{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:N7FM7243SIKEFAUTK5AAGMMC2R","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":"78018fb04db351e1f3b5d5cc2da355cf2d2fa637c373fe204b7f7e3c781361bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-06T23:25:38Z","title_canon_sha256":"c6462186ad1580c97efb1bdeedc45be40687a604f255ad89053b4d40f14bc35c"},"schema_version":"1.0","source":{"id":"1310.1645","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1645","created_at":"2026-05-18T03:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1645v1","created_at":"2026-05-18T03:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1645","created_at":"2026-05-18T03:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"N7FM7243SIKE","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"N7FM7243SIKEFAUT","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"N7FM7243","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:b29ab1dd33e8fee6af894950ff328793aae037a71fedb7d9ea5d3f324277a472","target":"graph","created_at":"2026-05-18T03:11:11Z","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 $q$ be a power of a prime number $p$, $k=\\mathbb{F}_{q}(t)$ be the rational function field over finite field $\\mathbb{F}_{q}$ and $K/k$ be a multi-cyclic extension of prime degree. In this paper we will give an exact formula for the degree of $K$ over $k$ by considering both Kummer and Artin-Schreier cases.","authors_text":"Su Hu, Yan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-06T23:25:38Z","title":"On the exact degree of multi-cyclic extension of $\\mathbb{F}_{q}(t)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1645","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:c255eacb10412231f1371688d664c29cbcf233696abe9275e1a180081faa86f2","target":"record","created_at":"2026-05-18T03:11:11Z","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":"78018fb04db351e1f3b5d5cc2da355cf2d2fa637c373fe204b7f7e3c781361bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-06T23:25:38Z","title_canon_sha256":"c6462186ad1580c97efb1bdeedc45be40687a604f255ad89053b4d40f14bc35c"},"schema_version":"1.0","source":{"id":"1310.1645","kind":"arxiv","version":1}},"canonical_sha256":"6fcacfeb9b92144282935740033182d474d8984cb8bd0583d55eadd4fa8b10b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fcacfeb9b92144282935740033182d474d8984cb8bd0583d55eadd4fa8b10b8","first_computed_at":"2026-05-18T03:11:11.119377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:11.119377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EdxYm5JsULfvtLOkaAwtAMFVMxG7z8NTZHQB7WtI3+Qw6qcGrMPfbl3urfNvREnfiCV+5/W10Ggjr9H7mEYcCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:11.120126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1645","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c255eacb10412231f1371688d664c29cbcf233696abe9275e1a180081faa86f2","sha256:b29ab1dd33e8fee6af894950ff328793aae037a71fedb7d9ea5d3f324277a472"],"state_sha256":"4935e2ec808ca182ebd154d73d339d2169da0a5465e2ba71631ac5f60860e5dd"}