{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XO3M7CK2ZP7UZHFKGC5AZV2LVD","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":"a369647d0073434fbe7a4ab3d780b3204cd49e26e8dd582930c35c2a73d80296","cross_cats_sorted":["cs.LG","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2013-06-03T06:56:47Z","title_canon_sha256":"17b0d2a9971cf323746df5bd934cb223e5b371989ad1b59c86cde7f2b633907e"},"schema_version":"1.0","source":{"id":"1306.0308","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0308","created_at":"2026-05-18T02:59:18Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0308v2","created_at":"2026-05-18T02:59:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0308","created_at":"2026-05-18T02:59:18Z"},{"alias_kind":"pith_short_12","alias_value":"XO3M7CK2ZP7U","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XO3M7CK2ZP7UZHFK","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XO3M7CK2","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:aebc339d1a83cac476f7c57a33911692d92c4147a44ceeafef597ea51d5e5b8b","target":"graph","created_at":"2026-05-18T02:59:18Z","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"},"paper":{"abstract_excerpt":"We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian manifolds, where non-analytic ordinary differential equations are involved in virtually all computations. The probabilistic formulation permits marginalising the uncertainty of the numerical solution such that statistics are less sensitive to inaccuracies. This leads to new Riemannian algorithms for mean value computations and principal geodesic analysis. Margina","authors_text":"Philipp Hennig, S{\\o}ren Hauberg","cross_cats":["cs.LG","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2013-06-03T06:56:47Z","title":"Probabilistic Solutions to Differential Equations and their Application to Riemannian Statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0308","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":"sha256:72a9c9a185fefbfb1ca72d2e721468e9b94e27c3ba448d42e331ed1f5a433410","target":"record","created_at":"2026-05-18T02:59:18Z","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":"a369647d0073434fbe7a4ab3d780b3204cd49e26e8dd582930c35c2a73d80296","cross_cats_sorted":["cs.LG","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2013-06-03T06:56:47Z","title_canon_sha256":"17b0d2a9971cf323746df5bd934cb223e5b371989ad1b59c86cde7f2b633907e"},"schema_version":"1.0","source":{"id":"1306.0308","kind":"arxiv","version":2}},"canonical_sha256":"bbb6cf895acbff4c9caa30ba0cd74ba8f44e3d0030b76d988dac5bfaa3c405f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbb6cf895acbff4c9caa30ba0cd74ba8f44e3d0030b76d988dac5bfaa3c405f3","first_computed_at":"2026-05-18T02:59:18.505243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:18.505243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SypFqxg44vHMNPVBDgewR/LNX34m0c5f7jpilImiBHocnRz/uA2L6Rl7l9hdkRyjmDGmI7mgOeq7fOLAWpRPDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:18.506069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.0308","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72a9c9a185fefbfb1ca72d2e721468e9b94e27c3ba448d42e331ed1f5a433410","sha256:aebc339d1a83cac476f7c57a33911692d92c4147a44ceeafef597ea51d5e5b8b"],"state_sha256":"18bb7f185f3719d778675b6e2e477c0287003ce1ba38a4c71c76ef3c5e26d564"}