{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:T2OL4JYI2C76GOQUDJ7OZ36YUD","short_pith_number":"pith:T2OL4JYI","canonical_record":{"source":{"id":"1011.2952","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-11-12T15:34:22Z","cross_cats_sorted":["math.DS","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"e9e0d8afd518339c86eec52773636426f3c612285ccea821a9559d2611de5457","abstract_canon_sha256":"7b42edd9d96fe29bee3624c3e1f9b22ea1cfe9bbcf36a24d5c0a1fd96c426a6c"},"schema_version":"1.0"},"canonical_sha256":"9e9cbe2708d0bfe33a141a7eecefd8a0f0ec506319b10d2d3a02e4a35619042d","source":{"kind":"arxiv","id":"1011.2952","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2952","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2952v1","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2952","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"pith_short_12","alias_value":"T2OL4JYI2C76","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"T2OL4JYI2C76GOQU","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"T2OL4JYI","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:T2OL4JYI2C76GOQUDJ7OZ36YUD","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2952","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-11-12T15:34:22Z","cross_cats_sorted":["math.DS","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"e9e0d8afd518339c86eec52773636426f3c612285ccea821a9559d2611de5457","abstract_canon_sha256":"7b42edd9d96fe29bee3624c3e1f9b22ea1cfe9bbcf36a24d5c0a1fd96c426a6c"},"schema_version":"1.0"},"canonical_sha256":"9e9cbe2708d0bfe33a141a7eecefd8a0f0ec506319b10d2d3a02e4a35619042d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:04.725713Z","signature_b64":"oSmadd5BiJD+MRI9oxGCrDKFn2XzyJ9lAt0wy20Z76TZMlI4lJqNGsGX/Al+nbGsPats4S3FFof7tasy6abUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e9cbe2708d0bfe33a141a7eecefd8a0f0ec506319b10d2d3a02e4a35619042d","last_reissued_at":"2026-05-18T04:20:04.725252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:04.725252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2952","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":"2026-05-18T04:20:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZouKEzI2g4xKt5EALqzsD3mMLValpvO+XDxxBWyzv+LNvdWSH/iwJdkbTQlYLp5e7DSo8lyoONUHlShMvagmAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:09:51.598303Z"},"content_sha256":"7debd80f80f67da037d1e096177ee749df3a8939842b53581a6a5d71cf23dbeb","schema_version":"1.0","event_id":"sha256:7debd80f80f67da037d1e096177ee749df3a8939842b53581a6a5d71cf23dbeb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:T2OL4JYI2C76GOQUDJ7OZ36YUD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Balanced Reduction of Nonlinear Control Systems in Reproducing Kernel Hilbert Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.ST","stat.ML","stat.TH"],"primary_cat":"math.OC","authors_text":"Boumediene Hamzi, Jake Bouvrie","submitted_at":"2010-11-12T15:34:22Z","abstract_excerpt":"We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space where balanced truncation may be carried out implicitly. This leads to a nonlinear reduction map which can be combined with a representation of the system belonging to a reproducing kernel Hilbert space to give a closed, reduced order dynamical system which captures the essential i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2952","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":"2026-05-18T04:20:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yPbhdcsElzl/uFRcfdJKFw+5cfwVlPtrNEJiZ8NQoMqXjQDMgtiAs3UM8ZXy15R8uxQSsvHqf0xBN+7b0FPSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:09:51.598666Z"},"content_sha256":"a4a9fd0b41fb8248e7442a3fb9f62139d887cd30862526ca10b41a4ff68f3bd8","schema_version":"1.0","event_id":"sha256:a4a9fd0b41fb8248e7442a3fb9f62139d887cd30862526ca10b41a4ff68f3bd8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T2OL4JYI2C76GOQUDJ7OZ36YUD/bundle.json","state_url":"https://pith.science/pith/T2OL4JYI2C76GOQUDJ7OZ36YUD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T2OL4JYI2C76GOQUDJ7OZ36YUD/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":"2026-05-28T12:09:51Z","links":{"resolver":"https://pith.science/pith/T2OL4JYI2C76GOQUDJ7OZ36YUD","bundle":"https://pith.science/pith/T2OL4JYI2C76GOQUDJ7OZ36YUD/bundle.json","state":"https://pith.science/pith/T2OL4JYI2C76GOQUDJ7OZ36YUD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T2OL4JYI2C76GOQUDJ7OZ36YUD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:T2OL4JYI2C76GOQUDJ7OZ36YUD","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":"7b42edd9d96fe29bee3624c3e1f9b22ea1cfe9bbcf36a24d5c0a1fd96c426a6c","cross_cats_sorted":["math.DS","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-11-12T15:34:22Z","title_canon_sha256":"e9e0d8afd518339c86eec52773636426f3c612285ccea821a9559d2611de5457"},"schema_version":"1.0","source":{"id":"1011.2952","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2952","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2952v1","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2952","created_at":"2026-05-18T04:20:04Z"},{"alias_kind":"pith_short_12","alias_value":"T2OL4JYI2C76","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"T2OL4JYI2C76GOQU","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"T2OL4JYI","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:a4a9fd0b41fb8248e7442a3fb9f62139d887cd30862526ca10b41a4ff68f3bd8","target":"graph","created_at":"2026-05-18T04:20:04Z","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":"We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space where balanced truncation may be carried out implicitly. This leads to a nonlinear reduction map which can be combined with a representation of the system belonging to a reproducing kernel Hilbert space to give a closed, reduced order dynamical system which captures the essential i","authors_text":"Boumediene Hamzi, Jake Bouvrie","cross_cats":["math.DS","math.ST","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-11-12T15:34:22Z","title":"Balanced Reduction of Nonlinear Control Systems in Reproducing Kernel Hilbert Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2952","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":"sha256:7debd80f80f67da037d1e096177ee749df3a8939842b53581a6a5d71cf23dbeb","target":"record","created_at":"2026-05-18T04:20:04Z","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":"7b42edd9d96fe29bee3624c3e1f9b22ea1cfe9bbcf36a24d5c0a1fd96c426a6c","cross_cats_sorted":["math.DS","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-11-12T15:34:22Z","title_canon_sha256":"e9e0d8afd518339c86eec52773636426f3c612285ccea821a9559d2611de5457"},"schema_version":"1.0","source":{"id":"1011.2952","kind":"arxiv","version":1}},"canonical_sha256":"9e9cbe2708d0bfe33a141a7eecefd8a0f0ec506319b10d2d3a02e4a35619042d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e9cbe2708d0bfe33a141a7eecefd8a0f0ec506319b10d2d3a02e4a35619042d","first_computed_at":"2026-05-18T04:20:04.725252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:04.725252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oSmadd5BiJD+MRI9oxGCrDKFn2XzyJ9lAt0wy20Z76TZMlI4lJqNGsGX/Al+nbGsPats4S3FFof7tasy6abUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:04.725713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2952","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7debd80f80f67da037d1e096177ee749df3a8939842b53581a6a5d71cf23dbeb","sha256:a4a9fd0b41fb8248e7442a3fb9f62139d887cd30862526ca10b41a4ff68f3bd8"],"state_sha256":"b6e4a673c41f80e2b1b3f05df9de7437c7836f44021a9a4ea19c96f48f59658d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FRUnghYw4XaU91WCyOWCHYqLgrKYRJry0V+z9SpKoxSQuXHIJwAUWOpH65JXG9FQcUq1o1440wFCAcq/RzOCAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:09:51.600627Z","bundle_sha256":"9daa41cf74de7e2d4b8741e0e7c3262035338b6b29c1d79201b782e6859a757d"}}