{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LY7IE6HDIDIE63OMFEV55LERZ5","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":"2a45d34735c43a3c172f821ecd299e0461db781b2c2ee6c1db6ed71c67040adb","cross_cats_sorted":["math.AC","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-12-03T00:47:03Z","title_canon_sha256":"10d7c2e8ecdae033808ba9f7615a110192f1e11346e18dc7270bb60d02e35be8"},"schema_version":"1.0","source":{"id":"1212.0266","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0266","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0266v1","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0266","created_at":"2026-05-18T02:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"LY7IE6HDIDIE","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LY7IE6HDIDIE63OM","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LY7IE6HD","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:dbf4248598827308e6cd3722477293d5f6ee6a7823b9e44c9701f6f48404bb22","target":"graph","created_at":"2026-05-18T02:50:13Z","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 concept of integro-differential algebra has been introduced recently in the study of boundary problems of differential equations. We generalize this concept to that of integro-differential algebra with a weight, in analogy to the differential Rota-Baxter algebra. We construct free commutative integro-differential algebras with weight generated by a base differential algebra. This in particular gives an explicit construction of the integro-differential algebra on one generator. Properties of these free objects are studied.","authors_text":"Georg Regensburger, Li Guo, Markus Rosenkranz","cross_cats":["math.AC","math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-12-03T00:47:03Z","title":"On Integro-Differential Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0266","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:dcb13c583c978162ffe76395d787f46de9f99985f777adfecc5df0125b52d414","target":"record","created_at":"2026-05-18T02:50:13Z","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":"2a45d34735c43a3c172f821ecd299e0461db781b2c2ee6c1db6ed71c67040adb","cross_cats_sorted":["math.AC","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-12-03T00:47:03Z","title_canon_sha256":"10d7c2e8ecdae033808ba9f7615a110192f1e11346e18dc7270bb60d02e35be8"},"schema_version":"1.0","source":{"id":"1212.0266","kind":"arxiv","version":1}},"canonical_sha256":"5e3e8278e340d04f6dcc292bdeac91cf724544fe338be74f3c02f5e438277b34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e3e8278e340d04f6dcc292bdeac91cf724544fe338be74f3c02f5e438277b34","first_computed_at":"2026-05-18T02:50:13.611011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:13.611011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D8yLMqeHTpsTXEbA8AusMU5Ts9UZi825I47Mb/wycLJ+BC6tsNSbPGbFIxFZvWYHBZcKmxKSgYWnM+sUGNiACw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:13.611735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0266","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcb13c583c978162ffe76395d787f46de9f99985f777adfecc5df0125b52d414","sha256:dbf4248598827308e6cd3722477293d5f6ee6a7823b9e44c9701f6f48404bb22"],"state_sha256":"8bbc5ab92dc1de04b73b5d682fa7d1fe0f9a602ae3175d59a3ff1fc26fe95ff4"}