{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:YMMLPLBHVTCAPTVTTJFJG3ULCL","short_pith_number":"pith:YMMLPLBH","canonical_record":{"source":{"id":"2503.21855","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-27T17:20:10Z","cross_cats_sorted":["cs.NA","math.CO","math.PR"],"title_canon_sha256":"c7a61c3d10f0eccd7e19ea76214545a77b7c9c7b7e29f578f80f3a1fcdb1df44","abstract_canon_sha256":"5f06a51a02306397d213766687adec36593d28c63c3b6a518a79799c67f7bcb1"},"schema_version":"1.0"},"canonical_sha256":"c318b7ac27acc407ceb39a4a936e8b12dc11df07dde74db7b31d4f7db0236e47","source":{"kind":"arxiv","id":"2503.21855","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.21855","created_at":"2026-07-05T11:23:26Z"},{"alias_kind":"arxiv_version","alias_value":"2503.21855v2","created_at":"2026-07-05T11:23:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.21855","created_at":"2026-07-05T11:23:26Z"},{"alias_kind":"pith_short_12","alias_value":"YMMLPLBHVTCA","created_at":"2026-07-05T11:23:26Z"},{"alias_kind":"pith_short_16","alias_value":"YMMLPLBHVTCAPTVT","created_at":"2026-07-05T11:23:26Z"},{"alias_kind":"pith_short_8","alias_value":"YMMLPLBH","created_at":"2026-07-05T11:23:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:YMMLPLBHVTCAPTVTTJFJG3ULCL","target":"record","payload":{"canonical_record":{"source":{"id":"2503.21855","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-27T17:20:10Z","cross_cats_sorted":["cs.NA","math.CO","math.PR"],"title_canon_sha256":"c7a61c3d10f0eccd7e19ea76214545a77b7c9c7b7e29f578f80f3a1fcdb1df44","abstract_canon_sha256":"5f06a51a02306397d213766687adec36593d28c63c3b6a518a79799c67f7bcb1"},"schema_version":"1.0"},"canonical_sha256":"c318b7ac27acc407ceb39a4a936e8b12dc11df07dde74db7b31d4f7db0236e47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:23:26.212997Z","signature_b64":"ZYUdujuk1b2bUUqywAPuPpg4LK/IyXryEoeS1vupO/4WLm/Sc+j6EUF34jre3SWV59ONgGWjjLDm8aw+MjtWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c318b7ac27acc407ceb39a4a936e8b12dc11df07dde74db7b31d4f7db0236e47","last_reissued_at":"2026-07-05T11:23:26.212375Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:23:26.212375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.21855","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:23:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"At636TdCiZg/5hnddkzVGFSXm3zytsEwdI0jeSDT5Ip3yHmz4nXFxcpVmstzPCMBxRNvTIecOtbOkz1LF5wsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:51:08.107834Z"},"content_sha256":"0d3aa5ee1f39e6d8f7d954cd133ad1535e868fcc8accf300407f69fde594ea1a","schema_version":"1.0","event_id":"sha256:0d3aa5ee1f39e6d8f7d954cd133ad1535e868fcc8accf300407f69fde594ea1a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:YMMLPLBHVTCAPTVTTJFJG3ULCL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"High order integration of stochastic dynamics on Riemannian manifolds with frozen flow methods","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.CO","math.PR"],"primary_cat":"math.NA","authors_text":"Adrien Busnot Laurent, Baptiste Huguet, Eugen Bronasco","submitted_at":"2025-03-27T17:20:10Z","abstract_excerpt":"We present a new class of numerical methods for solving stochastic differential equations with additive noise on general Riemannian manifolds with high weak order of accuracy. In opposition to the popular approach with projection methods, the proposed methods are intrinsic: they only rely on geometric operations and avoid coordinates and embeddings. We provide a robust and general convergence analysis and an algebraic formalism of exotic planar Butcher series for the computation of order conditions at any high order. To illustrate the methodology, an explicit method of second weak order is int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.21855","kind":"arxiv","version":2},"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/2503.21855/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:23:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dsfARyk0Siqj4A4ZQmqa10sapLK0xkN7LRR6cuKhbK1mxjDGCGffHtPbV/6xl9joBQrVVrLKKV5osSUPeJjNDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:51:08.108549Z"},"content_sha256":"9d4df28cce1be10d3be61a1d9093449600ddcf1da1579580b08a648644816567","schema_version":"1.0","event_id":"sha256:9d4df28cce1be10d3be61a1d9093449600ddcf1da1579580b08a648644816567"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YMMLPLBHVTCAPTVTTJFJG3ULCL/bundle.json","state_url":"https://pith.science/pith/YMMLPLBHVTCAPTVTTJFJG3ULCL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YMMLPLBHVTCAPTVTTJFJG3ULCL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T20:51:08Z","links":{"resolver":"https://pith.science/pith/YMMLPLBHVTCAPTVTTJFJG3ULCL","bundle":"https://pith.science/pith/YMMLPLBHVTCAPTVTTJFJG3ULCL/bundle.json","state":"https://pith.science/pith/YMMLPLBHVTCAPTVTTJFJG3ULCL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YMMLPLBHVTCAPTVTTJFJG3ULCL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YMMLPLBHVTCAPTVTTJFJG3ULCL","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":"5f06a51a02306397d213766687adec36593d28c63c3b6a518a79799c67f7bcb1","cross_cats_sorted":["cs.NA","math.CO","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-27T17:20:10Z","title_canon_sha256":"c7a61c3d10f0eccd7e19ea76214545a77b7c9c7b7e29f578f80f3a1fcdb1df44"},"schema_version":"1.0","source":{"id":"2503.21855","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.21855","created_at":"2026-07-05T11:23:26Z"},{"alias_kind":"arxiv_version","alias_value":"2503.21855v2","created_at":"2026-07-05T11:23:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.21855","created_at":"2026-07-05T11:23:26Z"},{"alias_kind":"pith_short_12","alias_value":"YMMLPLBHVTCA","created_at":"2026-07-05T11:23:26Z"},{"alias_kind":"pith_short_16","alias_value":"YMMLPLBHVTCAPTVT","created_at":"2026-07-05T11:23:26Z"},{"alias_kind":"pith_short_8","alias_value":"YMMLPLBH","created_at":"2026-07-05T11:23:26Z"}],"graph_snapshots":[{"event_id":"sha256:9d4df28cce1be10d3be61a1d9093449600ddcf1da1579580b08a648644816567","target":"graph","created_at":"2026-07-05T11:23:26Z","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/2503.21855/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a new class of numerical methods for solving stochastic differential equations with additive noise on general Riemannian manifolds with high weak order of accuracy. In opposition to the popular approach with projection methods, the proposed methods are intrinsic: they only rely on geometric operations and avoid coordinates and embeddings. We provide a robust and general convergence analysis and an algebraic formalism of exotic planar Butcher series for the computation of order conditions at any high order. To illustrate the methodology, an explicit method of second weak order is int","authors_text":"Adrien Busnot Laurent, Baptiste Huguet, Eugen Bronasco","cross_cats":["cs.NA","math.CO","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-27T17:20:10Z","title":"High order integration of stochastic dynamics on Riemannian manifolds with frozen flow methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.21855","kind":"arxiv","version":2},"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":"sha256:0d3aa5ee1f39e6d8f7d954cd133ad1535e868fcc8accf300407f69fde594ea1a","target":"record","created_at":"2026-07-05T11:23:26Z","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":"5f06a51a02306397d213766687adec36593d28c63c3b6a518a79799c67f7bcb1","cross_cats_sorted":["cs.NA","math.CO","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-27T17:20:10Z","title_canon_sha256":"c7a61c3d10f0eccd7e19ea76214545a77b7c9c7b7e29f578f80f3a1fcdb1df44"},"schema_version":"1.0","source":{"id":"2503.21855","kind":"arxiv","version":2}},"canonical_sha256":"c318b7ac27acc407ceb39a4a936e8b12dc11df07dde74db7b31d4f7db0236e47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c318b7ac27acc407ceb39a4a936e8b12dc11df07dde74db7b31d4f7db0236e47","first_computed_at":"2026-07-05T11:23:26.212375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:23:26.212375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZYUdujuk1b2bUUqywAPuPpg4LK/IyXryEoeS1vupO/4WLm/Sc+j6EUF34jre3SWV59ONgGWjjLDm8aw+MjtWAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:23:26.212997Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.21855","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d3aa5ee1f39e6d8f7d954cd133ad1535e868fcc8accf300407f69fde594ea1a","sha256:9d4df28cce1be10d3be61a1d9093449600ddcf1da1579580b08a648644816567"],"state_sha256":"837e126390b50225e540df718b2786d8a3e823fc9051c72150c518a439f28372"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OrW0x2Jx1RsRbfRHo2bE/NGJcgEUYsLVu7lhqNUvChLdSwk41nZcvBlueXUWvU+O67ARxMHDLXLwL0XRVBcgAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T20:51:08.115358Z","bundle_sha256":"d63965aa7fa1f7d158ba191003c4049ff8c42b9cda6aaf70670e3d967ab69b7f"}}