{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7E665LC2H77E2DZZ5FWAH64DAT","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":"abb68492bff2e592bccddf796ce78755dbc398817bd2f75b8f87afbacdeac276","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-20T14:29:58Z","title_canon_sha256":"090e3ca7e32af5f096ecb386979e65be811884561161835601941d4498fa415f"},"schema_version":"1.0","source":{"id":"1309.5282","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5282","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5282v1","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5282","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"pith_short_12","alias_value":"7E665LC2H77E","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7E665LC2H77E2DZZ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7E665LC2","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:1ab65a171d58258bca83d1b9dc8c8f354b0ca4148ffa18f428d3a9e25b8990ee","target":"graph","created_at":"2026-05-18T03:12:47Z","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 introduce a general notion of solution for a Noetherian differential $k$-algebra and study its relationship with simplicity, where k is an algebraically closed field; then we analyze conditions under which such solutions may exist and be unique, with special emphasis in the cases of k-algebras of finite type and formal series rings over k. Using that notion we generalize a criterion for simplicity due to Brumatti-Lequain-Levcovitz and give a geometric characterization of that; as an application we give a new proof of a classification theorem for local simplicity due to Hart and obtain a gen","authors_text":"Ivan Pan, Rene Baltazar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-20T14:29:58Z","title":"On solutions for derivations of a Noetherian k-algebra and local simplicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5282","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":"sha256:6f2f45b0e8513fdef9c70560bd0e79ea0f8fbb6be27f631d57f52fbc1c7077ef","target":"record","created_at":"2026-05-18T03:12:47Z","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":"abb68492bff2e592bccddf796ce78755dbc398817bd2f75b8f87afbacdeac276","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-20T14:29:58Z","title_canon_sha256":"090e3ca7e32af5f096ecb386979e65be811884561161835601941d4498fa415f"},"schema_version":"1.0","source":{"id":"1309.5282","kind":"arxiv","version":1}},"canonical_sha256":"f93deeac5a3ffe4d0f39e96c03fb8304f5eba84346c31e90dedb224ee757d413","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f93deeac5a3ffe4d0f39e96c03fb8304f5eba84346c31e90dedb224ee757d413","first_computed_at":"2026-05-18T03:12:47.105645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:47.105645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6w/0XgvfXQXvL29BPD/D5ZUjAxGNruBjsGdbEWy7q1bQ8I+s59lK/UT4M0N+IjzRXEOCUEJ1t6g0+1G5mF3BBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:47.106113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5282","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f2f45b0e8513fdef9c70560bd0e79ea0f8fbb6be27f631d57f52fbc1c7077ef","sha256:1ab65a171d58258bca83d1b9dc8c8f354b0ca4148ffa18f428d3a9e25b8990ee"],"state_sha256":"da97f02f8a604fff7ff4b42bb4e066eb907feb541d07c31cc8dc7bab5838fb35"}