{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CBRXYSAKAX5YDEUWC3TGVU3RFJ","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":"4f2f689f865ef54c4f3a2af4fe67ac8164b3895df90306f6369ab81c3424b3e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-12T13:07:33Z","title_canon_sha256":"4213cb32ca300ecee39577185030449a9fa7d144c46ff2c179f213898b1395e4"},"schema_version":"1.0","source":{"id":"1802.04022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04022","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04022v1","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04022","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"pith_short_12","alias_value":"CBRXYSAKAX5Y","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CBRXYSAKAX5YDEUW","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CBRXYSAK","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:1da01adaa7c6421e7860f3614b4c11a553ae082045a43c9f5400c99fb1892242","target":"graph","created_at":"2026-05-17T23:48:06Z","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 investigate the controllability of a linear time-invariant network following a Laplacian dynamics defined on a threshold graph. In this direction, an algorithm for deriving the modal matrix associated with the Laplacian matrix for this class of graphs is presented. Then, based on the Popov-Belevitch-Hautus criteria, a procedure for the selection of control nodes is proposed. The procedure involves partitioning the nodes of the graph into cells with the same degree; one node from each cell is then selected. We show that the remaining nodes can be chosen as the control nodes re","authors_text":"Mehran Mesbahi, Mohammad Haeri, Shima Sadat Mousavi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-12T13:07:33Z","title":"Controllability Analysis of Threshold Graphs and Cographs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04022","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":"sha256:440fefa37873a177f06f0f7aa701ac4a5302db3671b556bd9bb3380bb777ef9f","target":"record","created_at":"2026-05-17T23:48:06Z","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":"4f2f689f865ef54c4f3a2af4fe67ac8164b3895df90306f6369ab81c3424b3e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-12T13:07:33Z","title_canon_sha256":"4213cb32ca300ecee39577185030449a9fa7d144c46ff2c179f213898b1395e4"},"schema_version":"1.0","source":{"id":"1802.04022","kind":"arxiv","version":1}},"canonical_sha256":"10637c480a05fb81929616e66ad3712a4ad58a18a6cef8a8d708ae998e2d00e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10637c480a05fb81929616e66ad3712a4ad58a18a6cef8a8d708ae998e2d00e0","first_computed_at":"2026-05-17T23:48:06.779060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:06.779060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"if9AgZLXis/6I3uZOv28qv3uf0Ug8ChLzNrwej60u3KGa4eFUqnVZQNNlNCoC0MepnME5TlF19kODutAu2SICg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:06.779483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:440fefa37873a177f06f0f7aa701ac4a5302db3671b556bd9bb3380bb777ef9f","sha256:1da01adaa7c6421e7860f3614b4c11a553ae082045a43c9f5400c99fb1892242"],"state_sha256":"343d152f04df4f1a5ad14cb14f29dd4595c70aad72a27bc72b53ae0c44bcb5eb"}