{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:ZMFDS4CUNXWCSMMEN5LQJGX5UP","short_pith_number":"pith:ZMFDS4CU","schema_version":"1.0","canonical_sha256":"cb0a3970546dec2931846f57049afda3f7f8201f758c7b50e71da256d8d53d61","source":{"kind":"arxiv","id":"2306.04381","version":3},"attestation_state":"computed","paper":{"title":"A Survey on the Munthe-Kaas-Wright Hopf Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Kurusch Ebrahimi-Fard, Ludwig Rahm","submitted_at":"2023-06-07T12:25:38Z","abstract_excerpt":"We survey the Munthe-Kaas--Wright Hopf algebra defined on planar rooted trees. This algebra serves a role akin to that of the Butcher--Connes--Kreimer Hopf algebra on non-planar rooted trees within the domain of numerical methods for ordinary differential equations. In the course of our presentation, we revisit Foissy's work on finite-dimensional comodules over the Butcher--Connes--Kreimer Hopf algebra and expand on his findings to include the Munthe-Kaas--Wright Hopf algebra. This involves detailing its endomorphisms and recursively constructing its primitive elements. These results are appli"},"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":"2306.04381","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-06-07T12:25:38Z","cross_cats_sorted":[],"title_canon_sha256":"90124fbed649823c00a0cbe1c386c9993b25f507bb9194814472cf0dbc4da34b","abstract_canon_sha256":"e015e700fde11b62c95c71e20fc3651be62b60fc9f72d602c2caab36f4a877af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:09:52.400325Z","signature_b64":"SI0UIGAo9FVnVR60PVUC9L42IGk0cdCBryBel+zYSzWJ8UR9sk/9ZVuk3OnOcedp2ZjM32Pj2MpnpkirjDCSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb0a3970546dec2931846f57049afda3f7f8201f758c7b50e71da256d8d53d61","last_reissued_at":"2026-07-05T09:09:52.399842Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:09:52.399842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Survey on the Munthe-Kaas-Wright Hopf Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Kurusch Ebrahimi-Fard, Ludwig Rahm","submitted_at":"2023-06-07T12:25:38Z","abstract_excerpt":"We survey the Munthe-Kaas--Wright Hopf algebra defined on planar rooted trees. This algebra serves a role akin to that of the Butcher--Connes--Kreimer Hopf algebra on non-planar rooted trees within the domain of numerical methods for ordinary differential equations. In the course of our presentation, we revisit Foissy's work on finite-dimensional comodules over the Butcher--Connes--Kreimer Hopf algebra and expand on his findings to include the Munthe-Kaas--Wright Hopf algebra. This involves detailing its endomorphisms and recursively constructing its primitive elements. These results are appli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.04381","kind":"arxiv","version":3},"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/2306.04381/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":"2306.04381","created_at":"2026-07-05T09:09:52.399892+00:00"},{"alias_kind":"arxiv_version","alias_value":"2306.04381v3","created_at":"2026-07-05T09:09:52.399892+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.04381","created_at":"2026-07-05T09:09:52.399892+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZMFDS4CUNXWC","created_at":"2026-07-05T09:09:52.399892+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZMFDS4CUNXWCSMME","created_at":"2026-07-05T09:09:52.399892+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZMFDS4CU","created_at":"2026-07-05T09:09:52.399892+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2408.01345","citing_title":"On the sub-adjacent Hopf algebra of the universal enveloping algebra of a post-Lie algebra","ref_index":17,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZMFDS4CUNXWCSMMEN5LQJGX5UP","json":"https://pith.science/pith/ZMFDS4CUNXWCSMMEN5LQJGX5UP.json","graph_json":"https://pith.science/api/pith-number/ZMFDS4CUNXWCSMMEN5LQJGX5UP/graph.json","events_json":"https://pith.science/api/pith-number/ZMFDS4CUNXWCSMMEN5LQJGX5UP/events.json","paper":"https://pith.science/paper/ZMFDS4CU"},"agent_actions":{"view_html":"https://pith.science/pith/ZMFDS4CUNXWCSMMEN5LQJGX5UP","download_json":"https://pith.science/pith/ZMFDS4CUNXWCSMMEN5LQJGX5UP.json","view_paper":"https://pith.science/paper/ZMFDS4CU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2306.04381&json=true","fetch_graph":"https://pith.science/api/pith-number/ZMFDS4CUNXWCSMMEN5LQJGX5UP/graph.json","fetch_events":"https://pith.science/api/pith-number/ZMFDS4CUNXWCSMMEN5LQJGX5UP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZMFDS4CUNXWCSMMEN5LQJGX5UP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZMFDS4CUNXWCSMMEN5LQJGX5UP/action/storage_attestation","attest_author":"https://pith.science/pith/ZMFDS4CUNXWCSMMEN5LQJGX5UP/action/author_attestation","sign_citation":"https://pith.science/pith/ZMFDS4CUNXWCSMMEN5LQJGX5UP/action/citation_signature","submit_replication":"https://pith.science/pith/ZMFDS4CUNXWCSMMEN5LQJGX5UP/action/replication_record"}},"created_at":"2026-07-05T09:09:52.399892+00:00","updated_at":"2026-07-05T09:09:52.399892+00:00"}