{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:XQ75UUVU3GLGNMATMEPGL7PT6D","short_pith_number":"pith:XQ75UUVU","canonical_record":{"source":{"id":"2104.07200","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2021-04-15T02:20:43Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"947228cee33d053a9ebf6cc3ae08375a538caba20c69a434f236ff19c9510dcb","abstract_canon_sha256":"aab75ec82c89b8e198e5d32c9429dcc8a25f2c69e5ad8a0d04cdd4458a48b2c0"},"schema_version":"1.0"},"canonical_sha256":"bc3fda52b4d99666b013611e65fdf3f0d9cc141c182b434cb1e62a1f540d61ae","source":{"kind":"arxiv","id":"2104.07200","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.07200","created_at":"2026-07-05T03:36:02Z"},{"alias_kind":"arxiv_version","alias_value":"2104.07200v2","created_at":"2026-07-05T03:36:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.07200","created_at":"2026-07-05T03:36:02Z"},{"alias_kind":"pith_short_12","alias_value":"XQ75UUVU3GLG","created_at":"2026-07-05T03:36:02Z"},{"alias_kind":"pith_short_16","alias_value":"XQ75UUVU3GLGNMAT","created_at":"2026-07-05T03:36:02Z"},{"alias_kind":"pith_short_8","alias_value":"XQ75UUVU","created_at":"2026-07-05T03:36:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:XQ75UUVU3GLGNMATMEPGL7PT6D","target":"record","payload":{"canonical_record":{"source":{"id":"2104.07200","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2021-04-15T02:20:43Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"947228cee33d053a9ebf6cc3ae08375a538caba20c69a434f236ff19c9510dcb","abstract_canon_sha256":"aab75ec82c89b8e198e5d32c9429dcc8a25f2c69e5ad8a0d04cdd4458a48b2c0"},"schema_version":"1.0"},"canonical_sha256":"bc3fda52b4d99666b013611e65fdf3f0d9cc141c182b434cb1e62a1f540d61ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:36:02.753417Z","signature_b64":"32Zkjl9H9rXaTfCjpLym87aDbijBnNCLQUJ5yNcbk6wUDZEx9PGcQi+KG+ak2AmrHhQLa66X0fYf018JE8GNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc3fda52b4d99666b013611e65fdf3f0d9cc141c182b434cb1e62a1f540d61ae","last_reissued_at":"2026-07-05T03:36:02.752915Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:36:02.752915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.07200","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":"2026-07-05T03:36:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vfyrUIpTQ8oJ8cjUdBlPTzUo7TKKojX3GhTnBrV4tYxDXk5VXoUZaSngCftKh5Zalqhry8Tu9kx7AKYBHtAsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T06:40:13.847336Z"},"content_sha256":"0a7ecec963189f9630db6addd5d8df276b705399327a64246b97ea2c8336ce34","schema_version":"1.0","event_id":"sha256:0a7ecec963189f9630db6addd5d8df276b705399327a64246b97ea2c8336ce34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:XQ75UUVU3GLGNMATMEPGL7PT6D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Novel Unified Framework for Solving Reachability, Viability and Invariance Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Jizhou Lai, Taotao Liang, Wei Liao, Xiaohui Wei","submitted_at":"2021-04-15T02:20:43Z","abstract_excerpt":"The level set method is a widely used tool for solving reachability and invariance problems. However, some shortcomings, such as the difficulties of handling dissipation function and constructing terminal conditions for solving the Hamilton-Jacobi partial differential equation, limit the application of the level set method in some problems with non-affine nonlinear systems and irregular target sets. This paper proposes a method that can effectively avoid the above tricky issues and thus has better generality. In the proposed method, the reachable or invariant sets with different time horizons "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.07200","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/2104.07200/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":"2026-07-05T03:36:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ZJs85r28154Me2ubWkRmm+e7zMZuNlwLDiOfaPNOd0azrxIR1wRSwlWF/Z1RFfxR6abJMPGuTL3KRd1t6cwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T06:40:13.847718Z"},"content_sha256":"e39d8da92f141bd9097859916161ba29f889ee2230b0fff8f2a157a92a3c8f68","schema_version":"1.0","event_id":"sha256:e39d8da92f141bd9097859916161ba29f889ee2230b0fff8f2a157a92a3c8f68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XQ75UUVU3GLGNMATMEPGL7PT6D/bundle.json","state_url":"https://pith.science/pith/XQ75UUVU3GLGNMATMEPGL7PT6D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XQ75UUVU3GLGNMATMEPGL7PT6D/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":"2026-07-07T06:40:13Z","links":{"resolver":"https://pith.science/pith/XQ75UUVU3GLGNMATMEPGL7PT6D","bundle":"https://pith.science/pith/XQ75UUVU3GLGNMATMEPGL7PT6D/bundle.json","state":"https://pith.science/pith/XQ75UUVU3GLGNMATMEPGL7PT6D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XQ75UUVU3GLGNMATMEPGL7PT6D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:XQ75UUVU3GLGNMATMEPGL7PT6D","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":"aab75ec82c89b8e198e5d32c9429dcc8a25f2c69e5ad8a0d04cdd4458a48b2c0","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2021-04-15T02:20:43Z","title_canon_sha256":"947228cee33d053a9ebf6cc3ae08375a538caba20c69a434f236ff19c9510dcb"},"schema_version":"1.0","source":{"id":"2104.07200","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.07200","created_at":"2026-07-05T03:36:02Z"},{"alias_kind":"arxiv_version","alias_value":"2104.07200v2","created_at":"2026-07-05T03:36:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.07200","created_at":"2026-07-05T03:36:02Z"},{"alias_kind":"pith_short_12","alias_value":"XQ75UUVU3GLG","created_at":"2026-07-05T03:36:02Z"},{"alias_kind":"pith_short_16","alias_value":"XQ75UUVU3GLGNMAT","created_at":"2026-07-05T03:36:02Z"},{"alias_kind":"pith_short_8","alias_value":"XQ75UUVU","created_at":"2026-07-05T03:36:02Z"}],"graph_snapshots":[{"event_id":"sha256:e39d8da92f141bd9097859916161ba29f889ee2230b0fff8f2a157a92a3c8f68","target":"graph","created_at":"2026-07-05T03:36:02Z","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/2104.07200/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The level set method is a widely used tool for solving reachability and invariance problems. However, some shortcomings, such as the difficulties of handling dissipation function and constructing terminal conditions for solving the Hamilton-Jacobi partial differential equation, limit the application of the level set method in some problems with non-affine nonlinear systems and irregular target sets. This paper proposes a method that can effectively avoid the above tricky issues and thus has better generality. In the proposed method, the reachable or invariant sets with different time horizons ","authors_text":"Jizhou Lai, Taotao Liang, Wei Liao, Xiaohui Wei","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2021-04-15T02:20:43Z","title":"A Novel Unified Framework for Solving Reachability, Viability and Invariance Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.07200","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":"sha256:0a7ecec963189f9630db6addd5d8df276b705399327a64246b97ea2c8336ce34","target":"record","created_at":"2026-07-05T03:36:02Z","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":"aab75ec82c89b8e198e5d32c9429dcc8a25f2c69e5ad8a0d04cdd4458a48b2c0","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2021-04-15T02:20:43Z","title_canon_sha256":"947228cee33d053a9ebf6cc3ae08375a538caba20c69a434f236ff19c9510dcb"},"schema_version":"1.0","source":{"id":"2104.07200","kind":"arxiv","version":2}},"canonical_sha256":"bc3fda52b4d99666b013611e65fdf3f0d9cc141c182b434cb1e62a1f540d61ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc3fda52b4d99666b013611e65fdf3f0d9cc141c182b434cb1e62a1f540d61ae","first_computed_at":"2026-07-05T03:36:02.752915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:36:02.752915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"32Zkjl9H9rXaTfCjpLym87aDbijBnNCLQUJ5yNcbk6wUDZEx9PGcQi+KG+ak2AmrHhQLa66X0fYf018JE8GNCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:36:02.753417Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.07200","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a7ecec963189f9630db6addd5d8df276b705399327a64246b97ea2c8336ce34","sha256:e39d8da92f141bd9097859916161ba29f889ee2230b0fff8f2a157a92a3c8f68"],"state_sha256":"afc9c6d740b93a4e17523273ab068b72b91cd80418f12ceb3db3177650120305"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pUBq1dFlvPsh/gxnS0n6kkFHcfJsbCGteDUtsrJ33vZvZociIkTcU5m9oKeWCS0Yy3i3lE52lmygcDDrmUtKBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T06:40:13.849874Z","bundle_sha256":"cb93feae6f2ceafddc6a2e3259916362c9398afd13b0577a6493d4503bea59c7"}}