{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Q5R26O4GRO2JZ4NJVN2TIGSYN3","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":"629a2f9b1668b360b2877f6b1593790a84fdad9dfec57e463be098505d6c6f16","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-07-25T10:27:47Z","title_canon_sha256":"6d26172aaf5f23551131120b3f9c8062b79c861dca2fb6facee078dde1cffc38"},"schema_version":"1.0","source":{"id":"1607.07753","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07753","created_at":"2026-05-18T01:10:25Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07753v1","created_at":"2026-05-18T01:10:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07753","created_at":"2026-05-18T01:10:25Z"},{"alias_kind":"pith_short_12","alias_value":"Q5R26O4GRO2J","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q5R26O4GRO2JZ4NJ","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q5R26O4G","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:6e12fa002e1bfc90b63a368916f37f1353cd4554eff1d625e654e95e17e98408","target":"graph","created_at":"2026-05-18T01:10:25Z","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":"Controllability of multi-agent systems is determined by the interconnection topologies. In practice, losing agents can change the topologies of multi-agent systems, which may affect the controllability. This paper studies non-fragility of controllability influenced by losing agents. In virtue of the concept of cutsets, necessary and sufficient conditions are established from a graphic perspective, for strong non-fragility and weak non-fragility of controllability, respectively. For multi-agent systems which contain important agents, partial controllability is proposed in terms of the concept o","authors_text":"Bin Zhao, Long Wang, Yongqiang Guan","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-07-25T10:27:47Z","title":"Non-Fragility and Partial Controllability of Multi-Agent Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07753","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":"sha256:178405992813c1339589f62fd4365490003da23161809e50e16e5b2bcece9867","target":"record","created_at":"2026-05-18T01:10:25Z","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":"629a2f9b1668b360b2877f6b1593790a84fdad9dfec57e463be098505d6c6f16","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-07-25T10:27:47Z","title_canon_sha256":"6d26172aaf5f23551131120b3f9c8062b79c861dca2fb6facee078dde1cffc38"},"schema_version":"1.0","source":{"id":"1607.07753","kind":"arxiv","version":1}},"canonical_sha256":"8763af3b868bb49cf1a9ab75341a586efb8850c1afb618ff4a86464fc5809b7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8763af3b868bb49cf1a9ab75341a586efb8850c1afb618ff4a86464fc5809b7c","first_computed_at":"2026-05-18T01:10:25.361402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:25.361402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9R70CbGW+cyBqSnOagfM/8JwDAQW1kIox/WfbhzHXyLLmx5UvDwGGZraVCGkUG+7pMvmYdl5k0M4+MyoMw3SAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:25.361872Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07753","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:178405992813c1339589f62fd4365490003da23161809e50e16e5b2bcece9867","sha256:6e12fa002e1bfc90b63a368916f37f1353cd4554eff1d625e654e95e17e98408"],"state_sha256":"1f45d7248aec2298b22b5f54c919c1401e6453b328df50b72ef399716d81511c"}