{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:O6VSKO32XKAXLUDMNQ22BL6GXB","short_pith_number":"pith:O6VSKO32","canonical_record":{"source":{"id":"1908.00483","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-01T16:18:30Z","cross_cats_sorted":[],"title_canon_sha256":"a5d4505f65dd0bb8ba57c64deec2365c107fda742d0a8d783be6399eba8e6f9a","abstract_canon_sha256":"a071d0cf715d3f18e29d10ed7b39b2daa5fc86b343832235b8e04ecd7f5d0a31"},"schema_version":"1.0"},"canonical_sha256":"77ab253b7aba8175d06c6c35a0afc6b862b90ed2cc49e513bcd6b200f637d870","source":{"kind":"arxiv","id":"1908.00483","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00483","created_at":"2026-07-05T00:52:47Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00483v2","created_at":"2026-07-05T00:52:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00483","created_at":"2026-07-05T00:52:47Z"},{"alias_kind":"pith_short_12","alias_value":"O6VSKO32XKAX","created_at":"2026-07-05T00:52:47Z"},{"alias_kind":"pith_short_16","alias_value":"O6VSKO32XKAXLUDM","created_at":"2026-07-05T00:52:47Z"},{"alias_kind":"pith_short_8","alias_value":"O6VSKO32","created_at":"2026-07-05T00:52:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:O6VSKO32XKAXLUDMNQ22BL6GXB","target":"record","payload":{"canonical_record":{"source":{"id":"1908.00483","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-01T16:18:30Z","cross_cats_sorted":[],"title_canon_sha256":"a5d4505f65dd0bb8ba57c64deec2365c107fda742d0a8d783be6399eba8e6f9a","abstract_canon_sha256":"a071d0cf715d3f18e29d10ed7b39b2daa5fc86b343832235b8e04ecd7f5d0a31"},"schema_version":"1.0"},"canonical_sha256":"77ab253b7aba8175d06c6c35a0afc6b862b90ed2cc49e513bcd6b200f637d870","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:52:47.711764Z","signature_b64":"w5oPqQJRxm/2lCGz2NuUXbCRfjdok5zjIYSPVslwiCxPWA0YCCRbwEpWDVs9vcsQuVWmSq9mRpGs9UE1dl99AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77ab253b7aba8175d06c6c35a0afc6b862b90ed2cc49e513bcd6b200f637d870","last_reissued_at":"2026-07-05T00:52:47.711293Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:52:47.711293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.00483","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":"2026-07-05T00:52:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WYPoGYbxBbGiWOApMnAedK7n9oi7zcIGfJu7rahxMkWDBEi02cWR57oiBi5a+o3CsZ2UFr0ULL4jnIoRXCMHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T21:27:08.933388Z"},"content_sha256":"d936fe02ebe64a215db22298359523ca99ead135ac890ecab3c6e3eea9c37163","schema_version":"1.0","event_id":"sha256:d936fe02ebe64a215db22298359523ca99ead135ac890ecab3c6e3eea9c37163"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:O6VSKO32XKAXLUDMNQ22BL6GXB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of stochastic nonlinear systems and implications for Stochastic Model Predictive Control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Diego Mu\\~noz-Carpintero, Mark Cannon","submitted_at":"2019-08-01T16:18:30Z","abstract_excerpt":"The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that ensure closed-loop performance bounds and boundedness of the state, but tight ultimate bounds for the state and non-conservative performance bounds are typically not determined. In this work we use an input-to-state stability property to find conditions that imply convergence with probability 1 of a disturbed nonlinear system to a minimal robust positively invariant set. We discuss implications for the convergence of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00483","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.00483/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":"2026-07-05T00:52:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T3W9tohC55ouDtkpU0kfRuMhvZrTjUA89vVV7XRQdxjqHdeQ7cWIX1xpfRNySY6QO55/1ZFBHvQx4KKz3sscCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T21:27:08.933885Z"},"content_sha256":"8f719951f3afdf6ddaf1b4ba16ac961ba7c7aa85bf01a5527028be5f98de682a","schema_version":"1.0","event_id":"sha256:8f719951f3afdf6ddaf1b4ba16ac961ba7c7aa85bf01a5527028be5f98de682a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O6VSKO32XKAXLUDMNQ22BL6GXB/bundle.json","state_url":"https://pith.science/pith/O6VSKO32XKAXLUDMNQ22BL6GXB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O6VSKO32XKAXLUDMNQ22BL6GXB/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":"2026-08-16T21:27:08Z","links":{"resolver":"https://pith.science/pith/O6VSKO32XKAXLUDMNQ22BL6GXB","bundle":"https://pith.science/pith/O6VSKO32XKAXLUDMNQ22BL6GXB/bundle.json","state":"https://pith.science/pith/O6VSKO32XKAXLUDMNQ22BL6GXB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O6VSKO32XKAXLUDMNQ22BL6GXB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:O6VSKO32XKAXLUDMNQ22BL6GXB","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":"a071d0cf715d3f18e29d10ed7b39b2daa5fc86b343832235b8e04ecd7f5d0a31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-01T16:18:30Z","title_canon_sha256":"a5d4505f65dd0bb8ba57c64deec2365c107fda742d0a8d783be6399eba8e6f9a"},"schema_version":"1.0","source":{"id":"1908.00483","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00483","created_at":"2026-07-05T00:52:47Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00483v2","created_at":"2026-07-05T00:52:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00483","created_at":"2026-07-05T00:52:47Z"},{"alias_kind":"pith_short_12","alias_value":"O6VSKO32XKAX","created_at":"2026-07-05T00:52:47Z"},{"alias_kind":"pith_short_16","alias_value":"O6VSKO32XKAXLUDM","created_at":"2026-07-05T00:52:47Z"},{"alias_kind":"pith_short_8","alias_value":"O6VSKO32","created_at":"2026-07-05T00:52:47Z"}],"graph_snapshots":[{"event_id":"sha256:8f719951f3afdf6ddaf1b4ba16ac961ba7c7aa85bf01a5527028be5f98de682a","target":"graph","created_at":"2026-07-05T00:52:47Z","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/1908.00483/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that ensure closed-loop performance bounds and boundedness of the state, but tight ultimate bounds for the state and non-conservative performance bounds are typically not determined. In this work we use an input-to-state stability property to find conditions that imply convergence with probability 1 of a disturbed nonlinear system to a minimal robust positively invariant set. We discuss implications for the convergence of","authors_text":"Diego Mu\\~noz-Carpintero, Mark Cannon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-01T16:18:30Z","title":"Convergence of stochastic nonlinear systems and implications for Stochastic Model Predictive Control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00483","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:d936fe02ebe64a215db22298359523ca99ead135ac890ecab3c6e3eea9c37163","target":"record","created_at":"2026-07-05T00:52:47Z","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":"a071d0cf715d3f18e29d10ed7b39b2daa5fc86b343832235b8e04ecd7f5d0a31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-01T16:18:30Z","title_canon_sha256":"a5d4505f65dd0bb8ba57c64deec2365c107fda742d0a8d783be6399eba8e6f9a"},"schema_version":"1.0","source":{"id":"1908.00483","kind":"arxiv","version":2}},"canonical_sha256":"77ab253b7aba8175d06c6c35a0afc6b862b90ed2cc49e513bcd6b200f637d870","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77ab253b7aba8175d06c6c35a0afc6b862b90ed2cc49e513bcd6b200f637d870","first_computed_at":"2026-07-05T00:52:47.711293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:52:47.711293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w5oPqQJRxm/2lCGz2NuUXbCRfjdok5zjIYSPVslwiCxPWA0YCCRbwEpWDVs9vcsQuVWmSq9mRpGs9UE1dl99AA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:52:47.711764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.00483","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d936fe02ebe64a215db22298359523ca99ead135ac890ecab3c6e3eea9c37163","sha256:8f719951f3afdf6ddaf1b4ba16ac961ba7c7aa85bf01a5527028be5f98de682a"],"state_sha256":"876a877744f6fa7a07ace1af2f5864c71acba881ea32de6762fc90f98ad7d100"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LNnk+1D/1YmAZm4wLxarBTIViDd+u+hy2eTa3f/4oQK6+hzPhqtII9ISr6JAy/YeZ5lEzPCXmKeYfxFnCl3GBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T21:27:08.937130Z","bundle_sha256":"4b8542316eddccbdb14a202b7359dd7a28b172238d4ee0014c00d3b91948b694"}}