{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ESSMKMQOKXXG3DQUNEU2KFB652","short_pith_number":"pith:ESSMKMQO","canonical_record":{"source":{"id":"1507.05648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-20T20:48:40Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"91be41a58ba1eb57abb11d5b6a61352e54604a7cabd5c22539fd2da08ff02894","abstract_canon_sha256":"f884ff1973e1e864b8e900bf3c0c7ecdb146fa005fc54af0c8b8f331bed5c5d3"},"schema_version":"1.0"},"canonical_sha256":"24a4c5320e55ee6d8e146929a5143eeeb4174e28d4abf13d1c985138ba69231a","source":{"kind":"arxiv","id":"1507.05648","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05648","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05648v1","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05648","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"pith_short_12","alias_value":"ESSMKMQOKXXG","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ESSMKMQOKXXG3DQU","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ESSMKMQO","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ESSMKMQOKXXG3DQUNEU2KFB652","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-20T20:48:40Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"91be41a58ba1eb57abb11d5b6a61352e54604a7cabd5c22539fd2da08ff02894","abstract_canon_sha256":"f884ff1973e1e864b8e900bf3c0c7ecdb146fa005fc54af0c8b8f331bed5c5d3"},"schema_version":"1.0"},"canonical_sha256":"24a4c5320e55ee6d8e146929a5143eeeb4174e28d4abf13d1c985138ba69231a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:32.833186Z","signature_b64":"iNkLi/X3fQ5MU5dBiSWf5DPMLfTNJg4dTkQDwInDIqD+PyiBWUf5n62piK2aWZTF5jXUpCGJeAEMu5huIBEBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24a4c5320e55ee6d8e146929a5143eeeb4174e28d4abf13d1c985138ba69231a","last_reissued_at":"2026-05-18T01:36:32.832413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:32.832413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05648","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":"2026-05-18T01:36:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z1tSiWlNLRvjWjCBhzRdwDJgekYzue3ibYDbC2hZKRX0bm8XHSti7EVcmpqzABki/qoqVYFCA/Ct/NeHVRUOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:09:41.084665Z"},"content_sha256":"a485919cf2198de24853c2860e50f619605195ffd582ebb3ffa764280a57ed12","schema_version":"1.0","event_id":"sha256:a485919cf2198de24853c2860e50f619605195ffd582ebb3ffa764280a57ed12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ESSMKMQOKXXG3DQUNEU2KFB652","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lyapunov-based sufficient conditions for stability of hybrid systems with memory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"math.DS","authors_text":"Andrew R. Teel, Jun Liu","submitted_at":"2015-07-20T20:48:40Z","abstract_excerpt":"Hybrid systems with memory are dynamical systems exhibiting both hybrid and delay phenomena. In this note, we study the asymptotic stability of hybrid systems with memory using generalized concepts of solutions. These generalized solutions, motivated by studying robustness and well-posedness of such systems, are defined on hybrid time domains and parameterized by both continuous and discrete time. We establish Lyapunov-based sufficient conditions for asymptotic stability using both Lyapunov-Razumikhin functions and Lyapunov-Krasovskii functionals. Examples are provided to illustrate these cond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05648","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":"2026-05-18T01:36:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kkmdo6Y6q12Ay27psvGkx9EjckZ15G73IGRsBpnZ4oS6PWLiQ08rSmwHttODVgmxJHyvo1GXLi9YHlDCe0HrBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:09:41.085367Z"},"content_sha256":"db51dc8063b8f59707c9091e43ee1148aceb10a419b757df61a3b46f419f0788","schema_version":"1.0","event_id":"sha256:db51dc8063b8f59707c9091e43ee1148aceb10a419b757df61a3b46f419f0788"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ESSMKMQOKXXG3DQUNEU2KFB652/bundle.json","state_url":"https://pith.science/pith/ESSMKMQOKXXG3DQUNEU2KFB652/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ESSMKMQOKXXG3DQUNEU2KFB652/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":"2026-06-09T21:09:41Z","links":{"resolver":"https://pith.science/pith/ESSMKMQOKXXG3DQUNEU2KFB652","bundle":"https://pith.science/pith/ESSMKMQOKXXG3DQUNEU2KFB652/bundle.json","state":"https://pith.science/pith/ESSMKMQOKXXG3DQUNEU2KFB652/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ESSMKMQOKXXG3DQUNEU2KFB652/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ESSMKMQOKXXG3DQUNEU2KFB652","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":"f884ff1973e1e864b8e900bf3c0c7ecdb146fa005fc54af0c8b8f331bed5c5d3","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-20T20:48:40Z","title_canon_sha256":"91be41a58ba1eb57abb11d5b6a61352e54604a7cabd5c22539fd2da08ff02894"},"schema_version":"1.0","source":{"id":"1507.05648","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05648","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05648v1","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05648","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"pith_short_12","alias_value":"ESSMKMQOKXXG","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ESSMKMQOKXXG3DQU","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ESSMKMQO","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:db51dc8063b8f59707c9091e43ee1148aceb10a419b757df61a3b46f419f0788","target":"graph","created_at":"2026-05-18T01:36:32Z","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":"Hybrid systems with memory are dynamical systems exhibiting both hybrid and delay phenomena. In this note, we study the asymptotic stability of hybrid systems with memory using generalized concepts of solutions. These generalized solutions, motivated by studying robustness and well-posedness of such systems, are defined on hybrid time domains and parameterized by both continuous and discrete time. We establish Lyapunov-based sufficient conditions for asymptotic stability using both Lyapunov-Razumikhin functions and Lyapunov-Krasovskii functionals. Examples are provided to illustrate these cond","authors_text":"Andrew R. Teel, Jun Liu","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-20T20:48:40Z","title":"Lyapunov-based sufficient conditions for stability of hybrid systems with memory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05648","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:a485919cf2198de24853c2860e50f619605195ffd582ebb3ffa764280a57ed12","target":"record","created_at":"2026-05-18T01:36:32Z","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":"f884ff1973e1e864b8e900bf3c0c7ecdb146fa005fc54af0c8b8f331bed5c5d3","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-20T20:48:40Z","title_canon_sha256":"91be41a58ba1eb57abb11d5b6a61352e54604a7cabd5c22539fd2da08ff02894"},"schema_version":"1.0","source":{"id":"1507.05648","kind":"arxiv","version":1}},"canonical_sha256":"24a4c5320e55ee6d8e146929a5143eeeb4174e28d4abf13d1c985138ba69231a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24a4c5320e55ee6d8e146929a5143eeeb4174e28d4abf13d1c985138ba69231a","first_computed_at":"2026-05-18T01:36:32.832413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:32.832413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iNkLi/X3fQ5MU5dBiSWf5DPMLfTNJg4dTkQDwInDIqD+PyiBWUf5n62piK2aWZTF5jXUpCGJeAEMu5huIBEBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:32.833186Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05648","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a485919cf2198de24853c2860e50f619605195ffd582ebb3ffa764280a57ed12","sha256:db51dc8063b8f59707c9091e43ee1148aceb10a419b757df61a3b46f419f0788"],"state_sha256":"98ed0016230b0c7658d0d8b3595ce80d5e5bbef501cf93c72d902a942471dcf6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"blC/f8iBJVJ7+5xVM/ZgVapTwImlaMbq0AHFXAqqlNELXEZlpW+k6JRr7FnkrDuXy0BfAxiwBugTCccoNHcxAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T21:09:41.089410Z","bundle_sha256":"93978042900632e7135afc0325f9b77b7084213f83bfc50e58ae2f3a9bc750ff"}}