{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:UXHQJ6FA3XKLNTI7XJ4RRMUCTP","short_pith_number":"pith:UXHQJ6FA","canonical_record":{"source":{"id":"math-ph/0403027","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2004-03-15T15:12:15Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"2551300f8106ded654893e71861f64cb486baba7c8bb89a510b7c96daaf6adb0","abstract_canon_sha256":"ef9767961be32359696b4aca38c80b0cc2926119e50732b37d63319e5670fbc3"},"schema_version":"1.0"},"canonical_sha256":"a5cf04f8a0ddd4b6cd1fba7918b2829bc89b53a2869a30ad16ed9a89269b71fc","source":{"kind":"arxiv","id":"math-ph/0403027","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0403027","created_at":"2026-07-04T14:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0403027v1","created_at":"2026-07-04T14:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0403027","created_at":"2026-07-04T14:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"UXHQJ6FA3XKL","created_at":"2026-07-04T14:33:59Z"},{"alias_kind":"pith_short_16","alias_value":"UXHQJ6FA3XKLNTI7","created_at":"2026-07-04T14:33:59Z"},{"alias_kind":"pith_short_8","alias_value":"UXHQJ6FA","created_at":"2026-07-04T14:33:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:UXHQJ6FA3XKLNTI7XJ4RRMUCTP","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0403027","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2004-03-15T15:12:15Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"2551300f8106ded654893e71861f64cb486baba7c8bb89a510b7c96daaf6adb0","abstract_canon_sha256":"ef9767961be32359696b4aca38c80b0cc2926119e50732b37d63319e5670fbc3"},"schema_version":"1.0"},"canonical_sha256":"a5cf04f8a0ddd4b6cd1fba7918b2829bc89b53a2869a30ad16ed9a89269b71fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:33:59.843631Z","signature_b64":"q78I1fpsfaE5jeJSVUTx0uJX3UXZI1pM8muhq7eDfpQ0guwg5RJvAu6sGBNg9fdmyZfiaa+bXXyrkU5XOmOaDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5cf04f8a0ddd4b6cd1fba7918b2829bc89b53a2869a30ad16ed9a89269b71fc","last_reissued_at":"2026-07-04T14:33:59.843277Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:33:59.843277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0403027","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":"2026-07-04T14:33:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xR6NSIC51VamGzhhUjgRuj7AznD6MYp/cUDHH/kyhPKzVcSiudinDrEllnuakpxh4hd5il4fZgXnZjTNScmcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T00:35:39.361541Z"},"content_sha256":"cbadf928032d444abf12b7a3b959471ee6fc39b4ab910c86c1d68aba4a1ee77e","schema_version":"1.0","event_id":"sha256:cbadf928032d444abf12b7a3b959471ee6fc39b4ab910c86c1d68aba4a1ee77e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:UXHQJ6FA3XKLNTI7XJ4RRMUCTP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contraction Analysis of Nonlinear Distributed Systems","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jean-Jacques E. Slotine, Winfried Lohmiller","submitted_at":"2004-03-15T15:12:15Z","abstract_excerpt":"Contraction theory is a recently developed dynamic analysis and nonlinear control system design tool based on an exact differential analysis of convergence. This paper extends contraction theory to local and global stability analysis of important classes of nonlinear distributed dynamics, such as convection-diffusion-reaction processes, Lagrangian and Hamilton-Jacobi dynamics, and optimal controllers and observers. The Hamilton-Jacobi-Bellman controller and a similar optimal nonlinear observer design are studied. Explicit stability conditions are given, which extend the well-known conditions o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0403027","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0403027/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:33:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D6FvjSqxVN4g2F7MbSRGt2n4YuBd0c2lOGugkw8DZQERqWS3e/d71fEHLeQXHd5dg5SEDAaz3Fd0VoEcyn31Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T00:35:39.362354Z"},"content_sha256":"94b7fe7631be72379a7378715e0ffce85a4b14455e7878dcc547c4d5eb41c579","schema_version":"1.0","event_id":"sha256:94b7fe7631be72379a7378715e0ffce85a4b14455e7878dcc547c4d5eb41c579"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UXHQJ6FA3XKLNTI7XJ4RRMUCTP/bundle.json","state_url":"https://pith.science/pith/UXHQJ6FA3XKLNTI7XJ4RRMUCTP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UXHQJ6FA3XKLNTI7XJ4RRMUCTP/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":"2026-08-05T00:35:39Z","links":{"resolver":"https://pith.science/pith/UXHQJ6FA3XKLNTI7XJ4RRMUCTP","bundle":"https://pith.science/pith/UXHQJ6FA3XKLNTI7XJ4RRMUCTP/bundle.json","state":"https://pith.science/pith/UXHQJ6FA3XKLNTI7XJ4RRMUCTP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UXHQJ6FA3XKLNTI7XJ4RRMUCTP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:UXHQJ6FA3XKLNTI7XJ4RRMUCTP","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":"ef9767961be32359696b4aca38c80b0cc2926119e50732b37d63319e5670fbc3","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2004-03-15T15:12:15Z","title_canon_sha256":"2551300f8106ded654893e71861f64cb486baba7c8bb89a510b7c96daaf6adb0"},"schema_version":"1.0","source":{"id":"math-ph/0403027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0403027","created_at":"2026-07-04T14:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0403027v1","created_at":"2026-07-04T14:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0403027","created_at":"2026-07-04T14:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"UXHQJ6FA3XKL","created_at":"2026-07-04T14:33:59Z"},{"alias_kind":"pith_short_16","alias_value":"UXHQJ6FA3XKLNTI7","created_at":"2026-07-04T14:33:59Z"},{"alias_kind":"pith_short_8","alias_value":"UXHQJ6FA","created_at":"2026-07-04T14:33:59Z"}],"graph_snapshots":[{"event_id":"sha256:94b7fe7631be72379a7378715e0ffce85a4b14455e7878dcc547c4d5eb41c579","target":"graph","created_at":"2026-07-04T14:33:59Z","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/math-ph/0403027/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Contraction theory is a recently developed dynamic analysis and nonlinear control system design tool based on an exact differential analysis of convergence. This paper extends contraction theory to local and global stability analysis of important classes of nonlinear distributed dynamics, such as convection-diffusion-reaction processes, Lagrangian and Hamilton-Jacobi dynamics, and optimal controllers and observers. The Hamilton-Jacobi-Bellman controller and a similar optimal nonlinear observer design are studied. Explicit stability conditions are given, which extend the well-known conditions o","authors_text":"Jean-Jacques E. Slotine, Winfried Lohmiller","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2004-03-15T15:12:15Z","title":"Contraction Analysis of Nonlinear Distributed Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0403027","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:cbadf928032d444abf12b7a3b959471ee6fc39b4ab910c86c1d68aba4a1ee77e","target":"record","created_at":"2026-07-04T14:33:59Z","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":"ef9767961be32359696b4aca38c80b0cc2926119e50732b37d63319e5670fbc3","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2004-03-15T15:12:15Z","title_canon_sha256":"2551300f8106ded654893e71861f64cb486baba7c8bb89a510b7c96daaf6adb0"},"schema_version":"1.0","source":{"id":"math-ph/0403027","kind":"arxiv","version":1}},"canonical_sha256":"a5cf04f8a0ddd4b6cd1fba7918b2829bc89b53a2869a30ad16ed9a89269b71fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5cf04f8a0ddd4b6cd1fba7918b2829bc89b53a2869a30ad16ed9a89269b71fc","first_computed_at":"2026-07-04T14:33:59.843277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:33:59.843277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q78I1fpsfaE5jeJSVUTx0uJX3UXZI1pM8muhq7eDfpQ0guwg5RJvAu6sGBNg9fdmyZfiaa+bXXyrkU5XOmOaDA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:33:59.843631Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0403027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbadf928032d444abf12b7a3b959471ee6fc39b4ab910c86c1d68aba4a1ee77e","sha256:94b7fe7631be72379a7378715e0ffce85a4b14455e7878dcc547c4d5eb41c579"],"state_sha256":"dbc5fa4042b6dec96a1d8a78fa7519f81af719c890d8aab8602c415ebaceed9a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fs6w0l5jqIJ2BizNONTcZ7NYHpTt22gmZHpeJN8rYkjNtyHNVyBtaiwQQU/Ry1M+IdHwkCncQx/ENhcWZEMmBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T00:35:39.368018Z","bundle_sha256":"c5a3e1caf1dfbee5d7bd5dc95061d0f4b5a9ce5cafb125e7b235429e4962b08d"}}