{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:GB4PIEN7KDA44VFQXHM724NUHT","short_pith_number":"pith:GB4PIEN7","schema_version":"1.0","canonical_sha256":"3078f411bf50c1ce54b0b9d9fd71b43cdca12713afb74e123146e0a4924b780a","source":{"kind":"arxiv","id":"1407.5306","version":1},"attestation_state":"computed","paper":{"title":"Rota-Baxter operators on the polynomial algebras, integration and averaging operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CA"],"primary_cat":"math.RA","authors_text":"Li Guo, Markus Rosenkranz, Shanghua Zheng","submitted_at":"2014-07-20T16:33:31Z","abstract_excerpt":"Rota-Baxter operators are an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota-Baxter operators and integrals in the case of the polynomial algebra $\\mathbf{k}[x]$. We consider two classes of Rota-Baxter operators, monomial ones and injective ones. For the first class, we apply averaging operators to determine monomial Rota-Baxter operators. For the second class, we make use of the double product on Rota-Baxter algebras."},"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":"1407.5306","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-07-20T16:33:31Z","cross_cats_sorted":["math.AC","math.CA"],"title_canon_sha256":"021c09c8be675f6eed4313e41d9185eb5ce4d2cef4539dc2fceb7c13ba27ca41","abstract_canon_sha256":"a886a6339376b05a3546a1940ba68e1a9fffb1f5673ae5fa02014ac9ccb4cabb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:21.973602Z","signature_b64":"k/ymyWNZ/IoVUtBVwEyUzeWcWwugKtQY3RD5xOe0LtFJ7ZIyuCEwgkHV6URzhOzwkJi2NSkneTxnGg/55LkSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3078f411bf50c1ce54b0b9d9fd71b43cdca12713afb74e123146e0a4924b780a","last_reissued_at":"2026-05-18T01:22:21.972914Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:21.972914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rota-Baxter operators on the polynomial algebras, integration and averaging operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CA"],"primary_cat":"math.RA","authors_text":"Li Guo, Markus Rosenkranz, Shanghua Zheng","submitted_at":"2014-07-20T16:33:31Z","abstract_excerpt":"Rota-Baxter operators are an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota-Baxter operators and integrals in the case of the polynomial algebra $\\mathbf{k}[x]$. We consider two classes of Rota-Baxter operators, monomial ones and injective ones. For the first class, we apply averaging operators to determine monomial Rota-Baxter operators. For the second class, we make use of the double product on Rota-Baxter algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5306","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":""},"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":"1407.5306","created_at":"2026-05-18T01:22:21.973039+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.5306v1","created_at":"2026-05-18T01:22:21.973039+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5306","created_at":"2026-05-18T01:22:21.973039+00:00"},{"alias_kind":"pith_short_12","alias_value":"GB4PIEN7KDA4","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"GB4PIEN7KDA44VFQ","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"GB4PIEN7","created_at":"2026-05-18T12:28:30.664211+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GB4PIEN7KDA44VFQXHM724NUHT","json":"https://pith.science/pith/GB4PIEN7KDA44VFQXHM724NUHT.json","graph_json":"https://pith.science/api/pith-number/GB4PIEN7KDA44VFQXHM724NUHT/graph.json","events_json":"https://pith.science/api/pith-number/GB4PIEN7KDA44VFQXHM724NUHT/events.json","paper":"https://pith.science/paper/GB4PIEN7"},"agent_actions":{"view_html":"https://pith.science/pith/GB4PIEN7KDA44VFQXHM724NUHT","download_json":"https://pith.science/pith/GB4PIEN7KDA44VFQXHM724NUHT.json","view_paper":"https://pith.science/paper/GB4PIEN7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.5306&json=true","fetch_graph":"https://pith.science/api/pith-number/GB4PIEN7KDA44VFQXHM724NUHT/graph.json","fetch_events":"https://pith.science/api/pith-number/GB4PIEN7KDA44VFQXHM724NUHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GB4PIEN7KDA44VFQXHM724NUHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GB4PIEN7KDA44VFQXHM724NUHT/action/storage_attestation","attest_author":"https://pith.science/pith/GB4PIEN7KDA44VFQXHM724NUHT/action/author_attestation","sign_citation":"https://pith.science/pith/GB4PIEN7KDA44VFQXHM724NUHT/action/citation_signature","submit_replication":"https://pith.science/pith/GB4PIEN7KDA44VFQXHM724NUHT/action/replication_record"}},"created_at":"2026-05-18T01:22:21.973039+00:00","updated_at":"2026-05-18T01:22:21.973039+00:00"}