{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:M6OYHHL2KBJQXGQBJMMOFNA6CY","short_pith_number":"pith:M6OYHHL2","canonical_record":{"source":{"id":"1411.5979","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-21T18:57:25Z","cross_cats_sorted":[],"title_canon_sha256":"6523221401ad6523c60fe65d2a4a5f1b080365302b735b269446b29764fa3a7e","abstract_canon_sha256":"12de285c8808439f0bb73033db86bc236af14a2a5df4853da0789f0a1cefa7c6"},"schema_version":"1.0"},"canonical_sha256":"679d839d7a50530b9a014b18e2b41e162ee76361a5edc021ec5c8dd0b666322a","source":{"kind":"arxiv","id":"1411.5979","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5979","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5979v6","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5979","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"pith_short_12","alias_value":"M6OYHHL2KBJQ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M6OYHHL2KBJQXGQB","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M6OYHHL2","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:M6OYHHL2KBJQXGQBJMMOFNA6CY","target":"record","payload":{"canonical_record":{"source":{"id":"1411.5979","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-21T18:57:25Z","cross_cats_sorted":[],"title_canon_sha256":"6523221401ad6523c60fe65d2a4a5f1b080365302b735b269446b29764fa3a7e","abstract_canon_sha256":"12de285c8808439f0bb73033db86bc236af14a2a5df4853da0789f0a1cefa7c6"},"schema_version":"1.0"},"canonical_sha256":"679d839d7a50530b9a014b18e2b41e162ee76361a5edc021ec5c8dd0b666322a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:29.577078Z","signature_b64":"lzMTOXYU9N9OJ9oVcD/OQPmyhrZfB/KUBASyzS+ry5hl7QYbQGs2yoJxHFsZd3yE+FoyW0k6RANgwTo6X+VxAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"679d839d7a50530b9a014b18e2b41e162ee76361a5edc021ec5c8dd0b666322a","last_reissued_at":"2026-05-18T01:23:29.576409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:29.576409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.5979","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5loMKdbx04vnXwZWpTQ6Aj7lr9npSIMnhgNFJLYRyBGsKu6DN7BC2OcMVMJspHJSIibTIhTjh0xAfXr/gYCsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:42:02.803390Z"},"content_sha256":"e7ff12809be4049684f85a12ca065d3dace0d42b29bc7516692e167a4f9c6400","schema_version":"1.0","event_id":"sha256:e7ff12809be4049684f85a12ca065d3dace0d42b29bc7516692e167a4f9c6400"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:M6OYHHL2KBJQXGQBJMMOFNA6CY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Controllability of linear systems on solvable Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Adriano Da Silva","submitted_at":"2014-11-21T18:57:25Z","abstract_excerpt":"Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies controllability by taking in consideration the eigenvalues of an associated derivation D. When the state space is a solvable connected Lie group, controllability of the systems is guaranteed if the reachable set of the neutral element is open and the derivation D has only pure imaginary eigenvalues. For bounded systems on nilpotent Lie groups such conditions are also necessary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5979","kind":"arxiv","version":6},"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":"2026-05-18T01:23:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l8RTjZs3+CGZhmEEESTCLCh8UA+AtdwZaUuIISy89PCMD0tej4ID82hKu9f/d1CghKmRLooR5cY3j5LgFbYUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:42:02.803745Z"},"content_sha256":"388c9943d4a7068e0e71ab48173ffa9cce2d330c16ce8c6d622b751a561b9878","schema_version":"1.0","event_id":"sha256:388c9943d4a7068e0e71ab48173ffa9cce2d330c16ce8c6d622b751a561b9878"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6OYHHL2KBJQXGQBJMMOFNA6CY/bundle.json","state_url":"https://pith.science/pith/M6OYHHL2KBJQXGQBJMMOFNA6CY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6OYHHL2KBJQXGQBJMMOFNA6CY/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":"2026-06-23T14:42:02Z","links":{"resolver":"https://pith.science/pith/M6OYHHL2KBJQXGQBJMMOFNA6CY","bundle":"https://pith.science/pith/M6OYHHL2KBJQXGQBJMMOFNA6CY/bundle.json","state":"https://pith.science/pith/M6OYHHL2KBJQXGQBJMMOFNA6CY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6OYHHL2KBJQXGQBJMMOFNA6CY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:M6OYHHL2KBJQXGQBJMMOFNA6CY","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":"12de285c8808439f0bb73033db86bc236af14a2a5df4853da0789f0a1cefa7c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-21T18:57:25Z","title_canon_sha256":"6523221401ad6523c60fe65d2a4a5f1b080365302b735b269446b29764fa3a7e"},"schema_version":"1.0","source":{"id":"1411.5979","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5979","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5979v6","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5979","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"pith_short_12","alias_value":"M6OYHHL2KBJQ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M6OYHHL2KBJQXGQB","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M6OYHHL2","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:388c9943d4a7068e0e71ab48173ffa9cce2d330c16ce8c6d622b751a561b9878","target":"graph","created_at":"2026-05-18T01:23:29Z","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":"Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies controllability by taking in consideration the eigenvalues of an associated derivation D. When the state space is a solvable connected Lie group, controllability of the systems is guaranteed if the reachable set of the neutral element is open and the derivation D has only pure imaginary eigenvalues. For bounded systems on nilpotent Lie groups such conditions are also necessary.","authors_text":"Adriano Da Silva","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-21T18:57:25Z","title":"Controllability of linear systems on solvable Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5979","kind":"arxiv","version":6},"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:e7ff12809be4049684f85a12ca065d3dace0d42b29bc7516692e167a4f9c6400","target":"record","created_at":"2026-05-18T01:23:29Z","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":"12de285c8808439f0bb73033db86bc236af14a2a5df4853da0789f0a1cefa7c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-21T18:57:25Z","title_canon_sha256":"6523221401ad6523c60fe65d2a4a5f1b080365302b735b269446b29764fa3a7e"},"schema_version":"1.0","source":{"id":"1411.5979","kind":"arxiv","version":6}},"canonical_sha256":"679d839d7a50530b9a014b18e2b41e162ee76361a5edc021ec5c8dd0b666322a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"679d839d7a50530b9a014b18e2b41e162ee76361a5edc021ec5c8dd0b666322a","first_computed_at":"2026-05-18T01:23:29.576409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:29.576409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lzMTOXYU9N9OJ9oVcD/OQPmyhrZfB/KUBASyzS+ry5hl7QYbQGs2yoJxHFsZd3yE+FoyW0k6RANgwTo6X+VxAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:29.577078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.5979","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7ff12809be4049684f85a12ca065d3dace0d42b29bc7516692e167a4f9c6400","sha256:388c9943d4a7068e0e71ab48173ffa9cce2d330c16ce8c6d622b751a561b9878"],"state_sha256":"401eba0f90ef3dad7d93da462aea8ed217898a6f5941fd9e7f428c34b3e8ff65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z1ly+s5+rM9WyOF3TmSluKHjlle2cxA9liAGzpQNh7e2uPZO+WlTso+zTRCNGbvC0E6u0Ccb7C4wXxkxvPwWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:42:02.805894Z","bundle_sha256":"55f21f7e01bc07f31aab77324e959452c2cb9036444ccc5228a07ce3f0bdc010"}}