{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KF5RILH5HTITQS7JPP33GXP54C","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":"eb88c083b3f29d4e6f7e3246a2898497de7bd9936433457d0cb130a91a191a65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-02-08T21:04:00Z","title_canon_sha256":"64f2e65b93b551cc28cb4e0af4fee49a2180f31546557837ef8961943b6efbc7"},"schema_version":"1.0","source":{"id":"1402.1890","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.1890","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1402.1890v4","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1890","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"KF5RILH5HTIT","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KF5RILH5HTITQS7J","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KF5RILH5","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:86f9d43addeeecaeb68077518d91f91bc33c8a9226131d8651bae529b5984658","target":"graph","created_at":"2026-05-18T01:30:15Z","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":"The notion of commutative integro-differential algebra was introduced for the algebraic study of boundary problems for linear ordinary differential equations. Its noncommutative analog achieves a similar purpose for linear systems of such equations. In both cases, free objects are crucial for analyzing the underlying algebraic structures, e.g. of the (matrix) functions. In this paper we apply the method of Gr\\\"obner-Shirshov bases to construct the free (noncommutative) integro-differential algebra on a set. The construction is from the free Rota-Baxter algebra on the free differential algebra ","authors_text":"Li Guo, Markus Rosenkranz, Xing Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-02-08T21:04:00Z","title":"Free integro-differential algebras and Gr\\\"obner-Shirshov bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1890","kind":"arxiv","version":4},"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":"sha256:78c34ae34119364a5bf7c60ef3d4c3983443e97cdd8ea4d62e5073a1ca38826a","target":"record","created_at":"2026-05-18T01:30:15Z","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":"eb88c083b3f29d4e6f7e3246a2898497de7bd9936433457d0cb130a91a191a65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-02-08T21:04:00Z","title_canon_sha256":"64f2e65b93b551cc28cb4e0af4fee49a2180f31546557837ef8961943b6efbc7"},"schema_version":"1.0","source":{"id":"1402.1890","kind":"arxiv","version":4}},"canonical_sha256":"517b142cfd3cd1384be97bf7b35dfde09eab33144f672c0403187d87fab287a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"517b142cfd3cd1384be97bf7b35dfde09eab33144f672c0403187d87fab287a8","first_computed_at":"2026-05-18T01:30:15.642731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:15.642731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b0JRiPqWx7p/nQUiEEQyHmYj9isxunoiN1owGerSDh4BS58WjdXXe07Tu9MMR1TZCrrjTxKYJ4UX3NceasOrAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:15.643472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.1890","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78c34ae34119364a5bf7c60ef3d4c3983443e97cdd8ea4d62e5073a1ca38826a","sha256:86f9d43addeeecaeb68077518d91f91bc33c8a9226131d8651bae529b5984658"],"state_sha256":"405a8678a01758d8ac1c738d93df641c403e102c51d9aa0e1596d67866affe07"}