{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6G27MTOLPF65LO5PYJ57PDWTGH","short_pith_number":"pith:6G27MTOL","schema_version":"1.0","canonical_sha256":"f1b5f64dcb797dd5bbafc27bf78ed331ff85891879e41b77e29b8c9b3c24e859","source":{"kind":"arxiv","id":"1408.2416","version":1},"attestation_state":"computed","paper":{"title":"Invariance Entropy of Hyperbolic Control Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Adriano Da Silva, Christoph Kawan","submitted_at":"2014-08-11T14:17:00Z","abstract_excerpt":"In this paper, we improve the known estimates for the invariance entropy of a nonlinear control system. For sets of complete approximate controllability we derive an upper bound in terms of Lyapunov exponents and for uniformly hyperbolic sets we obtain a similar lower bound. Both estimates can be applied to hyperbolic chain control sets, and we prove that under mild assumptions they can be merged into a formula."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1408.2416","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-08-11T14:17:00Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"dc18deec1a70ac77ee058f1ef8e8a7a2d142d2422d9d2b3d3a82c66edd03cd58","abstract_canon_sha256":"f71a397b4ca55891b15afda14fccb004e945c1d058b35cf326782041aa4e2373"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:29.456952Z","signature_b64":"aqALv5aXIMZTcAhb2SPK2BOxwRfAmr60geRIOpHMs9l6RWDQceH/dh26z9s13qVXbzh+fXV97QO8jJScWOlECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1b5f64dcb797dd5bbafc27bf78ed331ff85891879e41b77e29b8c9b3c24e859","last_reissued_at":"2026-05-18T02:45:29.456287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:29.456287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariance Entropy of Hyperbolic Control Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Adriano Da Silva, Christoph Kawan","submitted_at":"2014-08-11T14:17:00Z","abstract_excerpt":"In this paper, we improve the known estimates for the invariance entropy of a nonlinear control system. For sets of complete approximate controllability we derive an upper bound in terms of Lyapunov exponents and for uniformly hyperbolic sets we obtain a similar lower bound. Both estimates can be applied to hyperbolic chain control sets, and we prove that under mild assumptions they can be merged into a formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2416","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.2416","created_at":"2026-05-18T02:45:29.456419+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.2416v1","created_at":"2026-05-18T02:45:29.456419+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2416","created_at":"2026-05-18T02:45:29.456419+00:00"},{"alias_kind":"pith_short_12","alias_value":"6G27MTOLPF65","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6G27MTOLPF65LO5P","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6G27MTOL","created_at":"2026-05-18T12:28:16.859392+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6G27MTOLPF65LO5PYJ57PDWTGH","json":"https://pith.science/pith/6G27MTOLPF65LO5PYJ57PDWTGH.json","graph_json":"https://pith.science/api/pith-number/6G27MTOLPF65LO5PYJ57PDWTGH/graph.json","events_json":"https://pith.science/api/pith-number/6G27MTOLPF65LO5PYJ57PDWTGH/events.json","paper":"https://pith.science/paper/6G27MTOL"},"agent_actions":{"view_html":"https://pith.science/pith/6G27MTOLPF65LO5PYJ57PDWTGH","download_json":"https://pith.science/pith/6G27MTOLPF65LO5PYJ57PDWTGH.json","view_paper":"https://pith.science/paper/6G27MTOL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.2416&json=true","fetch_graph":"https://pith.science/api/pith-number/6G27MTOLPF65LO5PYJ57PDWTGH/graph.json","fetch_events":"https://pith.science/api/pith-number/6G27MTOLPF65LO5PYJ57PDWTGH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6G27MTOLPF65LO5PYJ57PDWTGH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6G27MTOLPF65LO5PYJ57PDWTGH/action/storage_attestation","attest_author":"https://pith.science/pith/6G27MTOLPF65LO5PYJ57PDWTGH/action/author_attestation","sign_citation":"https://pith.science/pith/6G27MTOLPF65LO5PYJ57PDWTGH/action/citation_signature","submit_replication":"https://pith.science/pith/6G27MTOLPF65LO5PYJ57PDWTGH/action/replication_record"}},"created_at":"2026-05-18T02:45:29.456419+00:00","updated_at":"2026-05-18T02:45:29.456419+00:00"}