{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FVDTTVIFLGTBEUTY7YMR6HRR3N","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":"91738b0e76ceb3db14743919fcc3ff3d91cfd0950acb6950df8dcf48b1c72710","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-07-03T13:51:39Z","title_canon_sha256":"124e392b058ad5fdef58b14bb77a5661be14e1582367d7576dac7a350beddc18"},"schema_version":"1.0","source":{"id":"1707.00549","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00549","created_at":"2026-05-18T00:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00549v2","created_at":"2026-05-18T00:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00549","created_at":"2026-05-18T00:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"FVDTTVIFLGTB","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FVDTTVIFLGTBEUTY","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FVDTTVIF","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:bb00b0811ad2202aa33cc922f9b879d6b0742c52133baca2d866bcd4f390e996","target":"graph","created_at":"2026-05-18T00:33:49Z","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":"Permutation polynomials over finite fields are an interesting subject due to their important applications in the areas of mathematics and engineering. In this paper we investigate the trinomial $f(x)=x^{(p-1)q+1}+x^{pq}-x^{q+(p-1)}$ over the finite field $\\mathbb{F}_{q^2}$, where $p$ is an odd prime and $q=p^k$ with $k$ being a positive integer. It is shown that when $p=3$ or $5$, $f(x)$ is a permutation trinomial of $\\mathbb{F}_{q^2}$ if and only if $k$ is even. This property is also true for more general class of polynomials $g(x)=x^{(q+1)l+(p-1)q+1}+x^{(q+1)l+pq}-x^{(q+1)l+q+(p-1)}$, where ","authors_text":"Tao Bai, Yongbo Xia","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-07-03T13:51:39Z","title":"A new class of permutation trinomials constructed from Niho exponents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00549","kind":"arxiv","version":2},"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":"sha256:695c8ddde632dbb2ca1c0e44e033796ad70ce2a3090267d90e9f0ce306947e98","target":"record","created_at":"2026-05-18T00:33:49Z","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":"91738b0e76ceb3db14743919fcc3ff3d91cfd0950acb6950df8dcf48b1c72710","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-07-03T13:51:39Z","title_canon_sha256":"124e392b058ad5fdef58b14bb77a5661be14e1582367d7576dac7a350beddc18"},"schema_version":"1.0","source":{"id":"1707.00549","kind":"arxiv","version":2}},"canonical_sha256":"2d4739d50559a6125278fe191f1e31db51776b0167e12e60c3e5781c8062c9be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d4739d50559a6125278fe191f1e31db51776b0167e12e60c3e5781c8062c9be","first_computed_at":"2026-05-18T00:33:49.289991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:49.289991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"duAAHu0OI9saeFbtwqHXS12n+lJZkvw2ZUasLVq+4YfXomdwlyVslFTD228D/eGyniWSvjYGA4eYf5LlsDHRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:49.290607Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.00549","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:695c8ddde632dbb2ca1c0e44e033796ad70ce2a3090267d90e9f0ce306947e98","sha256:bb00b0811ad2202aa33cc922f9b879d6b0742c52133baca2d866bcd4f390e996"],"state_sha256":"a9106825822d27ecd59310451cb932d8e292836741171a9be2a27b21f551c550"}