{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:A67JLVZCX5VCFFPIBM7R2GEJRU","short_pith_number":"pith:A67JLVZC","canonical_record":{"source":{"id":"1607.02337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-07-08T12:33:43Z","cross_cats_sorted":[],"title_canon_sha256":"dcd1aff3a008fc4d1f33a8bc52260a49cfac05cbf4a6cba9aa3af875696ce433","abstract_canon_sha256":"824cb5e492ff06b17bf87e22bc6c7e52d15e2b208ca99d399dbaa14dff0a74c8"},"schema_version":"1.0"},"canonical_sha256":"07be95d722bf6a2295e80b3f1d18898d10c8deed9d44dff7f63857e0ca9dcf0b","source":{"kind":"arxiv","id":"1607.02337","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02337","created_at":"2026-05-18T01:11:20Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02337v1","created_at":"2026-05-18T01:11:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02337","created_at":"2026-05-18T01:11:20Z"},{"alias_kind":"pith_short_12","alias_value":"A67JLVZCX5VC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A67JLVZCX5VCFFPI","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A67JLVZC","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:A67JLVZCX5VCFFPIBM7R2GEJRU","target":"record","payload":{"canonical_record":{"source":{"id":"1607.02337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-07-08T12:33:43Z","cross_cats_sorted":[],"title_canon_sha256":"dcd1aff3a008fc4d1f33a8bc52260a49cfac05cbf4a6cba9aa3af875696ce433","abstract_canon_sha256":"824cb5e492ff06b17bf87e22bc6c7e52d15e2b208ca99d399dbaa14dff0a74c8"},"schema_version":"1.0"},"canonical_sha256":"07be95d722bf6a2295e80b3f1d18898d10c8deed9d44dff7f63857e0ca9dcf0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:20.647444Z","signature_b64":"mA2bkcbiDabUCFkxdeMoupi//ThuAKW0xfpP34TiM0oKBrj3lrYL+hTog32UKSZJlyM15wxViU9g17mneF1EAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07be95d722bf6a2295e80b3f1d18898d10c8deed9d44dff7f63857e0ca9dcf0b","last_reissued_at":"2026-05-18T01:11:20.646906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:20.646906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.02337","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":"2026-05-18T01:11:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e5JSZJqjlzkXIBiUL5Hspc1tDWB773Z/dPvPMkaocYtEPiRB1u0ucMSuA6kQSJRnmK/2KDCJTblORtqLcaFZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:23:43.703581Z"},"content_sha256":"f5e9abb832e2781484e4d4783e577c0bbd0504913c85636b4e08294b63e86395","schema_version":"1.0","event_id":"sha256:f5e9abb832e2781484e4d4783e577c0bbd0504913c85636b4e08294b63e86395"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:A67JLVZCX5VCFFPIBM7R2GEJRU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Model order reduction approaches for infinite horizon optimal control problems via the HJB equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alessandro Alla, Andreas Schmidt, Bernard Haasdonk","submitted_at":"2016-07-08T12:33:43Z","abstract_excerpt":"We investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is well-known that HJB equations suffer the so called curse of dimensionality and, therefore, a reduction of the dimension of the system is mandatory. In this report we focus on the infinite horizon optimal control problem with quadratic cost functionals. We compare several model reduction methods such as Proper Orthogonal Decomposition, Balanced Truncation and a n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02337","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":"2026-05-18T01:11:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3hrjiPsxUM1dheV38FBB10qDhR2sKrrVr4gt5QxC1TMEwxjqMdaaeL0LdEYaZZxNQXfEebBm8ht2y85QIZW4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:23:43.703934Z"},"content_sha256":"905dfc52e042b15bb75381ed73575b577ed28dd5c766eb02ea54d58827c4343b","schema_version":"1.0","event_id":"sha256:905dfc52e042b15bb75381ed73575b577ed28dd5c766eb02ea54d58827c4343b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A67JLVZCX5VCFFPIBM7R2GEJRU/bundle.json","state_url":"https://pith.science/pith/A67JLVZCX5VCFFPIBM7R2GEJRU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A67JLVZCX5VCFFPIBM7R2GEJRU/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":"2026-05-30T13:23:43Z","links":{"resolver":"https://pith.science/pith/A67JLVZCX5VCFFPIBM7R2GEJRU","bundle":"https://pith.science/pith/A67JLVZCX5VCFFPIBM7R2GEJRU/bundle.json","state":"https://pith.science/pith/A67JLVZCX5VCFFPIBM7R2GEJRU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A67JLVZCX5VCFFPIBM7R2GEJRU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A67JLVZCX5VCFFPIBM7R2GEJRU","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":"824cb5e492ff06b17bf87e22bc6c7e52d15e2b208ca99d399dbaa14dff0a74c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-07-08T12:33:43Z","title_canon_sha256":"dcd1aff3a008fc4d1f33a8bc52260a49cfac05cbf4a6cba9aa3af875696ce433"},"schema_version":"1.0","source":{"id":"1607.02337","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02337","created_at":"2026-05-18T01:11:20Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02337v1","created_at":"2026-05-18T01:11:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02337","created_at":"2026-05-18T01:11:20Z"},{"alias_kind":"pith_short_12","alias_value":"A67JLVZCX5VC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A67JLVZCX5VCFFPI","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A67JLVZC","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:905dfc52e042b15bb75381ed73575b577ed28dd5c766eb02ea54d58827c4343b","target":"graph","created_at":"2026-05-18T01:11:20Z","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 investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is well-known that HJB equations suffer the so called curse of dimensionality and, therefore, a reduction of the dimension of the system is mandatory. In this report we focus on the infinite horizon optimal control problem with quadratic cost functionals. We compare several model reduction methods such as Proper Orthogonal Decomposition, Balanced Truncation and a n","authors_text":"Alessandro Alla, Andreas Schmidt, Bernard Haasdonk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-07-08T12:33:43Z","title":"Model order reduction approaches for infinite horizon optimal control problems via the HJB equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02337","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:f5e9abb832e2781484e4d4783e577c0bbd0504913c85636b4e08294b63e86395","target":"record","created_at":"2026-05-18T01:11:20Z","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":"824cb5e492ff06b17bf87e22bc6c7e52d15e2b208ca99d399dbaa14dff0a74c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-07-08T12:33:43Z","title_canon_sha256":"dcd1aff3a008fc4d1f33a8bc52260a49cfac05cbf4a6cba9aa3af875696ce433"},"schema_version":"1.0","source":{"id":"1607.02337","kind":"arxiv","version":1}},"canonical_sha256":"07be95d722bf6a2295e80b3f1d18898d10c8deed9d44dff7f63857e0ca9dcf0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07be95d722bf6a2295e80b3f1d18898d10c8deed9d44dff7f63857e0ca9dcf0b","first_computed_at":"2026-05-18T01:11:20.646906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:20.646906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mA2bkcbiDabUCFkxdeMoupi//ThuAKW0xfpP34TiM0oKBrj3lrYL+hTog32UKSZJlyM15wxViU9g17mneF1EAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:20.647444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.02337","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5e9abb832e2781484e4d4783e577c0bbd0504913c85636b4e08294b63e86395","sha256:905dfc52e042b15bb75381ed73575b577ed28dd5c766eb02ea54d58827c4343b"],"state_sha256":"7a1ec8133a8023a425a04ca461b8fa5e5514b0026fcbaa4f1426faa7baa41157"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mpV79zerm9hu3AXZSrhSfmXy1ijT8xjW3Hf/52dEh5Jq1Nci6DCutMuXdpRCnKwKDDTqoYmi9jfCZFihXH/qBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:23:43.706007Z","bundle_sha256":"61a07d8038510e60f50ce07157e5afb025957f9609d49a96d2a6adcd1198ae33"}}