{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OUTQ3GT26KQ4UHDQGV3BQPODHW","short_pith_number":"pith:OUTQ3GT2","canonical_record":{"source":{"id":"1704.03555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-04-11T22:29:01Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"562ef76691e6e284a01322e312c95652f11ee1f402aa8c4b51c98eebb277265e","abstract_canon_sha256":"a199d12b7af9b84f0a43104a48edf2c2b4137eb619985641558905258fe5bd7f"},"schema_version":"1.0"},"canonical_sha256":"75270d9a7af2a1ca1c703576183dc33d9483db360d16162181f5dc3603d42c0a","source":{"kind":"arxiv","id":"1704.03555","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03555","created_at":"2026-05-18T00:46:27Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03555v1","created_at":"2026-05-18T00:46:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03555","created_at":"2026-05-18T00:46:27Z"},{"alias_kind":"pith_short_12","alias_value":"OUTQ3GT26KQ4","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OUTQ3GT26KQ4UHDQ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OUTQ3GT2","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OUTQ3GT26KQ4UHDQGV3BQPODHW","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-04-11T22:29:01Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"562ef76691e6e284a01322e312c95652f11ee1f402aa8c4b51c98eebb277265e","abstract_canon_sha256":"a199d12b7af9b84f0a43104a48edf2c2b4137eb619985641558905258fe5bd7f"},"schema_version":"1.0"},"canonical_sha256":"75270d9a7af2a1ca1c703576183dc33d9483db360d16162181f5dc3603d42c0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:27.471048Z","signature_b64":"go63lIcOtuO2BS8ywq4kzT9Gjl88l9l9zqA/HAJ38trPApQInKYZ2D6AWO5qJCWNmfXct2aS51kUL1RxPfbkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75270d9a7af2a1ca1c703576183dc33d9483db360d16162181f5dc3603d42c0a","last_reissued_at":"2026-05-18T00:46:27.470585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:27.470585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03555","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":"2026-05-18T00:46:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rom2hf1xT9D2pDOmsqC3L8Yw/lChNO/+MwoAGAGLfIBmV5W+IlIqSyWs6UD4cefCgDAxf6amfPnfmQiLxq40Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:21:15.308491Z"},"content_sha256":"a52d16b7d15471cc98e6ec0aec1ec7e48ba4adba877fb2a396374f5a718097c4","schema_version":"1.0","event_id":"sha256:a52d16b7d15471cc98e6ec0aec1ec7e48ba4adba877fb2a396374f5a718097c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OUTQ3GT26KQ4UHDQGV3BQPODHW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Underapproximation of Reach-Avoid Sets for Discrete-Time Stochastic Systems via Lagrangian Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.SY","authors_text":"Abraham P. Vinod, Joseph D. Gleason, Meeko. M. K. Oishi","submitted_at":"2017-04-11T22:29:01Z","abstract_excerpt":"We examine Lagrangian techniques for computing underapproximations of finite-time horizon, stochastic reach-avoid level-sets for discrete-time, nonlinear systems. We use the concept of reachability of a target tube in the control literature to define robust reach-avoid sets which are parameterized by the target set, safe set, and the set in which the disturbance is drawn from. We unify two existing Lagrangian approaches to compute these sets and establish that there exists an optimal control policy of the robust reach-avoid sets which is a Markov policy. Based on these results, we characterize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03555","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":"2026-05-18T00:46:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AsK5OTm61csb9KM08EXc7GdcbyhVH+OTSIRX9L8/yQ955LR8Mxzefq2qcdTSnvIgnHIfvmRst3SjoUwHh4CPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:21:15.309212Z"},"content_sha256":"24a3aa3491c2f4c86e0a43e48f5e00bd4c1816bed3d0c4bd8d17036fc89e1537","schema_version":"1.0","event_id":"sha256:24a3aa3491c2f4c86e0a43e48f5e00bd4c1816bed3d0c4bd8d17036fc89e1537"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OUTQ3GT26KQ4UHDQGV3BQPODHW/bundle.json","state_url":"https://pith.science/pith/OUTQ3GT26KQ4UHDQGV3BQPODHW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OUTQ3GT26KQ4UHDQGV3BQPODHW/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":"2026-05-31T17:21:15Z","links":{"resolver":"https://pith.science/pith/OUTQ3GT26KQ4UHDQGV3BQPODHW","bundle":"https://pith.science/pith/OUTQ3GT26KQ4UHDQGV3BQPODHW/bundle.json","state":"https://pith.science/pith/OUTQ3GT26KQ4UHDQGV3BQPODHW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OUTQ3GT26KQ4UHDQGV3BQPODHW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OUTQ3GT26KQ4UHDQGV3BQPODHW","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":"a199d12b7af9b84f0a43104a48edf2c2b4137eb619985641558905258fe5bd7f","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-04-11T22:29:01Z","title_canon_sha256":"562ef76691e6e284a01322e312c95652f11ee1f402aa8c4b51c98eebb277265e"},"schema_version":"1.0","source":{"id":"1704.03555","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03555","created_at":"2026-05-18T00:46:27Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03555v1","created_at":"2026-05-18T00:46:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03555","created_at":"2026-05-18T00:46:27Z"},{"alias_kind":"pith_short_12","alias_value":"OUTQ3GT26KQ4","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OUTQ3GT26KQ4UHDQ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OUTQ3GT2","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:24a3aa3491c2f4c86e0a43e48f5e00bd4c1816bed3d0c4bd8d17036fc89e1537","target":"graph","created_at":"2026-05-18T00:46:27Z","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":"We examine Lagrangian techniques for computing underapproximations of finite-time horizon, stochastic reach-avoid level-sets for discrete-time, nonlinear systems. We use the concept of reachability of a target tube in the control literature to define robust reach-avoid sets which are parameterized by the target set, safe set, and the set in which the disturbance is drawn from. We unify two existing Lagrangian approaches to compute these sets and establish that there exists an optimal control policy of the robust reach-avoid sets which is a Markov policy. Based on these results, we characterize","authors_text":"Abraham P. Vinod, Joseph D. Gleason, Meeko. M. K. Oishi","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-04-11T22:29:01Z","title":"Underapproximation of Reach-Avoid Sets for Discrete-Time Stochastic Systems via Lagrangian Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03555","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:a52d16b7d15471cc98e6ec0aec1ec7e48ba4adba877fb2a396374f5a718097c4","target":"record","created_at":"2026-05-18T00:46:27Z","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":"a199d12b7af9b84f0a43104a48edf2c2b4137eb619985641558905258fe5bd7f","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-04-11T22:29:01Z","title_canon_sha256":"562ef76691e6e284a01322e312c95652f11ee1f402aa8c4b51c98eebb277265e"},"schema_version":"1.0","source":{"id":"1704.03555","kind":"arxiv","version":1}},"canonical_sha256":"75270d9a7af2a1ca1c703576183dc33d9483db360d16162181f5dc3603d42c0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75270d9a7af2a1ca1c703576183dc33d9483db360d16162181f5dc3603d42c0a","first_computed_at":"2026-05-18T00:46:27.470585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:27.470585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"go63lIcOtuO2BS8ywq4kzT9Gjl88l9l9zqA/HAJ38trPApQInKYZ2D6AWO5qJCWNmfXct2aS51kUL1RxPfbkBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:27.471048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03555","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a52d16b7d15471cc98e6ec0aec1ec7e48ba4adba877fb2a396374f5a718097c4","sha256:24a3aa3491c2f4c86e0a43e48f5e00bd4c1816bed3d0c4bd8d17036fc89e1537"],"state_sha256":"6dfef104167fa7d276e79a6c12ba647cd0298cfb84e46156931ec84f22ae8145"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j/0kcaySivN1PqAWtECtiq2BkmJtpGjoYIiEnuQinxM0QXhy/mw4PVOtcW77ImaV0TxJ5oFadtDsawMR1LjRAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T17:21:15.313928Z","bundle_sha256":"40c2a07b8e28be8755dae4d0cb09509bb9e6bc7bc7d670e50226051fd82d89d5"}}