{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VFKZFP5HPVXH5LRRT7MYGIKNZY","short_pith_number":"pith:VFKZFP5H","canonical_record":{"source":{"id":"1104.5030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-04-26T20:41:07Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"27f0a74d1c77a2f0831e04af13872188b360dd768c6c4fde1af7181f3e31e7d1","abstract_canon_sha256":"f6c4a18ff2c34c29ff2777653604a165b54880b84cf8ca0fc8156ab9bfc797a0"},"schema_version":"1.0"},"canonical_sha256":"a95592bfa77d6e7eae319fd983214dce0efc194ae16cefd2d4aceacfb048f5e0","source":{"kind":"arxiv","id":"1104.5030","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5030","created_at":"2026-05-18T04:23:32Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5030v1","created_at":"2026-05-18T04:23:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5030","created_at":"2026-05-18T04:23:32Z"},{"alias_kind":"pith_short_12","alias_value":"VFKZFP5HPVXH","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VFKZFP5HPVXH5LRR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VFKZFP5H","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VFKZFP5HPVXH5LRRT7MYGIKNZY","target":"record","payload":{"canonical_record":{"source":{"id":"1104.5030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-04-26T20:41:07Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"27f0a74d1c77a2f0831e04af13872188b360dd768c6c4fde1af7181f3e31e7d1","abstract_canon_sha256":"f6c4a18ff2c34c29ff2777653604a165b54880b84cf8ca0fc8156ab9bfc797a0"},"schema_version":"1.0"},"canonical_sha256":"a95592bfa77d6e7eae319fd983214dce0efc194ae16cefd2d4aceacfb048f5e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:32.374852Z","signature_b64":"DIy0NGK5QGAqWtpvyqLx/2BbKD+Hq3zuPQ20OCGi1lxpcLBPJyrkD2D9l9Lq4jEIHAcMGP4wYBo83+ikNT8hCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a95592bfa77d6e7eae319fd983214dce0efc194ae16cefd2d4aceacfb048f5e0","last_reissued_at":"2026-05-18T04:23:32.374266Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:32.374266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.5030","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:23:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qfj8NGpQMjVm3lZGdn3rl+cJUela8WrRUpiR/ebVDTjugD9Qls/3azqkXAwvxi2RBozh6DyQzivVWBEjbkk8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T11:26:43.797676Z"},"content_sha256":"036024683d5bfb91a9df5d649b4c7d973a85caa641fe88cdd0eae7ab2d1d6015","schema_version":"1.0","event_id":"sha256:036024683d5bfb91a9df5d649b4c7d973a85caa641fe88cdd0eae7ab2d1d6015"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VFKZFP5HPVXH5LRRT7MYGIKNZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Controllability of control systems simple Lie groups and the topology of flag manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.OC","authors_text":"Ariane Luzia dos Santos, Luiz A. B. San Martin","submitted_at":"2011-04-26T20:41:07Z","abstract_excerpt":"Let $S$ be subsemigroup with nonempty interior of a complex simple Lie group $G$. It is proved that $S=G$ if $S$ contains a subgroup $G(\\alpha) \\approx \\mathrm{Sl}(2,\\mathbb{C}) $ generated by the $\\exp \\mathfrak{g}_{\\pm \\alpha}$, where $\\mathfrak{g}%_{\\alpha}$ is the root space of the root $\\alpha $. The proof uses the fact, proved before, that the invariant control set of $S$ is contractible in some flag manifold if $S$ is proper, and exploits the fact that several orbits of $G(\\alpha)$ are 2-spheres not null homotopic. The result is applied to revisit a controllability theorem and get some "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5030","kind":"arxiv","version":1},"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":"2026-05-18T04:23:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tcEkpgy9KVVu0enELgRQoBgGFx+6/wScBm9o9uMXZyMkkMnwA+pnYS09MDMs1En40wZQ7B/83SsPN0cXOhQDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T11:26:43.798010Z"},"content_sha256":"a6615648dd4b9caddaf5b13017058ea9d0c295e949ab18ec3ede1e900fdaa7cc","schema_version":"1.0","event_id":"sha256:a6615648dd4b9caddaf5b13017058ea9d0c295e949ab18ec3ede1e900fdaa7cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VFKZFP5HPVXH5LRRT7MYGIKNZY/bundle.json","state_url":"https://pith.science/pith/VFKZFP5HPVXH5LRRT7MYGIKNZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VFKZFP5HPVXH5LRRT7MYGIKNZY/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":"2026-06-29T11:26:43Z","links":{"resolver":"https://pith.science/pith/VFKZFP5HPVXH5LRRT7MYGIKNZY","bundle":"https://pith.science/pith/VFKZFP5HPVXH5LRRT7MYGIKNZY/bundle.json","state":"https://pith.science/pith/VFKZFP5HPVXH5LRRT7MYGIKNZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VFKZFP5HPVXH5LRRT7MYGIKNZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VFKZFP5HPVXH5LRRT7MYGIKNZY","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":"f6c4a18ff2c34c29ff2777653604a165b54880b84cf8ca0fc8156ab9bfc797a0","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-04-26T20:41:07Z","title_canon_sha256":"27f0a74d1c77a2f0831e04af13872188b360dd768c6c4fde1af7181f3e31e7d1"},"schema_version":"1.0","source":{"id":"1104.5030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5030","created_at":"2026-05-18T04:23:32Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5030v1","created_at":"2026-05-18T04:23:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5030","created_at":"2026-05-18T04:23:32Z"},{"alias_kind":"pith_short_12","alias_value":"VFKZFP5HPVXH","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VFKZFP5HPVXH5LRR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VFKZFP5H","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:a6615648dd4b9caddaf5b13017058ea9d0c295e949ab18ec3ede1e900fdaa7cc","target":"graph","created_at":"2026-05-18T04:23:32Z","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"},"paper":{"abstract_excerpt":"Let $S$ be subsemigroup with nonempty interior of a complex simple Lie group $G$. It is proved that $S=G$ if $S$ contains a subgroup $G(\\alpha) \\approx \\mathrm{Sl}(2,\\mathbb{C}) $ generated by the $\\exp \\mathfrak{g}_{\\pm \\alpha}$, where $\\mathfrak{g}%_{\\alpha}$ is the root space of the root $\\alpha $. The proof uses the fact, proved before, that the invariant control set of $S$ is contractible in some flag manifold if $S$ is proper, and exploits the fact that several orbits of $G(\\alpha)$ are 2-spheres not null homotopic. The result is applied to revisit a controllability theorem and get some ","authors_text":"Ariane Luzia dos Santos, Luiz A. B. San Martin","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-04-26T20:41:07Z","title":"Controllability of control systems simple Lie groups and the topology of flag manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5030","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":"sha256:036024683d5bfb91a9df5d649b4c7d973a85caa641fe88cdd0eae7ab2d1d6015","target":"record","created_at":"2026-05-18T04:23:32Z","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":"f6c4a18ff2c34c29ff2777653604a165b54880b84cf8ca0fc8156ab9bfc797a0","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-04-26T20:41:07Z","title_canon_sha256":"27f0a74d1c77a2f0831e04af13872188b360dd768c6c4fde1af7181f3e31e7d1"},"schema_version":"1.0","source":{"id":"1104.5030","kind":"arxiv","version":1}},"canonical_sha256":"a95592bfa77d6e7eae319fd983214dce0efc194ae16cefd2d4aceacfb048f5e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a95592bfa77d6e7eae319fd983214dce0efc194ae16cefd2d4aceacfb048f5e0","first_computed_at":"2026-05-18T04:23:32.374266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:32.374266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DIy0NGK5QGAqWtpvyqLx/2BbKD+Hq3zuPQ20OCGi1lxpcLBPJyrkD2D9l9Lq4jEIHAcMGP4wYBo83+ikNT8hCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:32.374852Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.5030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:036024683d5bfb91a9df5d649b4c7d973a85caa641fe88cdd0eae7ab2d1d6015","sha256:a6615648dd4b9caddaf5b13017058ea9d0c295e949ab18ec3ede1e900fdaa7cc"],"state_sha256":"e3bcd7ffbc27995a1ecd6f806bdd0441c3443dc4cf9a11a695cbbf15f54c277a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OKvRxOEWw2pF6wkRDT1AiwAAemfGyKCjoqVjOD5kYoYKDHGlSlIWFJtq3nxtIdiyrUGFN4DuU8Ga9Grd4/eqBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T11:26:43.800076Z","bundle_sha256":"d07ead8a002b7c9d01dc54e632581e7a359b45e4b176964bb0cac56a1af99e89"}}