{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:TU56DH6B25FAYASBZF4VVPT7CP","short_pith_number":"pith:TU56DH6B","schema_version":"1.0","canonical_sha256":"9d3be19fc1d74a0c0241c9795abe7f13c327ab2c8e7d7e6c906392311751be8a","source":{"kind":"arxiv","id":"2411.02633","version":1},"attestation_state":"computed","paper":{"title":"Generalized Reynolds algebras from Volterra integrals and their free construction by complete shuffle product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.RA","authors_text":"Li Guo, Richard Gustavson, Yunnan Li","submitted_at":"2024-11-04T21:49:49Z","abstract_excerpt":"This paper introduces algebraic structures for Volterra integral operators with separable kernels, in the style of differential algebra for derivations and Rota-Baxter algebra for operators with kernels dependent solely on a dummy variable. We demonstrate that these operators satisfy a generalization of the algebraic identity defining the classical Reynolds operator, which is rooted in Reynolds's influential work on fluid mechanics.\n  To study Volterra integral operators and their integral equations through this algebraic lens, particularly in providing a general form of these integral equatio"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2411.02633","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2024-11-04T21:49:49Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"bc05f7bd53d68bd3f5a1f270f4cc00467dca40aa7b05b5edd0cbe10c14debdf9","abstract_canon_sha256":"da9c704859e04b23fff26e03c5d8219483a343233197c3d16d93d631e545a27f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:31:15.052070Z","signature_b64":"0JBRQf0+Xd7KdjlKdbCR7ITklHzqH1uAS/jA32mVdFfPXQNiwXeHVBoU+5ETxUYLcH4pdRFYwqHPEvKu2VGgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d3be19fc1d74a0c0241c9795abe7f13c327ab2c8e7d7e6c906392311751be8a","last_reissued_at":"2026-07-05T09:31:15.051614Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:31:15.051614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Reynolds algebras from Volterra integrals and their free construction by complete shuffle product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.RA","authors_text":"Li Guo, Richard Gustavson, Yunnan Li","submitted_at":"2024-11-04T21:49:49Z","abstract_excerpt":"This paper introduces algebraic structures for Volterra integral operators with separable kernels, in the style of differential algebra for derivations and Rota-Baxter algebra for operators with kernels dependent solely on a dummy variable. We demonstrate that these operators satisfy a generalization of the algebraic identity defining the classical Reynolds operator, which is rooted in Reynolds's influential work on fluid mechanics.\n  To study Volterra integral operators and their integral equations through this algebraic lens, particularly in providing a general form of these integral equatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.02633","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.02633/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2411.02633","created_at":"2026-07-05T09:31:15.051673+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.02633v1","created_at":"2026-07-05T09:31:15.051673+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.02633","created_at":"2026-07-05T09:31:15.051673+00:00"},{"alias_kind":"pith_short_12","alias_value":"TU56DH6B25FA","created_at":"2026-07-05T09:31:15.051673+00:00"},{"alias_kind":"pith_short_16","alias_value":"TU56DH6B25FAYASB","created_at":"2026-07-05T09:31:15.051673+00:00"},{"alias_kind":"pith_short_8","alias_value":"TU56DH6B","created_at":"2026-07-05T09:31:15.051673+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.07009","citing_title":"Species of Rota-Baxter algebras by rooted trees, twisted bialgebras and Fock functors","ref_index":28,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TU56DH6B25FAYASBZF4VVPT7CP","json":"https://pith.science/pith/TU56DH6B25FAYASBZF4VVPT7CP.json","graph_json":"https://pith.science/api/pith-number/TU56DH6B25FAYASBZF4VVPT7CP/graph.json","events_json":"https://pith.science/api/pith-number/TU56DH6B25FAYASBZF4VVPT7CP/events.json","paper":"https://pith.science/paper/TU56DH6B"},"agent_actions":{"view_html":"https://pith.science/pith/TU56DH6B25FAYASBZF4VVPT7CP","download_json":"https://pith.science/pith/TU56DH6B25FAYASBZF4VVPT7CP.json","view_paper":"https://pith.science/paper/TU56DH6B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.02633&json=true","fetch_graph":"https://pith.science/api/pith-number/TU56DH6B25FAYASBZF4VVPT7CP/graph.json","fetch_events":"https://pith.science/api/pith-number/TU56DH6B25FAYASBZF4VVPT7CP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TU56DH6B25FAYASBZF4VVPT7CP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TU56DH6B25FAYASBZF4VVPT7CP/action/storage_attestation","attest_author":"https://pith.science/pith/TU56DH6B25FAYASBZF4VVPT7CP/action/author_attestation","sign_citation":"https://pith.science/pith/TU56DH6B25FAYASBZF4VVPT7CP/action/citation_signature","submit_replication":"https://pith.science/pith/TU56DH6B25FAYASBZF4VVPT7CP/action/replication_record"}},"created_at":"2026-07-05T09:31:15.051673+00:00","updated_at":"2026-07-05T09:31:15.051673+00:00"}