{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HJHGIGTFH5OINVD5HFXH7X7W3W","short_pith_number":"pith:HJHGIGTF","canonical_record":{"source":{"id":"1601.00508","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-04T14:03:00Z","cross_cats_sorted":[],"title_canon_sha256":"2449ad8684ec26695d0bce5aedb8b3a0f40bae649130f31792940b16e32b43f5","abstract_canon_sha256":"2b8c35343a2715f35714efabfb4b71ab05332933dc659737f99a7ffe72ecaf0e"},"schema_version":"1.0"},"canonical_sha256":"3a4e641a653f5c86d47d396e7fdff6dd9739cc6fd5b8ee50c6ddaa19d504566b","source":{"kind":"arxiv","id":"1601.00508","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00508","created_at":"2026-05-18T01:23:27Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00508v1","created_at":"2026-05-18T01:23:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00508","created_at":"2026-05-18T01:23:27Z"},{"alias_kind":"pith_short_12","alias_value":"HJHGIGTFH5OI","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HJHGIGTFH5OINVD5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HJHGIGTF","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HJHGIGTFH5OINVD5HFXH7X7W3W","target":"record","payload":{"canonical_record":{"source":{"id":"1601.00508","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-04T14:03:00Z","cross_cats_sorted":[],"title_canon_sha256":"2449ad8684ec26695d0bce5aedb8b3a0f40bae649130f31792940b16e32b43f5","abstract_canon_sha256":"2b8c35343a2715f35714efabfb4b71ab05332933dc659737f99a7ffe72ecaf0e"},"schema_version":"1.0"},"canonical_sha256":"3a4e641a653f5c86d47d396e7fdff6dd9739cc6fd5b8ee50c6ddaa19d504566b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:27.196779Z","signature_b64":"YWO1xbXZgVda7B1u2Fu6r4pmhCgRFCuE90rKN6Z8vUfkrKZ7jeRLPmxtNzkiIRM8HUImpMXqVbHlPr5EVJtrCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a4e641a653f5c86d47d396e7fdff6dd9739cc6fd5b8ee50c6ddaa19d504566b","last_reissued_at":"2026-05-18T01:23:27.196147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:27.196147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.00508","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":"2026-05-18T01:23:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lCJQOWJusFpLuUIThjouDvd/N9c8xGZDWXC3yRQL3cq+SRoJ9hxYaiLxjWlPEbvKk2jlmvj1QhJ3BlTsV1JzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:15:03.201025Z"},"content_sha256":"58e69c4f9fa9965cfffbc30402b2fff62000ea8c715658837f313f51dec4c020","schema_version":"1.0","event_id":"sha256:58e69c4f9fa9965cfffbc30402b2fff62000ea8c715658837f313f51dec4c020"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HJHGIGTFH5OINVD5HFXH7X7W3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transverse exponential stability and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bayu Jayawardhana, Laurent Praly (CAS), Vincent Andrieu (LAGEP)","submitted_at":"2016-01-04T14:03:00Z","abstract_excerpt":"We investigate how the following properties are related to each other: i)-A manifold is \"transversally\" exponentially stable; ii)-The \"transverse\" linearization along any solution in the manifold is exponentially stable; iii)-There exists a field of positive definite quadratic forms whose restrictions to the directions transversal to the manifold are decreasing along the flow. We illustrate their relevance with the study of exponential incremental stability. Finally, we apply these results to two control design problems, nonlinear observer design and synchronization. In particular, we provide "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00508","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":"2026-05-18T01:23:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kx/057AK4/Wa5SqbiRLSaJjkEosFDVjiqxYPfAbRZ9tbMZ9F3w1jG/GdM4p4dQ4/nSq9pGOHn0uj5IjmZqEWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:15:03.201389Z"},"content_sha256":"5d48ae610fd4fa9e8b68557c8ed5f92190435a6da94b98d5dc7afbc7a7d0303b","schema_version":"1.0","event_id":"sha256:5d48ae610fd4fa9e8b68557c8ed5f92190435a6da94b98d5dc7afbc7a7d0303b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HJHGIGTFH5OINVD5HFXH7X7W3W/bundle.json","state_url":"https://pith.science/pith/HJHGIGTFH5OINVD5HFXH7X7W3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HJHGIGTFH5OINVD5HFXH7X7W3W/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":"2026-06-01T18:15:03Z","links":{"resolver":"https://pith.science/pith/HJHGIGTFH5OINVD5HFXH7X7W3W","bundle":"https://pith.science/pith/HJHGIGTFH5OINVD5HFXH7X7W3W/bundle.json","state":"https://pith.science/pith/HJHGIGTFH5OINVD5HFXH7X7W3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HJHGIGTFH5OINVD5HFXH7X7W3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HJHGIGTFH5OINVD5HFXH7X7W3W","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":"2b8c35343a2715f35714efabfb4b71ab05332933dc659737f99a7ffe72ecaf0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-04T14:03:00Z","title_canon_sha256":"2449ad8684ec26695d0bce5aedb8b3a0f40bae649130f31792940b16e32b43f5"},"schema_version":"1.0","source":{"id":"1601.00508","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00508","created_at":"2026-05-18T01:23:27Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00508v1","created_at":"2026-05-18T01:23:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00508","created_at":"2026-05-18T01:23:27Z"},{"alias_kind":"pith_short_12","alias_value":"HJHGIGTFH5OI","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HJHGIGTFH5OINVD5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HJHGIGTF","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:5d48ae610fd4fa9e8b68557c8ed5f92190435a6da94b98d5dc7afbc7a7d0303b","target":"graph","created_at":"2026-05-18T01:23:27Z","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"},"paper":{"abstract_excerpt":"We investigate how the following properties are related to each other: i)-A manifold is \"transversally\" exponentially stable; ii)-The \"transverse\" linearization along any solution in the manifold is exponentially stable; iii)-There exists a field of positive definite quadratic forms whose restrictions to the directions transversal to the manifold are decreasing along the flow. We illustrate their relevance with the study of exponential incremental stability. Finally, we apply these results to two control design problems, nonlinear observer design and synchronization. In particular, we provide ","authors_text":"Bayu Jayawardhana, Laurent Praly (CAS), Vincent Andrieu (LAGEP)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-04T14:03:00Z","title":"Transverse exponential stability and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00508","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":"sha256:58e69c4f9fa9965cfffbc30402b2fff62000ea8c715658837f313f51dec4c020","target":"record","created_at":"2026-05-18T01:23:27Z","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":"2b8c35343a2715f35714efabfb4b71ab05332933dc659737f99a7ffe72ecaf0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-04T14:03:00Z","title_canon_sha256":"2449ad8684ec26695d0bce5aedb8b3a0f40bae649130f31792940b16e32b43f5"},"schema_version":"1.0","source":{"id":"1601.00508","kind":"arxiv","version":1}},"canonical_sha256":"3a4e641a653f5c86d47d396e7fdff6dd9739cc6fd5b8ee50c6ddaa19d504566b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a4e641a653f5c86d47d396e7fdff6dd9739cc6fd5b8ee50c6ddaa19d504566b","first_computed_at":"2026-05-18T01:23:27.196147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:27.196147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YWO1xbXZgVda7B1u2Fu6r4pmhCgRFCuE90rKN6Z8vUfkrKZ7jeRLPmxtNzkiIRM8HUImpMXqVbHlPr5EVJtrCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:27.196779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.00508","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58e69c4f9fa9965cfffbc30402b2fff62000ea8c715658837f313f51dec4c020","sha256:5d48ae610fd4fa9e8b68557c8ed5f92190435a6da94b98d5dc7afbc7a7d0303b"],"state_sha256":"c305fee1e74779f12b50b0df5a6c4df426be17b9d0637f28e6f0574d31a05f22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FGoBOGwXj3j716cFewCBeC2yfHRYkstwPPO89LPIxdCwzIe7NcmfFDp9BeewE5qjKE0UI2OmHqYsbXckmIM2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:15:03.203358Z","bundle_sha256":"5c7d50a1d5738dc86e7345f1a1ade856338601111b2384b9ddc4f135088045d9"}}