{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ERFFCNBQK45NRN4MJMJENND37M","short_pith_number":"pith:ERFFCNBQ","canonical_record":{"source":{"id":"1711.00700","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-11-02T12:05:48Z","cross_cats_sorted":[],"title_canon_sha256":"cb8c4f676e0fe03246524459e0ba5a61be5495b49d75b0c82d585882af6a4152","abstract_canon_sha256":"8e8100863b3403ee065d38e65409f894a7fd0307811cdcee4745e813f433170f"},"schema_version":"1.0"},"canonical_sha256":"244a513430573ad8b78c4b1246b47bfb27a4f5c15e0b571f881c6ce7fb49d932","source":{"kind":"arxiv","id":"1711.00700","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00700","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00700v1","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00700","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"ERFFCNBQK45N","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ERFFCNBQK45NRN4M","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ERFFCNBQ","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ERFFCNBQK45NRN4MJMJENND37M","target":"record","payload":{"canonical_record":{"source":{"id":"1711.00700","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-11-02T12:05:48Z","cross_cats_sorted":[],"title_canon_sha256":"cb8c4f676e0fe03246524459e0ba5a61be5495b49d75b0c82d585882af6a4152","abstract_canon_sha256":"8e8100863b3403ee065d38e65409f894a7fd0307811cdcee4745e813f433170f"},"schema_version":"1.0"},"canonical_sha256":"244a513430573ad8b78c4b1246b47bfb27a4f5c15e0b571f881c6ce7fb49d932","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:29.771220Z","signature_b64":"dde8azsBg2vw6m/f1tbQQ8meIbc5Tkg7x+1CtmMYyQqSXweOJxOPJrtgerJAoBOX+CejtqNoDwQI6bRXCpn0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"244a513430573ad8b78c4b1246b47bfb27a4f5c15e0b571f881c6ce7fb49d932","last_reissued_at":"2026-05-18T00:31:29.770605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:29.770605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.00700","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":"2026-05-18T00:31:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YMFg+wNLj8nk9E5cgxpHwu2iTKDT1uSaZ8ZiYUFhZGsNMj3PYlN2mQ58t8cCXE9F2mu/G5MSTli46fTNTrW8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-28T18:27:01.748964Z"},"content_sha256":"9358bad0b5be143d063913f272bd2058815ca0d3c4ff707d7f89073ed9a428eb","schema_version":"1.0","event_id":"sha256:9358bad0b5be143d063913f272bd2058815ca0d3c4ff707d7f89073ed9a428eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ERFFCNBQK45NRN4MJMJENND37M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Joachim Deutscher, Nicole Gehring, Richard Kern","submitted_at":"2017-11-02T12:05:48Z","abstract_excerpt":"This paper presents a backstepping solution for the output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients. Thereby, the coupling in the PDE is in-domain and at the uncontrolled boundary, whereby the ODE is coupled with the latter boundary. For the state feedback design a two-step backstepping approach is developed, that yields the conventional kernel equations and additional decoupling equations of simple form. The latter can be traced back to simple Volterra integral equations of the second kind, which are directly solvable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00700","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":"2026-05-18T00:31:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wVPR827o/ZIoljXwWxO/56medwIkz06/F0nxZKscvkrcvqKuymcVAfU5SlC8oeMKEBja6dOD9Xmpfnj0xOaWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-28T18:27:01.749300Z"},"content_sha256":"0d704b80fd46aae3ebe0331a4dc7947f8fa8366fc0a1a493a739d2f7c59bdff7","schema_version":"1.0","event_id":"sha256:0d704b80fd46aae3ebe0331a4dc7947f8fa8366fc0a1a493a739d2f7c59bdff7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ERFFCNBQK45NRN4MJMJENND37M/bundle.json","state_url":"https://pith.science/pith/ERFFCNBQK45NRN4MJMJENND37M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ERFFCNBQK45NRN4MJMJENND37M/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":"2026-07-28T18:27:01Z","links":{"resolver":"https://pith.science/pith/ERFFCNBQK45NRN4MJMJENND37M","bundle":"https://pith.science/pith/ERFFCNBQK45NRN4MJMJENND37M/bundle.json","state":"https://pith.science/pith/ERFFCNBQK45NRN4MJMJENND37M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ERFFCNBQK45NRN4MJMJENND37M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ERFFCNBQK45NRN4MJMJENND37M","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":"8e8100863b3403ee065d38e65409f894a7fd0307811cdcee4745e813f433170f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-11-02T12:05:48Z","title_canon_sha256":"cb8c4f676e0fe03246524459e0ba5a61be5495b49d75b0c82d585882af6a4152"},"schema_version":"1.0","source":{"id":"1711.00700","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00700","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00700v1","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00700","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"ERFFCNBQK45N","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"ERFFCNBQK45NRN4M","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"ERFFCNBQ","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:0d704b80fd46aae3ebe0331a4dc7947f8fa8366fc0a1a493a739d2f7c59bdff7","target":"graph","created_at":"2026-05-18T00:31:29Z","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 presents a backstepping solution for the output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients. Thereby, the coupling in the PDE is in-domain and at the uncontrolled boundary, whereby the ODE is coupled with the latter boundary. For the state feedback design a two-step backstepping approach is developed, that yields the conventional kernel equations and additional decoupling equations of simple form. The latter can be traced back to simple Volterra integral equations of the second kind, which are directly solvable ","authors_text":"Joachim Deutscher, Nicole Gehring, Richard Kern","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-11-02T12:05:48Z","title":"Output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00700","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":"sha256:9358bad0b5be143d063913f272bd2058815ca0d3c4ff707d7f89073ed9a428eb","target":"record","created_at":"2026-05-18T00:31:29Z","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":"8e8100863b3403ee065d38e65409f894a7fd0307811cdcee4745e813f433170f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-11-02T12:05:48Z","title_canon_sha256":"cb8c4f676e0fe03246524459e0ba5a61be5495b49d75b0c82d585882af6a4152"},"schema_version":"1.0","source":{"id":"1711.00700","kind":"arxiv","version":1}},"canonical_sha256":"244a513430573ad8b78c4b1246b47bfb27a4f5c15e0b571f881c6ce7fb49d932","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"244a513430573ad8b78c4b1246b47bfb27a4f5c15e0b571f881c6ce7fb49d932","first_computed_at":"2026-05-18T00:31:29.770605Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:29.770605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dde8azsBg2vw6m/f1tbQQ8meIbc5Tkg7x+1CtmMYyQqSXweOJxOPJrtgerJAoBOX+CejtqNoDwQI6bRXCpn0AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:29.771220Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.00700","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9358bad0b5be143d063913f272bd2058815ca0d3c4ff707d7f89073ed9a428eb","sha256:0d704b80fd46aae3ebe0331a4dc7947f8fa8366fc0a1a493a739d2f7c59bdff7"],"state_sha256":"15e841e6ca8c8ffd2ad41a085140e0ab38f1acbc5275d30ae5d58186778ed04d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AyUCXoyOe8evsRF5FwPJHHvI2fSRVJc1xfvggDPVqcAdf3n8tALyLfFxCMdi92auL3snmjsaNfQKttpAr3mKAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-28T18:27:01.751574Z","bundle_sha256":"0495697feabdf7e897494f7f73686a4bf8c396d82906ba60f00633ae1a3e42e8"}}