{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QXS43NT2YZR5DGJNJDAXST3O4H","short_pith_number":"pith:QXS43NT2","canonical_record":{"source":{"id":"1309.5317","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-20T16:43:51Z","cross_cats_sorted":[],"title_canon_sha256":"e69bcb7b97c9c9f04d05e2e9fa5ff17ae83214acf539a747e0d2517f26d23177","abstract_canon_sha256":"b8317abc07864674de7611e9246325385e7b3fb404d6c83a77afbcf827fa4bf1"},"schema_version":"1.0"},"canonical_sha256":"85e5cdb67ac663d1992d48c1794f6ee1d1d3d0abd440a1b601666263f43f91af","source":{"kind":"arxiv","id":"1309.5317","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5317","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5317v2","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5317","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"QXS43NT2YZR5","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QXS43NT2YZR5DGJN","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QXS43NT2","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QXS43NT2YZR5DGJNJDAXST3O4H","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5317","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-20T16:43:51Z","cross_cats_sorted":[],"title_canon_sha256":"e69bcb7b97c9c9f04d05e2e9fa5ff17ae83214acf539a747e0d2517f26d23177","abstract_canon_sha256":"b8317abc07864674de7611e9246325385e7b3fb404d6c83a77afbcf827fa4bf1"},"schema_version":"1.0"},"canonical_sha256":"85e5cdb67ac663d1992d48c1794f6ee1d1d3d0abd440a1b601666263f43f91af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:11.148355Z","signature_b64":"pdYmmQq/PNmHJQA83E+PsoEigXnEXinDwJD5yuSDYtQOZBQUSeVPjm2nAi+Dt3uWQyucwHie/gtpFfkBwkP1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85e5cdb67ac663d1992d48c1794f6ee1d1d3d0abd440a1b601666263f43f91af","last_reissued_at":"2026-05-18T03:12:11.147589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:11.147589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5317","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xOrr1YAP7oQvobZH95C0GYLUNggojN7zaZi22vm2j9YJg+Kcnloi2JbOYRpzG0HVA9GCZyzX8fpA6bdsexxXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:12:11.584754Z"},"content_sha256":"f866a1c1331cb623a88f5b6e988e26ad580de0dd6e3c38ba83c2fa6a9791c001","schema_version":"1.0","event_id":"sha256:f866a1c1331cb623a88f5b6e988e26ad580de0dd6e3c38ba83c2fa6a9791c001"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QXS43NT2YZR5DGJNJDAXST3O4H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contraction analysis of nonlinear random dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jean-Jacques Slotine (MIT), LINA), Nicolas Tabareau (INRIA - EMN","submitted_at":"2013-09-20T16:43:51Z","abstract_excerpt":"In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \\cite{Lohmiller98} to random differential equations. We propose new definitions of contraction (almost sure contraction and contraction in mean square) which allow to master the evolution of a stochastic system in two manners. The first one guarantees eventual exponential convergence of the system for almost all draws, whereas the other guarantees the exponential convergence in $L_2$ of to a unique trajectory. We then illustrate the relativ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5317","kind":"arxiv","version":2},"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":"2026-05-18T03:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m2jYqswJqD3bA1f8JKfCypqExJTtlvQfHmo0k9aSR38p7+PfVcv7F5ZdqEjkfxLgvQr9PfouVjwfku7Si5AXBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:12:11.585454Z"},"content_sha256":"32b1b1f384eeca1c3dcd579490248898422075d42ae0ef47ca2938914298b887","schema_version":"1.0","event_id":"sha256:32b1b1f384eeca1c3dcd579490248898422075d42ae0ef47ca2938914298b887"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QXS43NT2YZR5DGJNJDAXST3O4H/bundle.json","state_url":"https://pith.science/pith/QXS43NT2YZR5DGJNJDAXST3O4H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QXS43NT2YZR5DGJNJDAXST3O4H/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":"2026-06-06T04:12:11Z","links":{"resolver":"https://pith.science/pith/QXS43NT2YZR5DGJNJDAXST3O4H","bundle":"https://pith.science/pith/QXS43NT2YZR5DGJNJDAXST3O4H/bundle.json","state":"https://pith.science/pith/QXS43NT2YZR5DGJNJDAXST3O4H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QXS43NT2YZR5DGJNJDAXST3O4H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QXS43NT2YZR5DGJNJDAXST3O4H","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":"b8317abc07864674de7611e9246325385e7b3fb404d6c83a77afbcf827fa4bf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-20T16:43:51Z","title_canon_sha256":"e69bcb7b97c9c9f04d05e2e9fa5ff17ae83214acf539a747e0d2517f26d23177"},"schema_version":"1.0","source":{"id":"1309.5317","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5317","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5317v2","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5317","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"QXS43NT2YZR5","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QXS43NT2YZR5DGJN","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QXS43NT2","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:32b1b1f384eeca1c3dcd579490248898422075d42ae0ef47ca2938914298b887","target":"graph","created_at":"2026-05-18T03:12:11Z","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":"In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \\cite{Lohmiller98} to random differential equations. We propose new definitions of contraction (almost sure contraction and contraction in mean square) which allow to master the evolution of a stochastic system in two manners. The first one guarantees eventual exponential convergence of the system for almost all draws, whereas the other guarantees the exponential convergence in $L_2$ of to a unique trajectory. We then illustrate the relativ","authors_text":"Jean-Jacques Slotine (MIT), LINA), Nicolas Tabareau (INRIA - EMN","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-20T16:43:51Z","title":"Contraction analysis of nonlinear random dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5317","kind":"arxiv","version":2},"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:f866a1c1331cb623a88f5b6e988e26ad580de0dd6e3c38ba83c2fa6a9791c001","target":"record","created_at":"2026-05-18T03:12:11Z","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":"b8317abc07864674de7611e9246325385e7b3fb404d6c83a77afbcf827fa4bf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-20T16:43:51Z","title_canon_sha256":"e69bcb7b97c9c9f04d05e2e9fa5ff17ae83214acf539a747e0d2517f26d23177"},"schema_version":"1.0","source":{"id":"1309.5317","kind":"arxiv","version":2}},"canonical_sha256":"85e5cdb67ac663d1992d48c1794f6ee1d1d3d0abd440a1b601666263f43f91af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85e5cdb67ac663d1992d48c1794f6ee1d1d3d0abd440a1b601666263f43f91af","first_computed_at":"2026-05-18T03:12:11.147589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:11.147589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pdYmmQq/PNmHJQA83E+PsoEigXnEXinDwJD5yuSDYtQOZBQUSeVPjm2nAi+Dt3uWQyucwHie/gtpFfkBwkP1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:11.148355Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5317","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f866a1c1331cb623a88f5b6e988e26ad580de0dd6e3c38ba83c2fa6a9791c001","sha256:32b1b1f384eeca1c3dcd579490248898422075d42ae0ef47ca2938914298b887"],"state_sha256":"0b397df7dd950610da114c054b068b7eea078664259358344eef1fa691806abd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rC+CncPv+Ddo8QIuETZmCm0BBgyIq/cXQSpWleOqdchEVlE6SSN7vJ7OhoXScZhNItKAcuREwbIxxrXWSrNGAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T04:12:11.589038Z","bundle_sha256":"b8423aa8a2e4a26fd47f147152a3f3b777b601f64abcc6522fee413dd67b2778"}}