{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:LPWKK7DNYEWPULOLW4W2YSLZAS","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":"b961c6145b025f666bc1c7127d2db78b5be578d234e9951add31a0639d61a975","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2021-02-07T14:49:06Z","title_canon_sha256":"d560c47525d28cc19886afba0eac361288bbc43239c91a8e7e5c87ac9c45285b"},"schema_version":"1.0","source":{"id":"2102.03804","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.03804","created_at":"2026-07-05T02:52:27Z"},{"alias_kind":"arxiv_version","alias_value":"2102.03804v3","created_at":"2026-07-05T02:52:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.03804","created_at":"2026-07-05T02:52:27Z"},{"alias_kind":"pith_short_12","alias_value":"LPWKK7DNYEWP","created_at":"2026-07-05T02:52:27Z"},{"alias_kind":"pith_short_16","alias_value":"LPWKK7DNYEWPULOL","created_at":"2026-07-05T02:52:27Z"},{"alias_kind":"pith_short_8","alias_value":"LPWKK7DN","created_at":"2026-07-05T02:52:27Z"}],"graph_snapshots":[{"event_id":"sha256:9c5c7e09a52191426b291fa53e82853c69e2dd2605264ad45bec173349e9afef","target":"graph","created_at":"2026-07-05T02:52:27Z","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/2102.03804/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Kalman filter is presumably one of the most important and extensively used filtering techniques in modern control systems. Yet, nearly all current variants of Kalman filters are formulated in the Euclidean space $\\mathbb{R}^n$, while many real-world systems (e.g., robotic systems) are really evolving on manifolds. In this paper, we propose a method to develop Kalman filters for such on-manifold systems. Utilizing $\\boxplus$, $\\boxminus$ operations and further defining an oplus operation on the respective manifold, we propose a canonical representation of the on-manifold system. Such a canonica","authors_text":"Dongjiao He, Fu Zhang, Wei Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2021-02-07T14:49:06Z","title":"Kalman Filters on Differentiable Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.03804","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":"sha256:19e99d6037a6e84e77d0b0c25d7eb12e28113599963b2362bb832e4353659e0f","target":"record","created_at":"2026-07-05T02:52:27Z","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":"b961c6145b025f666bc1c7127d2db78b5be578d234e9951add31a0639d61a975","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2021-02-07T14:49:06Z","title_canon_sha256":"d560c47525d28cc19886afba0eac361288bbc43239c91a8e7e5c87ac9c45285b"},"schema_version":"1.0","source":{"id":"2102.03804","kind":"arxiv","version":3}},"canonical_sha256":"5beca57c6dc12cfa2dcbb72dac497904830150939516fb9896f77cebebf2fe2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5beca57c6dc12cfa2dcbb72dac497904830150939516fb9896f77cebebf2fe2d","first_computed_at":"2026-07-05T02:52:27.875445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:52:27.875445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"soJGCJWE/GcRS0vsL/tGkkEcXx7fqPLtr1PibwaS38eqRLZGmj9lwNq/rSXWogUD1YXiXB6ke317rBcu5/2EDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:52:27.875919Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.03804","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19e99d6037a6e84e77d0b0c25d7eb12e28113599963b2362bb832e4353659e0f","sha256:9c5c7e09a52191426b291fa53e82853c69e2dd2605264ad45bec173349e9afef"],"state_sha256":"fe6d43793b8b811343f4b9638b6eb1128a4c46c40a8f4380731a944b40738e31"}