{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ELF5CDLGQOIPMCCRJPOWITSAY2","short_pith_number":"pith:ELF5CDLG","canonical_record":{"source":{"id":"1903.06439","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-03-15T10:14:45Z","cross_cats_sorted":[],"title_canon_sha256":"e93a0861adcc1f5728e3007147a8c5e31e2dc83a6bccd52418e015df7df9eb41","abstract_canon_sha256":"0a7b6408056c703d313d7a07937a4e7614175994e825cea7ff30474bdea21843"},"schema_version":"1.0"},"canonical_sha256":"22cbd10d668390f608514bdd644e40c6858b3664e7c2c74d7d7b96fae87ad17c","source":{"kind":"arxiv","id":"1903.06439","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06439","created_at":"2026-05-17T23:51:10Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06439v1","created_at":"2026-05-17T23:51:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06439","created_at":"2026-05-17T23:51:10Z"},{"alias_kind":"pith_short_12","alias_value":"ELF5CDLGQOIP","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"ELF5CDLGQOIPMCCR","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"ELF5CDLG","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ELF5CDLGQOIPMCCRJPOWITSAY2","target":"record","payload":{"canonical_record":{"source":{"id":"1903.06439","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-03-15T10:14:45Z","cross_cats_sorted":[],"title_canon_sha256":"e93a0861adcc1f5728e3007147a8c5e31e2dc83a6bccd52418e015df7df9eb41","abstract_canon_sha256":"0a7b6408056c703d313d7a07937a4e7614175994e825cea7ff30474bdea21843"},"schema_version":"1.0"},"canonical_sha256":"22cbd10d668390f608514bdd644e40c6858b3664e7c2c74d7d7b96fae87ad17c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:10.871079Z","signature_b64":"LDtUVqSXvYr/fHdSneE7MOIBtnIs/JfrnNJ5rbUyqOK0PW+Op6IUYJu0Hxs0UfdKZEo2bhWcvOEyy6Ykd4TTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22cbd10d668390f608514bdd644e40c6858b3664e7c2c74d7d7b96fae87ad17c","last_reissued_at":"2026-05-17T23:51:10.870630Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:10.870630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.06439","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":"2026-05-17T23:51:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SSJv0g5xKk2cu0CjZqUGUCTOn377roYJ6TOQPwkO3cO6DdJDgRaGY1+EIpvAfrC6AttJ5ktMWuCO9p6ePkMqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:07:51.303106Z"},"content_sha256":"ea0169c38a3668436597b611fd42dee724b1ec5f24ed4d8ee29b9673f843152d","schema_version":"1.0","event_id":"sha256:ea0169c38a3668436597b611fd42dee724b1ec5f24ed4d8ee29b9673f843152d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ELF5CDLGQOIPMCCRJPOWITSAY2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector Contraction Analysis for Nonlinear Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Antonella Ferrara, Bhawana Singh, Debdas Ghosh, Sandip Ghosh, Shyam Kamal","submitted_at":"2019-03-15T10:14:45Z","abstract_excerpt":"This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently induces a vector distance between any pair of trajectories of the system, offers an amenable framework as each component of vector-valued norm function satisfies fewer strict conditions as that of standard contraction analysis. Particularly, every element of vector-valued norm derivative need not be strictly negative definite for convergence of any pair of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06439","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":"2026-05-17T23:51:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IqfhcQY2zuPpNmKTfVeJ70VBKG/2/gI58gr2Z0eLb3Yp8Np3wNxT8UvoaXcCb/QOxGf6oiDMQ+T1fugBx9qCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:07:51.303750Z"},"content_sha256":"6c46544a46a9f2b9e8d9e036349aec48d46e0a70aa9cf47893f7980e94ad4d76","schema_version":"1.0","event_id":"sha256:6c46544a46a9f2b9e8d9e036349aec48d46e0a70aa9cf47893f7980e94ad4d76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELF5CDLGQOIPMCCRJPOWITSAY2/bundle.json","state_url":"https://pith.science/pith/ELF5CDLGQOIPMCCRJPOWITSAY2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELF5CDLGQOIPMCCRJPOWITSAY2/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":"2026-05-28T01:07:51Z","links":{"resolver":"https://pith.science/pith/ELF5CDLGQOIPMCCRJPOWITSAY2","bundle":"https://pith.science/pith/ELF5CDLGQOIPMCCRJPOWITSAY2/bundle.json","state":"https://pith.science/pith/ELF5CDLGQOIPMCCRJPOWITSAY2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELF5CDLGQOIPMCCRJPOWITSAY2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ELF5CDLGQOIPMCCRJPOWITSAY2","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":"0a7b6408056c703d313d7a07937a4e7614175994e825cea7ff30474bdea21843","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-03-15T10:14:45Z","title_canon_sha256":"e93a0861adcc1f5728e3007147a8c5e31e2dc83a6bccd52418e015df7df9eb41"},"schema_version":"1.0","source":{"id":"1903.06439","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06439","created_at":"2026-05-17T23:51:10Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06439v1","created_at":"2026-05-17T23:51:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06439","created_at":"2026-05-17T23:51:10Z"},{"alias_kind":"pith_short_12","alias_value":"ELF5CDLGQOIP","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"ELF5CDLGQOIPMCCR","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"ELF5CDLG","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:6c46544a46a9f2b9e8d9e036349aec48d46e0a70aa9cf47893f7980e94ad4d76","target":"graph","created_at":"2026-05-17T23:51:10Z","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":"This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently induces a vector distance between any pair of trajectories of the system, offers an amenable framework as each component of vector-valued norm function satisfies fewer strict conditions as that of standard contraction analysis. Particularly, every element of vector-valued norm derivative need not be strictly negative definite for convergence of any pair of t","authors_text":"Antonella Ferrara, Bhawana Singh, Debdas Ghosh, Sandip Ghosh, Shyam Kamal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-03-15T10:14:45Z","title":"Vector Contraction Analysis for Nonlinear Dynamical Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06439","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:ea0169c38a3668436597b611fd42dee724b1ec5f24ed4d8ee29b9673f843152d","target":"record","created_at":"2026-05-17T23:51:10Z","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":"0a7b6408056c703d313d7a07937a4e7614175994e825cea7ff30474bdea21843","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-03-15T10:14:45Z","title_canon_sha256":"e93a0861adcc1f5728e3007147a8c5e31e2dc83a6bccd52418e015df7df9eb41"},"schema_version":"1.0","source":{"id":"1903.06439","kind":"arxiv","version":1}},"canonical_sha256":"22cbd10d668390f608514bdd644e40c6858b3664e7c2c74d7d7b96fae87ad17c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22cbd10d668390f608514bdd644e40c6858b3664e7c2c74d7d7b96fae87ad17c","first_computed_at":"2026-05-17T23:51:10.870630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:10.870630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LDtUVqSXvYr/fHdSneE7MOIBtnIs/JfrnNJ5rbUyqOK0PW+Op6IUYJu0Hxs0UfdKZEo2bhWcvOEyy6Ykd4TTAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:10.871079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.06439","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea0169c38a3668436597b611fd42dee724b1ec5f24ed4d8ee29b9673f843152d","sha256:6c46544a46a9f2b9e8d9e036349aec48d46e0a70aa9cf47893f7980e94ad4d76"],"state_sha256":"904625ae82ff2d8413c185cb76a6df3c4752c0e09477197de9d4755e5e62e681"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"reB8t5Lc67NZFxKmd5Uad+24kinIluODCzLuMvSbvpGSi3JRHWGAXWHnaIvp4o2IDuJGrE8pcmxvEIvy4A1oCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:07:51.306240Z","bundle_sha256":"4fd6c5f9e9fac07e6330dfab117e64808c9eba01510740069eba0e4f39a2f395"}}