{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:BBZI3FBVYXLZRTSIAPFHQF42M5","short_pith_number":"pith:BBZI3FBV","canonical_record":{"source":{"id":"2210.09902","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2022-10-18T14:42:08Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"da072157fba27f6b144eb6313c1749ce928868d2dbb146089e8ce97dab089040","abstract_canon_sha256":"cdf5eaa9b532eef64eea7d472c870836362a7a6c114bd577989be2c7a8469cf5"},"schema_version":"1.0"},"canonical_sha256":"08728d9435c5d798ce4803ca78179a677fa89429b195d910dc06a060de6a364c","source":{"kind":"arxiv","id":"2210.09902","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.09902","created_at":"2026-07-05T06:01:14Z"},{"alias_kind":"arxiv_version","alias_value":"2210.09902v2","created_at":"2026-07-05T06:01:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.09902","created_at":"2026-07-05T06:01:14Z"},{"alias_kind":"pith_short_12","alias_value":"BBZI3FBVYXLZ","created_at":"2026-07-05T06:01:14Z"},{"alias_kind":"pith_short_16","alias_value":"BBZI3FBVYXLZRTSI","created_at":"2026-07-05T06:01:14Z"},{"alias_kind":"pith_short_8","alias_value":"BBZI3FBV","created_at":"2026-07-05T06:01:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:BBZI3FBVYXLZRTSIAPFHQF42M5","target":"record","payload":{"canonical_record":{"source":{"id":"2210.09902","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2022-10-18T14:42:08Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"da072157fba27f6b144eb6313c1749ce928868d2dbb146089e8ce97dab089040","abstract_canon_sha256":"cdf5eaa9b532eef64eea7d472c870836362a7a6c114bd577989be2c7a8469cf5"},"schema_version":"1.0"},"canonical_sha256":"08728d9435c5d798ce4803ca78179a677fa89429b195d910dc06a060de6a364c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:01:14.084215Z","signature_b64":"5i0cF3AbhPlqs3dGea217txf5UWmvy+ZKR69ZkMxZZBb3PHKQOM5OI3TFJp1YnrMR7Bq1/uC4xQAY3/rHypTDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08728d9435c5d798ce4803ca78179a677fa89429b195d910dc06a060de6a364c","last_reissued_at":"2026-07-05T06:01:14.083822Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:01:14.083822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.09902","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":"2026-07-05T06:01:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eTDB2yWSMRPkRBqyvJxMw4Ew5XKsSpaHyCb0c+0sUqIRPExKl0zmCN7mcdE7Rc2lRwEH3a145szFUTbWs9nCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T01:10:17.032365Z"},"content_sha256":"b948c53ff796d3455f53989c1f423d3fb9aa69876810d86ba3715b668ce43e43","schema_version":"1.0","event_id":"sha256:b948c53ff796d3455f53989c1f423d3fb9aa69876810d86ba3715b668ce43e43"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:BBZI3FBVYXLZRTSIAPFHQF42M5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Successor Sets of Discrete-time Nonlinear Systems Using Hybrid Zonotopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Herschel C. Pangborn, Jacob A. Siefert, Justin P. Koeln, Neera Jain, Trevor J. Bird","submitted_at":"2022-10-18T14:42:08Z","abstract_excerpt":"This paper presents identities for calculating over-approximated successor sets of discrete-time nonlinear systems using hybrid zonotopes. The proposed technique extends the state-update set construct, previously developed for linear hybrid systems, to nonlinear systems. Forward reachability of nonlinear systems can then be performed using only projection, intersection, and Cartesian product set operations with the state-update set. It is shown that use of an over-approximation of the state-update set yields over-approximations of successor sets. A technique to over-approximate a nonlinear fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.09902","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/2210.09902/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":"2026-07-05T06:01:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fHrOyC4skTmdnCH4g6CkXiApO6t1TtuW1GOlSn4NWP/KkmILyj5BDuLOun1KIvW3snKfVJ5k7QervWZ4BPhNDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T01:10:17.032883Z"},"content_sha256":"6efa95eae2a322649308f844ffacd40881598ec1c5490bc2aa2421ac71e099ed","schema_version":"1.0","event_id":"sha256:6efa95eae2a322649308f844ffacd40881598ec1c5490bc2aa2421ac71e099ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BBZI3FBVYXLZRTSIAPFHQF42M5/bundle.json","state_url":"https://pith.science/pith/BBZI3FBVYXLZRTSIAPFHQF42M5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BBZI3FBVYXLZRTSIAPFHQF42M5/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":"2026-08-17T01:10:17Z","links":{"resolver":"https://pith.science/pith/BBZI3FBVYXLZRTSIAPFHQF42M5","bundle":"https://pith.science/pith/BBZI3FBVYXLZRTSIAPFHQF42M5/bundle.json","state":"https://pith.science/pith/BBZI3FBVYXLZRTSIAPFHQF42M5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BBZI3FBVYXLZRTSIAPFHQF42M5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:BBZI3FBVYXLZRTSIAPFHQF42M5","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":"cdf5eaa9b532eef64eea7d472c870836362a7a6c114bd577989be2c7a8469cf5","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2022-10-18T14:42:08Z","title_canon_sha256":"da072157fba27f6b144eb6313c1749ce928868d2dbb146089e8ce97dab089040"},"schema_version":"1.0","source":{"id":"2210.09902","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.09902","created_at":"2026-07-05T06:01:14Z"},{"alias_kind":"arxiv_version","alias_value":"2210.09902v2","created_at":"2026-07-05T06:01:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.09902","created_at":"2026-07-05T06:01:14Z"},{"alias_kind":"pith_short_12","alias_value":"BBZI3FBVYXLZ","created_at":"2026-07-05T06:01:14Z"},{"alias_kind":"pith_short_16","alias_value":"BBZI3FBVYXLZRTSI","created_at":"2026-07-05T06:01:14Z"},{"alias_kind":"pith_short_8","alias_value":"BBZI3FBV","created_at":"2026-07-05T06:01:14Z"}],"graph_snapshots":[{"event_id":"sha256:6efa95eae2a322649308f844ffacd40881598ec1c5490bc2aa2421ac71e099ed","target":"graph","created_at":"2026-07-05T06:01:14Z","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/2210.09902/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper presents identities for calculating over-approximated successor sets of discrete-time nonlinear systems using hybrid zonotopes. The proposed technique extends the state-update set construct, previously developed for linear hybrid systems, to nonlinear systems. Forward reachability of nonlinear systems can then be performed using only projection, intersection, and Cartesian product set operations with the state-update set. It is shown that use of an over-approximation of the state-update set yields over-approximations of successor sets. A technique to over-approximate a nonlinear fun","authors_text":"Herschel C. Pangborn, Jacob A. Siefert, Justin P. Koeln, Neera Jain, Trevor J. Bird","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2022-10-18T14:42:08Z","title":"Successor Sets of Discrete-time Nonlinear Systems Using Hybrid Zonotopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.09902","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:b948c53ff796d3455f53989c1f423d3fb9aa69876810d86ba3715b668ce43e43","target":"record","created_at":"2026-07-05T06:01:14Z","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":"cdf5eaa9b532eef64eea7d472c870836362a7a6c114bd577989be2c7a8469cf5","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2022-10-18T14:42:08Z","title_canon_sha256":"da072157fba27f6b144eb6313c1749ce928868d2dbb146089e8ce97dab089040"},"schema_version":"1.0","source":{"id":"2210.09902","kind":"arxiv","version":2}},"canonical_sha256":"08728d9435c5d798ce4803ca78179a677fa89429b195d910dc06a060de6a364c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08728d9435c5d798ce4803ca78179a677fa89429b195d910dc06a060de6a364c","first_computed_at":"2026-07-05T06:01:14.083822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:01:14.083822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5i0cF3AbhPlqs3dGea217txf5UWmvy+ZKR69ZkMxZZBb3PHKQOM5OI3TFJp1YnrMR7Bq1/uC4xQAY3/rHypTDA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:01:14.084215Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.09902","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b948c53ff796d3455f53989c1f423d3fb9aa69876810d86ba3715b668ce43e43","sha256:6efa95eae2a322649308f844ffacd40881598ec1c5490bc2aa2421ac71e099ed"],"state_sha256":"da0f15ee871ad95663aa36fbd0d2568eac716e065c497a4f8fb22daaa7db7898"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YpcBNdRejxMcoV/krqKmBNZxw1PPBJWT/F+Ty8gGiQeQn9zUcMScMDmo+sYvzeUJ6TIfXX00l4x4Tr8CBeOwAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T01:10:17.037167Z","bundle_sha256":"4017c5ba55434f32852196ce678b0ec9271e054adadb2c829f9203d161ad9696"}}