{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5MSUQG6OT5XGVM5RJUZBSV47OF","short_pith_number":"pith:5MSUQG6O","canonical_record":{"source":{"id":"1403.4101","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-03-17T14:06:35Z","cross_cats_sorted":[],"title_canon_sha256":"f98f858e6a02c8aed181837dec630a0a47190386f36b05958d4de00d876030d8","abstract_canon_sha256":"0e1e1f06911760f386b9c0c2d67e14cc64889449eede5756592480c18d676d05"},"schema_version":"1.0"},"canonical_sha256":"eb25481bce9f6e6ab3b14d3219579f716f497feb423d16096a0707032efd35e3","source":{"kind":"arxiv","id":"1403.4101","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4101","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4101v1","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4101","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"5MSUQG6OT5XG","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5MSUQG6OT5XGVM5R","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5MSUQG6O","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5MSUQG6OT5XGVM5RJUZBSV47OF","target":"record","payload":{"canonical_record":{"source":{"id":"1403.4101","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-03-17T14:06:35Z","cross_cats_sorted":[],"title_canon_sha256":"f98f858e6a02c8aed181837dec630a0a47190386f36b05958d4de00d876030d8","abstract_canon_sha256":"0e1e1f06911760f386b9c0c2d67e14cc64889449eede5756592480c18d676d05"},"schema_version":"1.0"},"canonical_sha256":"eb25481bce9f6e6ab3b14d3219579f716f497feb423d16096a0707032efd35e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:12.187784Z","signature_b64":"nfeWIr9wV6J/s1+U8PbKeAj2R+USTbnM+djs0vsaYAIbYgVwqPGtcmMgg6/y9u6wQi04enRkDhSBWLIarcbKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb25481bce9f6e6ab3b14d3219579f716f497feb423d16096a0707032efd35e3","last_reissued_at":"2026-05-18T02:56:12.187380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:12.187380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.4101","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":"2026-05-18T02:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JsRSksi72rX/+w2fWOvuSq/BxZOSNCUS2ZgstTE4r8jmwsqTHFG/4AYI8qA2r8Q7Fk0ELLnRV7jK7kQqKTW0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:40:27.666526Z"},"content_sha256":"bf9de78c23f12a4561c99d9824648270f47e9b5b61244d18cd55ea35b594560d","schema_version":"1.0","event_id":"sha256:bf9de78c23f12a4561c99d9824648270f47e9b5b61244d18cd55ea35b594560d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5MSUQG6OT5XGVM5RJUZBSV47OF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New criterion of asymptotic stability for delay systems with time-varying structures and delays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bao Liu, Tianping Chen, Wenlian Lu","submitted_at":"2014-03-17T14:06:35Z","abstract_excerpt":"In this paper, we study asymptotic stability of the zero solution of a class of differential systems governed by a scalar differential inequality with time-varying structures and delays. We establish a new generalized Halanay inequality for the asymptotic stability of the zero solution for such systems under more relaxed conditions than the existing ones. We also apply the theoretical results to the analysis of self synchronization in networks of delayed differential systems and obtained a more general sufficient condition for self synchronization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4101","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":"2026-05-18T02:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W1GGE2BCPJsXw/ULAKjNceHVTeZO09lWoJlIyaQi2n7ZfXWG0laOJvQ3aoVdI/B0hkoDpJzudjaMQ4p/16dUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:40:27.666858Z"},"content_sha256":"ad9c464d82ebf5014963165f637bac5616f7998a02df262e0f71e5137315c2b8","schema_version":"1.0","event_id":"sha256:ad9c464d82ebf5014963165f637bac5616f7998a02df262e0f71e5137315c2b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5MSUQG6OT5XGVM5RJUZBSV47OF/bundle.json","state_url":"https://pith.science/pith/5MSUQG6OT5XGVM5RJUZBSV47OF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5MSUQG6OT5XGVM5RJUZBSV47OF/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":"2026-06-28T09:40:27Z","links":{"resolver":"https://pith.science/pith/5MSUQG6OT5XGVM5RJUZBSV47OF","bundle":"https://pith.science/pith/5MSUQG6OT5XGVM5RJUZBSV47OF/bundle.json","state":"https://pith.science/pith/5MSUQG6OT5XGVM5RJUZBSV47OF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5MSUQG6OT5XGVM5RJUZBSV47OF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5MSUQG6OT5XGVM5RJUZBSV47OF","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":"0e1e1f06911760f386b9c0c2d67e14cc64889449eede5756592480c18d676d05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-03-17T14:06:35Z","title_canon_sha256":"f98f858e6a02c8aed181837dec630a0a47190386f36b05958d4de00d876030d8"},"schema_version":"1.0","source":{"id":"1403.4101","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4101","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4101v1","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4101","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"5MSUQG6OT5XG","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5MSUQG6OT5XGVM5R","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5MSUQG6O","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:ad9c464d82ebf5014963165f637bac5616f7998a02df262e0f71e5137315c2b8","target":"graph","created_at":"2026-05-18T02:56:12Z","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":"In this paper, we study asymptotic stability of the zero solution of a class of differential systems governed by a scalar differential inequality with time-varying structures and delays. We establish a new generalized Halanay inequality for the asymptotic stability of the zero solution for such systems under more relaxed conditions than the existing ones. We also apply the theoretical results to the analysis of self synchronization in networks of delayed differential systems and obtained a more general sufficient condition for self synchronization.","authors_text":"Bao Liu, Tianping Chen, Wenlian Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-03-17T14:06:35Z","title":"New criterion of asymptotic stability for delay systems with time-varying structures and delays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4101","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:bf9de78c23f12a4561c99d9824648270f47e9b5b61244d18cd55ea35b594560d","target":"record","created_at":"2026-05-18T02:56:12Z","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":"0e1e1f06911760f386b9c0c2d67e14cc64889449eede5756592480c18d676d05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-03-17T14:06:35Z","title_canon_sha256":"f98f858e6a02c8aed181837dec630a0a47190386f36b05958d4de00d876030d8"},"schema_version":"1.0","source":{"id":"1403.4101","kind":"arxiv","version":1}},"canonical_sha256":"eb25481bce9f6e6ab3b14d3219579f716f497feb423d16096a0707032efd35e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb25481bce9f6e6ab3b14d3219579f716f497feb423d16096a0707032efd35e3","first_computed_at":"2026-05-18T02:56:12.187380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:12.187380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nfeWIr9wV6J/s1+U8PbKeAj2R+USTbnM+djs0vsaYAIbYgVwqPGtcmMgg6/y9u6wQi04enRkDhSBWLIarcbKCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:12.187784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.4101","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf9de78c23f12a4561c99d9824648270f47e9b5b61244d18cd55ea35b594560d","sha256:ad9c464d82ebf5014963165f637bac5616f7998a02df262e0f71e5137315c2b8"],"state_sha256":"db7419f20cd63db847189c1ea1a5199c91072eafe580a0241008e503d48a8a81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ESYbyS+Qe4e+I7BW0VFzMjTzPYaAA/GZl2eXBR7ckVmLNgy3a2XxGVrgGEsujuhVRl86S2Rb5t0LOHtcvRAvBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T09:40:27.668758Z","bundle_sha256":"140a984294aacf6448b8d3273429c2ef79c134071eebf29359682bc5d8d341fa"}}