{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3O534SUHBCEE3TJX4AZM2UEYRI","short_pith_number":"pith:3O534SUH","canonical_record":{"source":{"id":"1010.6007","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-10-28T16:27:36Z","cross_cats_sorted":[],"title_canon_sha256":"fbf10764a8d6f3816663c44412a049cfa04a8d3a6f690ab81cc8c136795f112d","abstract_canon_sha256":"ab59ba61d4a58f039c4208d2cd16fa9f93fe85422a411d479bb9d9725a845958"},"schema_version":"1.0"},"canonical_sha256":"dbbbbe4a8708884dcd37e032cd50988a2e7f79ac370b564f08bc6b19adbd7905","source":{"kind":"arxiv","id":"1010.6007","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.6007","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"arxiv_version","alias_value":"1010.6007v1","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.6007","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"pith_short_12","alias_value":"3O534SUHBCEE","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3O534SUHBCEE3TJX","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3O534SUH","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3O534SUHBCEE3TJX4AZM2UEYRI","target":"record","payload":{"canonical_record":{"source":{"id":"1010.6007","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-10-28T16:27:36Z","cross_cats_sorted":[],"title_canon_sha256":"fbf10764a8d6f3816663c44412a049cfa04a8d3a6f690ab81cc8c136795f112d","abstract_canon_sha256":"ab59ba61d4a58f039c4208d2cd16fa9f93fe85422a411d479bb9d9725a845958"},"schema_version":"1.0"},"canonical_sha256":"dbbbbe4a8708884dcd37e032cd50988a2e7f79ac370b564f08bc6b19adbd7905","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:14.770076Z","signature_b64":"Dpq7UoyBl66ipTSVxbOyFruDsUsF9KqYFcO6UNpJjJYtqfnmzk2emebw70x+Dzvd7WsHMB7BD/r91GRon0jwAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbbbbe4a8708884dcd37e032cd50988a2e7f79ac370b564f08bc6b19adbd7905","last_reissued_at":"2026-05-18T04:38:14.769572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:14.769572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.6007","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:38:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G/fJZBr2JAGyxmbqfpTVhH9PpFwF5Q1a0aMbkA1JBTLhXTekgx/nyKR1vKPAvZ8ZNeMdfduo7gI4JqJM5kS8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T17:08:59.162563Z"},"content_sha256":"2b8f993274a5fb6eee3bb53fdc8f6e227f28e639f242a94aaff773fa80b9a2dd","schema_version":"1.0","event_id":"sha256:2b8f993274a5fb6eee3bb53fdc8f6e227f28e639f242a94aaff773fa80b9a2dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3O534SUHBCEE3TJX4AZM2UEYRI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Separation Principle on Lie Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Erwan Salaun, Philippe Martin, Pierre Rouchon, Silvere Bonnabel","submitted_at":"2010-10-28T16:27:36Z","abstract_excerpt":"For linear time-invariant systems, a separation principle holds: stable observer and stable state feedback can be designed for the time-invariant system, and the combined observer and feedback will be stable. For non-linear systems, a local separation principle holds around steady-states, as the linearized system is time-invariant. This paper addresses the issue of a non-linear separation principle on Lie groups. For invariant systems on Lie groups, we prove there exists a large set of (time-varying) trajectories around which the linearized observer-controler system is time-invariant, as soon "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.6007","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T04:38:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BuXJ6AfUsdB1sxvcU4uFMNjCkUj3UAMm53XwJb25mtjjfftyVaSbwqPX2wPfDp3dbuBjpvJbALEbLzfDGhE/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T17:08:59.162900Z"},"content_sha256":"c11838481c8b21d878c0fa599674760fed9c60a15a048a612371b3b952e8c7c1","schema_version":"1.0","event_id":"sha256:c11838481c8b21d878c0fa599674760fed9c60a15a048a612371b3b952e8c7c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3O534SUHBCEE3TJX4AZM2UEYRI/bundle.json","state_url":"https://pith.science/pith/3O534SUHBCEE3TJX4AZM2UEYRI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3O534SUHBCEE3TJX4AZM2UEYRI/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":"2026-07-04T17:08:59Z","links":{"resolver":"https://pith.science/pith/3O534SUHBCEE3TJX4AZM2UEYRI","bundle":"https://pith.science/pith/3O534SUHBCEE3TJX4AZM2UEYRI/bundle.json","state":"https://pith.science/pith/3O534SUHBCEE3TJX4AZM2UEYRI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3O534SUHBCEE3TJX4AZM2UEYRI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3O534SUHBCEE3TJX4AZM2UEYRI","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":"ab59ba61d4a58f039c4208d2cd16fa9f93fe85422a411d479bb9d9725a845958","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-10-28T16:27:36Z","title_canon_sha256":"fbf10764a8d6f3816663c44412a049cfa04a8d3a6f690ab81cc8c136795f112d"},"schema_version":"1.0","source":{"id":"1010.6007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.6007","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"arxiv_version","alias_value":"1010.6007v1","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.6007","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"pith_short_12","alias_value":"3O534SUHBCEE","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3O534SUHBCEE3TJX","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3O534SUH","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:c11838481c8b21d878c0fa599674760fed9c60a15a048a612371b3b952e8c7c1","target":"graph","created_at":"2026-05-18T04:38:14Z","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":"For linear time-invariant systems, a separation principle holds: stable observer and stable state feedback can be designed for the time-invariant system, and the combined observer and feedback will be stable. For non-linear systems, a local separation principle holds around steady-states, as the linearized system is time-invariant. This paper addresses the issue of a non-linear separation principle on Lie groups. For invariant systems on Lie groups, we prove there exists a large set of (time-varying) trajectories around which the linearized observer-controler system is time-invariant, as soon ","authors_text":"Erwan Salaun, Philippe Martin, Pierre Rouchon, Silvere Bonnabel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-10-28T16:27:36Z","title":"A Separation Principle on Lie Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.6007","kind":"arxiv","version":1},"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":"sha256:2b8f993274a5fb6eee3bb53fdc8f6e227f28e639f242a94aaff773fa80b9a2dd","target":"record","created_at":"2026-05-18T04:38:14Z","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":"ab59ba61d4a58f039c4208d2cd16fa9f93fe85422a411d479bb9d9725a845958","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-10-28T16:27:36Z","title_canon_sha256":"fbf10764a8d6f3816663c44412a049cfa04a8d3a6f690ab81cc8c136795f112d"},"schema_version":"1.0","source":{"id":"1010.6007","kind":"arxiv","version":1}},"canonical_sha256":"dbbbbe4a8708884dcd37e032cd50988a2e7f79ac370b564f08bc6b19adbd7905","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbbbbe4a8708884dcd37e032cd50988a2e7f79ac370b564f08bc6b19adbd7905","first_computed_at":"2026-05-18T04:38:14.769572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:14.769572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dpq7UoyBl66ipTSVxbOyFruDsUsF9KqYFcO6UNpJjJYtqfnmzk2emebw70x+Dzvd7WsHMB7BD/r91GRon0jwAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:14.770076Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.6007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b8f993274a5fb6eee3bb53fdc8f6e227f28e639f242a94aaff773fa80b9a2dd","sha256:c11838481c8b21d878c0fa599674760fed9c60a15a048a612371b3b952e8c7c1"],"state_sha256":"f3653d82b1c425447849d46cb6b378df8ae0a2704bbaf726c6d15e08aeedce6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+SOG1hJFntMgOT6cRyDAI5TOsW0OAcyxAnS0l+Kk/5uq2/Gjwmp+/Q/2mt+GzpV1eBURVo2x+jjT3EHUXtWADA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T17:08:59.164789Z","bundle_sha256":"bd3d5aa08365351966a51f1b1adb9e627ecb0f604640acc718788e8e6b7e5a61"}}