solve a few","authors_text":"Amela Muratovi\\'c-Ribi\\'c, Enes Pasalic, Nastja Cepak","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-01-25T15:52:59Z","title":"Frobenius linear translators giving rise to new infinite classes of permutations and bent functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08460","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":"sha256:2e8fbcdaef9c8671c5829387f95f1e379b057f5a749c5e89d899a1bb9218e28d","target":"record","created_at":"2026-05-18T00:25:06Z","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":"df66088af6ae0327585394af7bb54b99deb34995c55d28843aaf0982105a8f58","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-01-25T15:52:59Z","title_canon_sha256":"bab0c629dada20ff0f1101736ad85c956ba451409bad91760d7b664776f5ab4d"},"schema_version":"1.0","source":{"id":"1801.08460","kind":"arxiv","version":1}},"canonical_sha256":"9eb9935293b65d261c50c859d4d9339304f07d9ab4bd612c1feb52ebd8b432d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9eb9935293b65d261c50c859d4d9339304f07d9ab4bd612c1feb52ebd8b432d8","first_computed_at":"2026-05-18T00:25:06.277688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:06.277688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3koRDixpmm2zuwRoZiko46pvkzNbY8Xhi622TZE6yLoPOuegDqvtmytaXO7oY1sNgv5EWdA7dcYuNXHoaZz0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:06.278056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.08460","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e8fbcdaef9c8671c5829387f95f1e379b057f5a749c5e89d899a1bb9218e28d","sha256:4571b8ec35287f02916dc8f4848d3f9512f7e45d2d4b96b17e3a6664a9e4b108"],"state_sha256":"1ba0c8c56222489edcb6488fa3205c1f5598a93f0949052c71e2745b16a37f5a"}