{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ZMFDS4CUNXWCSMMEN5LQJGX5UP","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":"e015e700fde11b62c95c71e20fc3651be62b60fc9f72d602c2caab36f4a877af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-06-07T12:25:38Z","title_canon_sha256":"90124fbed649823c00a0cbe1c386c9993b25f507bb9194814472cf0dbc4da34b"},"schema_version":"1.0","source":{"id":"2306.04381","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.04381","created_at":"2026-07-05T09:09:52Z"},{"alias_kind":"arxiv_version","alias_value":"2306.04381v3","created_at":"2026-07-05T09:09:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.04381","created_at":"2026-07-05T09:09:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZMFDS4CUNXWC","created_at":"2026-07-05T09:09:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZMFDS4CUNXWCSMME","created_at":"2026-07-05T09:09:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZMFDS4CU","created_at":"2026-07-05T09:09:52Z"}],"graph_snapshots":[{"event_id":"sha256:238942eaa6ed8bb1be56f785a3affbb532cefd4cc3248501491152f6d0731373","target":"graph","created_at":"2026-07-05T09:09:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2306.04381/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Kurusch Ebrahimi-Fard, Ludwig Rahm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-06-07T12:25:38Z","title":"A Survey on the Munthe-Kaas-Wright Hopf Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.04381","kind":"arxiv","version":3},"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:bcd301cc2424a9c21d1de69c434774281fa7a076ada4fe5bdc7f997ecdcae174","target":"record","created_at":"2026-07-05T09:09:52Z","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":"e015e700fde11b62c95c71e20fc3651be62b60fc9f72d602c2caab36f4a877af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-06-07T12:25:38Z","title_canon_sha256":"90124fbed649823c00a0cbe1c386c9993b25f507bb9194814472cf0dbc4da34b"},"schema_version":"1.0","source":{"id":"2306.04381","kind":"arxiv","version":3}},"canonical_sha256":"cb0a3970546dec2931846f57049afda3f7f8201f758c7b50e71da256d8d53d61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb0a3970546dec2931846f57049afda3f7f8201f758c7b50e71da256d8d53d61","first_computed_at":"2026-07-05T09:09:52.399842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:09:52.399842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SI0UIGAo9FVnVR60PVUC9L42IGk0cdCBryBel+zYSzWJ8UR9sk/9ZVuk3OnOcedp2ZjM32Pj2MpnpkirjDCSAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:09:52.400325Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.04381","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcd301cc2424a9c21d1de69c434774281fa7a076ada4fe5bdc7f997ecdcae174","sha256:238942eaa6ed8bb1be56f785a3affbb532cefd4cc3248501491152f6d0731373"],"state_sha256":"a44787a173cd5a9519d25d57bcd29156213e59c736477b94511eb68c8b604047"}