{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NW2OKZODMUJ2HTWVZGPKYGDOOO","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":"fa8f01bda03dae0491e5ef9918b6b95c89490e9c1d240a9ce8f29ff2ca280d09","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-05-02T09:39:38Z","title_canon_sha256":"a1ddd0a0b03d9d5aed52b8b1b81618609a975ebb1ecbd654d3a41397fee8cb7e"},"schema_version":"1.0","source":{"id":"1305.0380","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0380","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0380v1","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0380","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"pith_short_12","alias_value":"NW2OKZODMUJ2","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NW2OKZODMUJ2HTWV","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NW2OKZOD","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:d1672da1aee222a2f5323d0598f0ac124c97baa4da2996aa8bcda3d1e420e0ad","target":"graph","created_at":"2026-05-18T01:24:11Z","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":"We prove some algebraic results on the ring of matrix differential operators over a differential field in the generality of non-commutative principal ideal rings. These results are used in the theory of non-local Poisson structures.","authors_text":"Alberto De Sole, Sylvain Carpentier, Victor G. Kac","cross_cats":["math-ph","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-05-02T09:39:38Z","title":"Some remarks on non-commutative principal ideal rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0380","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":"sha256:1439a6e7499c52e82e9e798b94dc68bc4713c9453bbf93479cacce12a32ccc09","target":"record","created_at":"2026-05-18T01:24:11Z","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":"fa8f01bda03dae0491e5ef9918b6b95c89490e9c1d240a9ce8f29ff2ca280d09","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-05-02T09:39:38Z","title_canon_sha256":"a1ddd0a0b03d9d5aed52b8b1b81618609a975ebb1ecbd654d3a41397fee8cb7e"},"schema_version":"1.0","source":{"id":"1305.0380","kind":"arxiv","version":1}},"canonical_sha256":"6db4e565c36513a3ced5c99eac186e739a46d868c0cadfdf3afefcaeb3e95299","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6db4e565c36513a3ced5c99eac186e739a46d868c0cadfdf3afefcaeb3e95299","first_computed_at":"2026-05-18T01:24:11.445618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:11.445618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fhTPxBMCYHLvUFVpcedqaHhlcMd8TJJse1Y8MGLee7IdnA/EsacN8W0ZMivtu28Q38Gt+JRIdcdYVT2XlxwFCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:11.446195Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0380","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1439a6e7499c52e82e9e798b94dc68bc4713c9453bbf93479cacce12a32ccc09","sha256:d1672da1aee222a2f5323d0598f0ac124c97baa4da2996aa8bcda3d1e420e0ad"],"state_sha256":"7b3b89e6daec12e821b87cac2a3317e93f2b66e0b6d45c6887169e68aa232d63"}