{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C47TRWHMFT6X6JLPBW4PYMFD4M","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":"f831a4f2b0d43760fc85f15395249b8d2f13f0fa6264f963b372dacb5ab480f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-23T21:04:08Z","title_canon_sha256":"bde45e09b41041947dc1a57a8016ae289bf4a3ddb8b71c83ab17662393636ef1"},"schema_version":"1.0","source":{"id":"1602.07312","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07312","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07312v2","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07312","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"C47TRWHMFT6X","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C47TRWHMFT6X6JLP","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C47TRWHM","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:2d25f66882b1a2052254e23f75a89f39d7d5b29e913644fda1cce11b13b5fc1d","target":"graph","created_at":"2026-05-18T01:12:19Z","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 shown that the chain control sets of induced systems on flag manifolds coincides with their analogous one defined via semigroup actions. Consequently, any chain control set of the system contains a control set with nonempty interior and, if the number of the control sets with nonempty interior coincides with the number of the chain control sets, then the closure of any control set with nonempty interior is a chain control set.","authors_text":"Adriano Da Silva, Luiz A.B. San Martin, Victor Ayala","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-23T21:04:08Z","title":"Control Systems on Flag Manifolds and their chain Control sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07312","kind":"arxiv","version":2},"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:d9c9a0e62f68d03fefca90f9958fadf662443caef734398ae2292e9fad0d0f70","target":"record","created_at":"2026-05-18T01:12:19Z","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":"f831a4f2b0d43760fc85f15395249b8d2f13f0fa6264f963b372dacb5ab480f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-23T21:04:08Z","title_canon_sha256":"bde45e09b41041947dc1a57a8016ae289bf4a3ddb8b71c83ab17662393636ef1"},"schema_version":"1.0","source":{"id":"1602.07312","kind":"arxiv","version":2}},"canonical_sha256":"173f38d8ec2cfd7f256f0db8fc30a3e3268ee90eeb936dcebe03144f87f35df6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"173f38d8ec2cfd7f256f0db8fc30a3e3268ee90eeb936dcebe03144f87f35df6","first_computed_at":"2026-05-18T01:12:19.793558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:19.793558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W/rQ70Tp3Q4zxr8SGcXUkmyE9ljlkk6SrppoFD+7Oyn3i5pQZcM1Gcim/6a80cPQe/yO+M0HgKDVx8dIfs6eBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:19.793880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07312","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9c9a0e62f68d03fefca90f9958fadf662443caef734398ae2292e9fad0d0f70","sha256:2d25f66882b1a2052254e23f75a89f39d7d5b29e913644fda1cce11b13b5fc1d"],"state_sha256":"3513d7878530d001eab038f690392dd55dc79a01086cb4dd630b44f3f8e4049e"}