{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AO3KOKONUBIREBZ2NXSXWZ6TED","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":"e45afb69c9e8a07e70990d68c17086e927805a660c35ce78bd5da8e06f6275b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-08T16:08:43Z","title_canon_sha256":"467874026e87f54fef4ab1d94ab3d825ff1ff3d45ab51c119e07593227d0658d"},"schema_version":"1.0","source":{"id":"1304.2254","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2254","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2254v1","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2254","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"pith_short_12","alias_value":"AO3KOKONUBIR","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AO3KOKONUBIREBZ2","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AO3KOKON","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:3e952072eb796bc5f788b97ae8cf93fd9f81432cbba3f58d5465f4227476ecac","target":"graph","created_at":"2026-05-18T03:28:43Z","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 $k$ be a positive integer and $S_{2k}={\\tt x}+{\\tt x}^4+...+{\\tt x}^{4^{2k-1}}\\in\\Bbb F_2[{\\tt x}]$. It was recently conjectured that ${\\tt x}+S_{2k}^{4^{2k}}+S_{2k}^{4^k+3}$ is a permutation polynomial of $\\Bbb F_{4^{3k}}$. In this note, the conjecture is confirmed and a generalization is obtained.","authors_text":"Xiang-dong Hou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-08T16:08:43Z","title":"Proof of a Conjecture on Permutation Polynomials over Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2254","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":"sha256:37bdd566d870aeb429a7cf239d25ac0e8a9359c0e1c3f12b30b643deafe247f7","target":"record","created_at":"2026-05-18T03:28:43Z","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":"e45afb69c9e8a07e70990d68c17086e927805a660c35ce78bd5da8e06f6275b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-08T16:08:43Z","title_canon_sha256":"467874026e87f54fef4ab1d94ab3d825ff1ff3d45ab51c119e07593227d0658d"},"schema_version":"1.0","source":{"id":"1304.2254","kind":"arxiv","version":1}},"canonical_sha256":"03b6a729cda05112073a6de57b67d320de469d0fb4615c49a84d7b772cc224eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03b6a729cda05112073a6de57b67d320de469d0fb4615c49a84d7b772cc224eb","first_computed_at":"2026-05-18T03:28:43.587670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:43.587670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lGDD5Orb4cqCB/zyeJChvSCIn+dbELRbfb7uC1g0woWZEegQZ8vGLlzU+UA0cKi5CO+2c/8vSUuFszgtMZqnCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:43.588260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2254","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37bdd566d870aeb429a7cf239d25ac0e8a9359c0e1c3f12b30b643deafe247f7","sha256:3e952072eb796bc5f788b97ae8cf93fd9f81432cbba3f58d5465f4227476ecac"],"state_sha256":"e7d7072ed5ace492ec8be75a709383135ff53b5045c844ba1c65da9b279c2775"}