{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:MWMLXG7S2WO7DYPQIB533AS2GH","short_pith_number":"pith:MWMLXG7S","schema_version":"1.0","canonical_sha256":"6598bb9bf2d59df1e1f0407bbd825a31e4e22e6f69528f286eba49a74c20e9c3","source":{"kind":"arxiv","id":"2006.04361","version":3},"attestation_state":"computed","paper":{"title":"Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG","cs.RO","cs.SY","math.OC"],"primary_cat":"eess.SY","authors_text":"Hiroyasu Tsukamoto, Soon-Jo Chung","submitted_at":"2020-06-08T05:29:38Z","abstract_excerpt":"This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global approximation of an optimal contraction metric, the existence of which is a necessary and sufficient condition for exponential stability of nonlinear systems. The optimality stems from the fact that the contraction metrics sampled offline are the solutions of a convex optimization problem to minimize an upper bound of the steady-state Euclidean distance between"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2006.04361","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2020-06-08T05:29:38Z","cross_cats_sorted":["cs.AI","cs.LG","cs.RO","cs.SY","math.OC"],"title_canon_sha256":"8a3d8f8839ffe4fe7e84199ab839f7aa2398cba8ed3bdef3f898475797c8e38e","abstract_canon_sha256":"e51dacaf7fe058dddb6abe0328091f3a3f75782387a1ed7eebcadd7e1b394a6d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:52:59.087308Z","signature_b64":"jz5L6ZLaWYWUi37bT6/OhwHXDCUvQFPLJLKRwNIV5CIKh+WwILb18FXU8oPcmbO2KftDVwuoWX/0DvNFfQtyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6598bb9bf2d59df1e1f0407bbd825a31e4e22e6f69528f286eba49a74c20e9c3","last_reissued_at":"2026-07-05T01:52:59.086899Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:52:59.086899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG","cs.RO","cs.SY","math.OC"],"primary_cat":"eess.SY","authors_text":"Hiroyasu Tsukamoto, Soon-Jo Chung","submitted_at":"2020-06-08T05:29:38Z","abstract_excerpt":"This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global approximation of an optimal contraction metric, the existence of which is a necessary and sufficient condition for exponential stability of nonlinear systems. The optimality stems from the fact that the contraction metrics sampled offline are the solutions of a convex optimization problem to minimize an upper bound of the steady-state Euclidean distance between"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.04361","kind":"arxiv","version":3},"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/2006.04361/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2006.04361","created_at":"2026-07-05T01:52:59.086954+00:00"},{"alias_kind":"arxiv_version","alias_value":"2006.04361v3","created_at":"2026-07-05T01:52:59.086954+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.04361","created_at":"2026-07-05T01:52:59.086954+00:00"},{"alias_kind":"pith_short_12","alias_value":"MWMLXG7S2WO7","created_at":"2026-07-05T01:52:59.086954+00:00"},{"alias_kind":"pith_short_16","alias_value":"MWMLXG7S2WO7DYPQ","created_at":"2026-07-05T01:52:59.086954+00:00"},{"alias_kind":"pith_short_8","alias_value":"MWMLXG7S","created_at":"2026-07-05T01:52:59.086954+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MWMLXG7S2WO7DYPQIB533AS2GH","json":"https://pith.science/pith/MWMLXG7S2WO7DYPQIB533AS2GH.json","graph_json":"https://pith.science/api/pith-number/MWMLXG7S2WO7DYPQIB533AS2GH/graph.json","events_json":"https://pith.science/api/pith-number/MWMLXG7S2WO7DYPQIB533AS2GH/events.json","paper":"https://pith.science/paper/MWMLXG7S"},"agent_actions":{"view_html":"https://pith.science/pith/MWMLXG7S2WO7DYPQIB533AS2GH","download_json":"https://pith.science/pith/MWMLXG7S2WO7DYPQIB533AS2GH.json","view_paper":"https://pith.science/paper/MWMLXG7S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2006.04361&json=true","fetch_graph":"https://pith.science/api/pith-number/MWMLXG7S2WO7DYPQIB533AS2GH/graph.json","fetch_events":"https://pith.science/api/pith-number/MWMLXG7S2WO7DYPQIB533AS2GH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MWMLXG7S2WO7DYPQIB533AS2GH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MWMLXG7S2WO7DYPQIB533AS2GH/action/storage_attestation","attest_author":"https://pith.science/pith/MWMLXG7S2WO7DYPQIB533AS2GH/action/author_attestation","sign_citation":"https://pith.science/pith/MWMLXG7S2WO7DYPQIB533AS2GH/action/citation_signature","submit_replication":"https://pith.science/pith/MWMLXG7S2WO7DYPQIB533AS2GH/action/replication_record"}},"created_at":"2026-07-05T01:52:59.086954+00:00","updated_at":"2026-07-05T01:52:59.086954+00:00"}