{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:WD44N5FPRNF27GWTWJWRLUX6MP","short_pith_number":"pith:WD44N5FP","canonical_record":{"source":{"id":"0711.3632","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OC","submitted_at":"2007-11-22T18:22:55Z","cross_cats_sorted":[],"title_canon_sha256":"dbfad015336369429807a370c10613a9f273ec9601da056c338c83ee0599073c","abstract_canon_sha256":"6bdba371916c12f4cdd0262e225c6e1871d763b8d5830f023a5111aa640dd003"},"schema_version":"1.0"},"canonical_sha256":"b0f9c6f4af8b4baf9ad3b26d15d2fe63e24c10a1b0424f530b1741876ddaf12e","source":{"kind":"arxiv","id":"0711.3632","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.3632","created_at":"2026-05-18T04:41:16Z"},{"alias_kind":"arxiv_version","alias_value":"0711.3632v1","created_at":"2026-05-18T04:41:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.3632","created_at":"2026-05-18T04:41:16Z"},{"alias_kind":"pith_short_12","alias_value":"WD44N5FPRNF2","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"WD44N5FPRNF27GWT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"WD44N5FP","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:WD44N5FPRNF27GWTWJWRLUX6MP","target":"record","payload":{"canonical_record":{"source":{"id":"0711.3632","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OC","submitted_at":"2007-11-22T18:22:55Z","cross_cats_sorted":[],"title_canon_sha256":"dbfad015336369429807a370c10613a9f273ec9601da056c338c83ee0599073c","abstract_canon_sha256":"6bdba371916c12f4cdd0262e225c6e1871d763b8d5830f023a5111aa640dd003"},"schema_version":"1.0"},"canonical_sha256":"b0f9c6f4af8b4baf9ad3b26d15d2fe63e24c10a1b0424f530b1741876ddaf12e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:16.537794Z","signature_b64":"00JVRJleCk4FWtSGPbQPzYZDUaF9kdQynKQRgaaeOe/p4aseVvR4SnljJLERGKzb8FHL9IvFsPgTOq/1OYjHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0f9c6f4af8b4baf9ad3b26d15d2fe63e24c10a1b0424f530b1741876ddaf12e","last_reissued_at":"2026-05-18T04:41:16.537204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:16.537204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0711.3632","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":"2026-05-18T04:41:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AvR6mwUKT+qggFs1iEPq7Rp2kXw0f0MBQtJCMXmXRkyQNBU+zSkrFzxFfM0jRhRi4E9Sfkt8vV2rvnxMucxdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:54:51.298116Z"},"content_sha256":"fbb6e05d1962ac69e7f204a725265fa65f7d70eb6d39476076423334aa223db4","schema_version":"1.0","event_id":"sha256:fbb6e05d1962ac69e7f204a725265fa65f7d70eb6d39476076423334aa223db4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:WD44N5FPRNF27GWTWJWRLUX6MP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On stability of randomly switched nonlinear systems","license":"","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daniel Liberzon, Debasish Chatterjee","submitted_at":"2007-11-22T18:22:55Z","abstract_excerpt":"This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic process which is independent of the state of the system, and between two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure global asymptotic stability using Lyapunov-based methods when individual subsystems are stable and a certain ``slow switching'' condition holds. This slow switching cond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.3632","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":"2026-05-18T04:41:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+sz/j5Ckwqq58s6VUAXF/GfehEg0KSA7IJdkAGtycEJzAJw4GSBZVR1GIkjl/DGIOfPVRdlDJtnGYTqtecluAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:54:51.298476Z"},"content_sha256":"6760b959fba257f0f076aef2b7d9440e59fe22f909d986904bc6ec3b8db0fbe5","schema_version":"1.0","event_id":"sha256:6760b959fba257f0f076aef2b7d9440e59fe22f909d986904bc6ec3b8db0fbe5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WD44N5FPRNF27GWTWJWRLUX6MP/bundle.json","state_url":"https://pith.science/pith/WD44N5FPRNF27GWTWJWRLUX6MP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WD44N5FPRNF27GWTWJWRLUX6MP/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":"2026-05-28T14:54:51Z","links":{"resolver":"https://pith.science/pith/WD44N5FPRNF27GWTWJWRLUX6MP","bundle":"https://pith.science/pith/WD44N5FPRNF27GWTWJWRLUX6MP/bundle.json","state":"https://pith.science/pith/WD44N5FPRNF27GWTWJWRLUX6MP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WD44N5FPRNF27GWTWJWRLUX6MP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:WD44N5FPRNF27GWTWJWRLUX6MP","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":"6bdba371916c12f4cdd0262e225c6e1871d763b8d5830f023a5111aa640dd003","cross_cats_sorted":[],"license":"","primary_cat":"math.OC","submitted_at":"2007-11-22T18:22:55Z","title_canon_sha256":"dbfad015336369429807a370c10613a9f273ec9601da056c338c83ee0599073c"},"schema_version":"1.0","source":{"id":"0711.3632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.3632","created_at":"2026-05-18T04:41:16Z"},{"alias_kind":"arxiv_version","alias_value":"0711.3632v1","created_at":"2026-05-18T04:41:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.3632","created_at":"2026-05-18T04:41:16Z"},{"alias_kind":"pith_short_12","alias_value":"WD44N5FPRNF2","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"WD44N5FPRNF27GWT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"WD44N5FP","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:6760b959fba257f0f076aef2b7d9440e59fe22f909d986904bc6ec3b8db0fbe5","target":"graph","created_at":"2026-05-18T04:41:16Z","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 article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic process which is independent of the state of the system, and between two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure global asymptotic stability using Lyapunov-based methods when individual subsystems are stable and a certain ``slow switching'' condition holds. This slow switching cond","authors_text":"Daniel Liberzon, Debasish Chatterjee","cross_cats":[],"headline":"","license":"","primary_cat":"math.OC","submitted_at":"2007-11-22T18:22:55Z","title":"On stability of randomly switched nonlinear systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.3632","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:fbb6e05d1962ac69e7f204a725265fa65f7d70eb6d39476076423334aa223db4","target":"record","created_at":"2026-05-18T04:41:16Z","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":"6bdba371916c12f4cdd0262e225c6e1871d763b8d5830f023a5111aa640dd003","cross_cats_sorted":[],"license":"","primary_cat":"math.OC","submitted_at":"2007-11-22T18:22:55Z","title_canon_sha256":"dbfad015336369429807a370c10613a9f273ec9601da056c338c83ee0599073c"},"schema_version":"1.0","source":{"id":"0711.3632","kind":"arxiv","version":1}},"canonical_sha256":"b0f9c6f4af8b4baf9ad3b26d15d2fe63e24c10a1b0424f530b1741876ddaf12e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0f9c6f4af8b4baf9ad3b26d15d2fe63e24c10a1b0424f530b1741876ddaf12e","first_computed_at":"2026-05-18T04:41:16.537204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:16.537204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"00JVRJleCk4FWtSGPbQPzYZDUaF9kdQynKQRgaaeOe/p4aseVvR4SnljJLERGKzb8FHL9IvFsPgTOq/1OYjHAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:16.537794Z","signed_message":"canonical_sha256_bytes"},"source_id":"0711.3632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbb6e05d1962ac69e7f204a725265fa65f7d70eb6d39476076423334aa223db4","sha256:6760b959fba257f0f076aef2b7d9440e59fe22f909d986904bc6ec3b8db0fbe5"],"state_sha256":"eb197796d3cd693895639cefa27ecef251619ab5bafa721b94b15d1007782e2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YSC1kpMm8nOuX50gB93MYGPQ1eU0xta7/LjnjOFELfbhj8TUBXRorwt3P5whjKbIQ06Mh8HQMTqSpJV9x/t1Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:54:51.300470Z","bundle_sha256":"4bea2e011f0f0a782bc90cdecee85cc8f87dd6ed82267d257d311eb9015ead8f"}}