{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:F4TQAI7ABXHD5PG6D4VMSBLKB5","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":"443bf40060d86d79daf7673ea4131ffed619904258d84f014f779b8aacc9965f","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-11-27T21:42:46Z","title_canon_sha256":"9ef8a7bb4cda71069447b7f38f4215ffd3d1af4da1d18f329c1f4ba09f162794"},"schema_version":"1.0","source":{"id":"2411.18766","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18766","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18766v1","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18766","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"F4TQAI7ABXHD","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"pith_short_16","alias_value":"F4TQAI7ABXHD5PG6","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"pith_short_8","alias_value":"F4TQAI7A","created_at":"2026-07-05T09:41:51Z"}],"graph_snapshots":[{"event_id":"sha256:e1df4d2b2a8a258c53d81b7a6925544724b8b0f7a432be5d6888965783428ec3","target":"graph","created_at":"2026-07-05T09:41:51Z","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/2411.18766/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of steering a collection of n particles that obey identical n-dimensional linear dynamics via a common state feedback law towards a rearrangement of their positions, cast as a controllability problem for a dynamical system evolving on the space of matrices with positive determinant. We show that such a task is always feasible and, moreover, that it can be achieved arbitrarily fast. We also show that an optimal feedback control policy to achieve a similar feat, may not exist. Furthermore, we show that there is no universal formula for a linear feedback control law to ach","authors_text":"Mahmoud Abdelgalil, Tryphon T. Georgiou","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-11-27T21:42:46Z","title":"Collective steering in finite time: controllability on $\\text{GL}^+(n,\\mathbb{R})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18766","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":"sha256:2603154f89c56dd9e21bf1d93bb5c99655b40e27feb2e1137f954e4ab5cc77c2","target":"record","created_at":"2026-07-05T09:41:51Z","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":"443bf40060d86d79daf7673ea4131ffed619904258d84f014f779b8aacc9965f","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-11-27T21:42:46Z","title_canon_sha256":"9ef8a7bb4cda71069447b7f38f4215ffd3d1af4da1d18f329c1f4ba09f162794"},"schema_version":"1.0","source":{"id":"2411.18766","kind":"arxiv","version":1}},"canonical_sha256":"2f270023e00dce3ebcde1f2ac9056a0f69ad62950eac27ea0778163907764b0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f270023e00dce3ebcde1f2ac9056a0f69ad62950eac27ea0778163907764b0a","first_computed_at":"2026-07-05T09:41:51.262633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:51.262633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OylbOL3aNIjg5eyLLZ4squbMV7noHvaUJ4lpB83kmFTevIdU46KNSI2TBw6fuanQlsndcmrEwzte8+bGPkZYBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:51.263153Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.18766","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2603154f89c56dd9e21bf1d93bb5c99655b40e27feb2e1137f954e4ab5cc77c2","sha256:e1df4d2b2a8a258c53d81b7a6925544724b8b0f7a432be5d6888965783428ec3"],"state_sha256":"54907ff16b67d612acfe0aa18d83e64c0e93ac65d4b5cb5b64cf7d79ac1d4267"}