{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:37QKPWA6OTN6GTYWPTPI3XE3C6","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":"dd1639d195f356e67a2a920142709bf705e8f2f13406d796062ff5ee3904e839","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2025-06-09T13:33:36Z","title_canon_sha256":"4ce9e353cad7c18237fa2a9fc116b2c6c38e5eb0aee00fe7216bb400329b1dff"},"schema_version":"1.0","source":{"id":"2506.07749","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07749","created_at":"2026-07-05T11:18:32Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07749v1","created_at":"2026-07-05T11:18:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07749","created_at":"2026-07-05T11:18:32Z"},{"alias_kind":"pith_short_12","alias_value":"37QKPWA6OTN6","created_at":"2026-07-05T11:18:32Z"},{"alias_kind":"pith_short_16","alias_value":"37QKPWA6OTN6GTYW","created_at":"2026-07-05T11:18:32Z"},{"alias_kind":"pith_short_8","alias_value":"37QKPWA6","created_at":"2026-07-05T11:18:32Z"}],"graph_snapshots":[{"event_id":"sha256:a57fee8104a437ee61367a6060c6ee117494754e13c1bd29471f737db0acee6c","target":"graph","created_at":"2026-07-05T11:18:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.07749/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate the controllability of bilinear control systems of the form $\\dot{s} = As + uBs$, where $s \\in \\mathbb{S}^2$ and $A, B \\in gl(3, \\mathbb{R})$ are skew-symmetric matrices. First, we prove that the algebraic condition $[A, B] \\neq 0$ ensures that the Lie algebra rank condition is satisfied for these systems. Next, we show that this same condition implies the controllability of the system. Finally, in an explicit and descriptive manner, we demonstrate controllability by exhibiting trajectories that transfer a given initial state to another.","authors_text":"Efrain Cruz-Mullisaca, Marco A. Colque-Choquecallata, Victor H. Patty-Yujra","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2025-06-09T13:33:36Z","title":"Controllability of induced bilinear systems on the sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07749","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:fadcd12bdedcdee49b4a5c123223d167d81cbb8f2a61f9bc75431cc7be09a998","target":"record","created_at":"2026-07-05T11:18:32Z","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":"dd1639d195f356e67a2a920142709bf705e8f2f13406d796062ff5ee3904e839","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2025-06-09T13:33:36Z","title_canon_sha256":"4ce9e353cad7c18237fa2a9fc116b2c6c38e5eb0aee00fe7216bb400329b1dff"},"schema_version":"1.0","source":{"id":"2506.07749","kind":"arxiv","version":1}},"canonical_sha256":"dfe0a7d81e74dbe34f167cde8ddc9b17b718925772fd49d74b25bc3133a99cd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfe0a7d81e74dbe34f167cde8ddc9b17b718925772fd49d74b25bc3133a99cd3","first_computed_at":"2026-07-05T11:18:32.659903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:18:32.659903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zFEk7oTTvR9Q4XVQsqASF9BWsIJn/7o/tMPav3ypUr8wYY4He8Z3zpdnjlvcYDnS05cB7DE57uTALEY5Q864BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:18:32.660411Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.07749","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fadcd12bdedcdee49b4a5c123223d167d81cbb8f2a61f9bc75431cc7be09a998","sha256:a57fee8104a437ee61367a6060c6ee117494754e13c1bd29471f737db0acee6c"],"state_sha256":"1f2af233e6b9759a12d6d4da9e6fe49a9f62addbb8301dfe0aaf9c518b5f39ac"}