{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ITC3M5POOFIWLTUU7LHZ6VFIZT","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":"c9d08ea12d5387891f58864dc360131e59b02709abb5599efb400da64007818f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-11T11:06:14Z","title_canon_sha256":"50fa92a8661cf901d14bb6981f3cf5fb6cafc942b0a10da3998d373abf3400f1"},"schema_version":"1.0","source":{"id":"1605.03375","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03375","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03375v1","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03375","created_at":"2026-05-18T01:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"ITC3M5POOFIW","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"ITC3M5POOFIWLTUU","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"ITC3M5PO","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:b9c08fa3fd9c6f6d5832d2af2cbf5c48189424c4350ceaea89f4241533a7ca38","target":"graph","created_at":"2026-05-18T01:15:05Z","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 work, we completely characterize (i) permutation binomials of the form $x^{{{2^n -1}\\over {2^t-1}}+1}+ ax \\in \\mathbb{F}_{2^n}[x], n = 2^st, a \\in \\mathbb{F}_{2^{2t}}^{*}$, and (ii) permutation trinomials of the form $x^{2^s+1}+x^{2^{s-1}+1}+\\alpha x \\in \\mathbb{F}_{2^t}[x]$, \\end{enumerate} where $s,t$ are positive integers. The first result, which was our primary motivation, is a consequence of the second result. The second result may be of independent interest.","authors_text":"Srimanta Bhattacharya, Sumanta Sarkar","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-11T11:06:14Z","title":"On Some Permutation Binomials and Trinomials Over $\\mathbb{F}_{2^n}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03375","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:eb44adef14464299b48be08fa0c65bb3b9bb595995848b092c6a38cd5918191c","target":"record","created_at":"2026-05-18T01:15:05Z","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":"c9d08ea12d5387891f58864dc360131e59b02709abb5599efb400da64007818f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-11T11:06:14Z","title_canon_sha256":"50fa92a8661cf901d14bb6981f3cf5fb6cafc942b0a10da3998d373abf3400f1"},"schema_version":"1.0","source":{"id":"1605.03375","kind":"arxiv","version":1}},"canonical_sha256":"44c5b675ee715165ce94facf9f54a8ccd1ca3cb7bccb615c317377707dcd88a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44c5b675ee715165ce94facf9f54a8ccd1ca3cb7bccb615c317377707dcd88a0","first_computed_at":"2026-05-18T01:15:05.487725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:05.487725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nJR/joeD+lTS8iwku0SoeWnDL2TmsvQoMcoZF3CHgX5d9YUM4eGFFCtHbWgxfhp2uMiVFfQX9uu4ktJW3yr+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:05.488234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.03375","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb44adef14464299b48be08fa0c65bb3b9bb595995848b092c6a38cd5918191c","sha256:b9c08fa3fd9c6f6d5832d2af2cbf5c48189424c4350ceaea89f4241533a7ca38"],"state_sha256":"751d4bb2fcafdb461aa3214fe2aa0ebadd69641412e44a7491e3f930e1c1877f"}