{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:P5ABEDNVJUAJ62TSWSAMRL2ZEN","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":"66654b1ed386b294aab5f544b9a2b5828ef1fcf50b59c3a135b4a723967f7605","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-02-04T22:00:29Z","title_canon_sha256":"cc1712f95636bc5c9036563fb9c185adade0c4f1e97463df245cae073bcde5db"},"schema_version":"1.0","source":{"id":"1402.0896","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0896","created_at":"2026-05-18T03:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0896v1","created_at":"2026-05-18T03:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0896","created_at":"2026-05-18T03:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"P5ABEDNVJUAJ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"P5ABEDNVJUAJ62TS","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"P5ABEDNV","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:aedfe090fb9b6ce7bb3d138e57fdd766a4d8a4e62dd38f50f3c65d14e93b8ee9","target":"graph","created_at":"2026-05-18T03:00:02Z","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 reprove two results of Saltman, Theorem 5.1 and Corollary 5.2 of [Sa07]: If F is the function field of a smooth p-adic curve and D is an F-division algebra of prime degree l\\neq p, then D is Z/l-cyclic, and that if D is an F-division algebra of prime period l\\neq p then D has index l if and only if its ramification locus on a suitable 2-dimensional model forF has no \"hot points\".","authors_text":"Eric Brussel","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-02-04T22:00:29Z","title":"Division Algebra Cyclicity in Prime Degree over a p-Adic Curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0896","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":"sha256:6dfdf59870fac16bb878a90e2154028cc45c0131a7694dadd26c04028d288132","target":"record","created_at":"2026-05-18T03:00:02Z","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":"66654b1ed386b294aab5f544b9a2b5828ef1fcf50b59c3a135b4a723967f7605","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-02-04T22:00:29Z","title_canon_sha256":"cc1712f95636bc5c9036563fb9c185adade0c4f1e97463df245cae073bcde5db"},"schema_version":"1.0","source":{"id":"1402.0896","kind":"arxiv","version":1}},"canonical_sha256":"7f40120db54d009f6a72b480c8af59237ccc81285efcebd0b9bafb06dbb86dc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f40120db54d009f6a72b480c8af59237ccc81285efcebd0b9bafb06dbb86dc0","first_computed_at":"2026-05-18T03:00:02.390366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:02.390366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xN9ch8oLL9fsUnXi/rtVHIx6I0Higs2UIJUcwiOfLHoNdqpc6DmmMTYZcH07tGPR+TBdrkYfCnGZEoMKy27fBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:02.391276Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0896","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dfdf59870fac16bb878a90e2154028cc45c0131a7694dadd26c04028d288132","sha256:aedfe090fb9b6ce7bb3d138e57fdd766a4d8a4e62dd38f50f3c65d14e93b8ee9"],"state_sha256":"725ffaec374bf182bd19485155057dbd7b092d9306a643686f86cf86de7ddf1a"}