{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MWEJ4RAIGR3MEHWPACDXTD7AA7","short_pith_number":"pith:MWEJ4RAI","canonical_record":{"source":{"id":"1511.08138","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-25T17:58:20Z","cross_cats_sorted":[],"title_canon_sha256":"a1290bf5977c4d541950e387e980deebf43c3017540004fea643a87cae563f85","abstract_canon_sha256":"c3f4377b5ce4c424ef52ad4758f3fe317f54a7ff7737cea5551cbeb5c81059b6"},"schema_version":"1.0"},"canonical_sha256":"65889e44083476c21ecf0087798fe007fe2340db420c7fb90d24f242ef8664b7","source":{"kind":"arxiv","id":"1511.08138","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08138","created_at":"2026-05-18T00:52:55Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08138v4","created_at":"2026-05-18T00:52:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08138","created_at":"2026-05-18T00:52:55Z"},{"alias_kind":"pith_short_12","alias_value":"MWEJ4RAIGR3M","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MWEJ4RAIGR3MEHWP","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MWEJ4RAI","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MWEJ4RAIGR3MEHWPACDXTD7AA7","target":"record","payload":{"canonical_record":{"source":{"id":"1511.08138","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-25T17:58:20Z","cross_cats_sorted":[],"title_canon_sha256":"a1290bf5977c4d541950e387e980deebf43c3017540004fea643a87cae563f85","abstract_canon_sha256":"c3f4377b5ce4c424ef52ad4758f3fe317f54a7ff7737cea5551cbeb5c81059b6"},"schema_version":"1.0"},"canonical_sha256":"65889e44083476c21ecf0087798fe007fe2340db420c7fb90d24f242ef8664b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:55.491371Z","signature_b64":"bnAlPopZTPAy318UG3zPCQK2Wj6qwU444Si7GpCsLLfc/I/+NSCTSlzyQ7nSqByHWldq6pd21hkQ6M3LED9+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65889e44083476c21ecf0087798fe007fe2340db420c7fb90d24f242ef8664b7","last_reissued_at":"2026-05-18T00:52:55.490857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:55.490857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.08138","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q08InP3WEdEsgxtd3olyE0/tP4xwC/p8xOA5tKviOBYnZWBop/AWiPm8t33Qbq00PFrSavb+oNFOKfLn2SWDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:37:10.076645Z"},"content_sha256":"3e7d3b094897d5e8f8ade8c21401d96f6de874f9502cfc9df1433baa06a7f70f","schema_version":"1.0","event_id":"sha256:3e7d3b094897d5e8f8ade8c21401d96f6de874f9502cfc9df1433baa06a7f70f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MWEJ4RAIGR3MEHWPACDXTD7AA7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniformly hyperbolic control theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Christoph Kawan","submitted_at":"2015-11-25T17:58:20Z","abstract_excerpt":"This paper gives a summary of a body of work at the intersection of control theory and smooth nonlinear dynamics. The main idea is to transfer the concept of uniform hyperbolicity, central to the theory of smooth dynamical systems, to control-affine systems. Combining the strength of geometric control theory and the hyperbolic theory of dynamical systems, it is possible to deduce control-theoretic results of non-local nature that reveal remarkable analogies to the classical hyperbolic theory of dynamical systems. This includes results on controllability, robustness, and practical stabilizabili"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08138","kind":"arxiv","version":4},"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":"2026-05-18T00:52:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b3caoxM3rvfD0Keltap1A/VDkAYsPEy5kJz9ATJVjoupfUi4bLFwu3KPKgk2A9DYUxMi7+taTKqMdRDGM5loBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:37:10.076999Z"},"content_sha256":"0b2df1c4e6afec9094fdd83e12b983b398ebaca937d217f6cadfcde361e198a4","schema_version":"1.0","event_id":"sha256:0b2df1c4e6afec9094fdd83e12b983b398ebaca937d217f6cadfcde361e198a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MWEJ4RAIGR3MEHWPACDXTD7AA7/bundle.json","state_url":"https://pith.science/pith/MWEJ4RAIGR3MEHWPACDXTD7AA7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MWEJ4RAIGR3MEHWPACDXTD7AA7/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":"2026-06-02T18:37:10Z","links":{"resolver":"https://pith.science/pith/MWEJ4RAIGR3MEHWPACDXTD7AA7","bundle":"https://pith.science/pith/MWEJ4RAIGR3MEHWPACDXTD7AA7/bundle.json","state":"https://pith.science/pith/MWEJ4RAIGR3MEHWPACDXTD7AA7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MWEJ4RAIGR3MEHWPACDXTD7AA7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MWEJ4RAIGR3MEHWPACDXTD7AA7","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":"c3f4377b5ce4c424ef52ad4758f3fe317f54a7ff7737cea5551cbeb5c81059b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-25T17:58:20Z","title_canon_sha256":"a1290bf5977c4d541950e387e980deebf43c3017540004fea643a87cae563f85"},"schema_version":"1.0","source":{"id":"1511.08138","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08138","created_at":"2026-05-18T00:52:55Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08138v4","created_at":"2026-05-18T00:52:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08138","created_at":"2026-05-18T00:52:55Z"},{"alias_kind":"pith_short_12","alias_value":"MWEJ4RAIGR3M","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MWEJ4RAIGR3MEHWP","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MWEJ4RAI","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:0b2df1c4e6afec9094fdd83e12b983b398ebaca937d217f6cadfcde361e198a4","target":"graph","created_at":"2026-05-18T00:52:55Z","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":"This paper gives a summary of a body of work at the intersection of control theory and smooth nonlinear dynamics. The main idea is to transfer the concept of uniform hyperbolicity, central to the theory of smooth dynamical systems, to control-affine systems. Combining the strength of geometric control theory and the hyperbolic theory of dynamical systems, it is possible to deduce control-theoretic results of non-local nature that reveal remarkable analogies to the classical hyperbolic theory of dynamical systems. This includes results on controllability, robustness, and practical stabilizabili","authors_text":"Christoph Kawan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-25T17:58:20Z","title":"Uniformly hyperbolic control theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08138","kind":"arxiv","version":4},"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":"sha256:3e7d3b094897d5e8f8ade8c21401d96f6de874f9502cfc9df1433baa06a7f70f","target":"record","created_at":"2026-05-18T00:52:55Z","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":"c3f4377b5ce4c424ef52ad4758f3fe317f54a7ff7737cea5551cbeb5c81059b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-25T17:58:20Z","title_canon_sha256":"a1290bf5977c4d541950e387e980deebf43c3017540004fea643a87cae563f85"},"schema_version":"1.0","source":{"id":"1511.08138","kind":"arxiv","version":4}},"canonical_sha256":"65889e44083476c21ecf0087798fe007fe2340db420c7fb90d24f242ef8664b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65889e44083476c21ecf0087798fe007fe2340db420c7fb90d24f242ef8664b7","first_computed_at":"2026-05-18T00:52:55.490857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:55.490857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bnAlPopZTPAy318UG3zPCQK2Wj6qwU444Si7GpCsLLfc/I/+NSCTSlzyQ7nSqByHWldq6pd21hkQ6M3LED9+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:55.491371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.08138","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e7d3b094897d5e8f8ade8c21401d96f6de874f9502cfc9df1433baa06a7f70f","sha256:0b2df1c4e6afec9094fdd83e12b983b398ebaca937d217f6cadfcde361e198a4"],"state_sha256":"fba73a748d5a0728aabaf3a171250b4ffa7903072173c91199c21745f076546c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qW1CeZVovonksSkAa87WWnMPOEqZJdF5cRkQ6sIMrUMZRFnE0XdG1g65CFLtrmsS3+VX4W8hSHm79LIkKl8UAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T18:37:10.078964Z","bundle_sha256":"ec0ad9f62633a6df8395208ed2b7215a78a1b5cdf4ada7389384404c8470af9b"}}