{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6JQ5AUVBGVQQ6YJK5KUKIN4W7V","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":"0252e37bc1d37d8d5798188ba8069c89bd8e7de5b7eaf9fe690960b64072c1b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-01-28T02:19:41Z","title_canon_sha256":"a5c1af741282cd06c88c7392713f112c03b1ee49be6b59671695f031002e0ad1"},"schema_version":"1.0","source":{"id":"1401.7066","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7066","created_at":"2026-05-18T03:00:50Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7066v1","created_at":"2026-05-18T03:00:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7066","created_at":"2026-05-18T03:00:50Z"},{"alias_kind":"pith_short_12","alias_value":"6JQ5AUVBGVQQ","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6JQ5AUVBGVQQ6YJK","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6JQ5AUVB","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:c4865e57666a2e0def0f3fa91e4d33aa492cf9bfc1e130157f0caa1a0f57d009","target":"graph","created_at":"2026-05-18T03:00:50Z","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 work is concerned with the exact controllability/observability of abstract cascade hyperbolic systems by a reduced number of controls/observations. We prove that the observation of the last component of the vector state allows to recover the initial energies of all of its components in suitable functional spaces under a necessary and sufficient condition on the coupling operators for cascade bi-diagonal systems. The approach is based on a multi-level energy method which involves $n$-levels of weakened energies.\n  We establish this result for the case of bounded as well as unbounded dual c","authors_text":"Fatiha Alabau-Boussouira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-01-28T02:19:41Z","title":"A hierarchic multi-level energy method for the control of bi-diagonal and mixed n-coupled cascade systems of PDE's by a reduced number of controls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7066","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:cae0acb9cda4c8bcdf1d9de2565604337989187586bbed89958ca959f4e97dd9","target":"record","created_at":"2026-05-18T03:00:50Z","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":"0252e37bc1d37d8d5798188ba8069c89bd8e7de5b7eaf9fe690960b64072c1b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-01-28T02:19:41Z","title_canon_sha256":"a5c1af741282cd06c88c7392713f112c03b1ee49be6b59671695f031002e0ad1"},"schema_version":"1.0","source":{"id":"1401.7066","kind":"arxiv","version":1}},"canonical_sha256":"f261d052a135610f612aeaa8a43796fd40dfe52934942a41892228c5469c34e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f261d052a135610f612aeaa8a43796fd40dfe52934942a41892228c5469c34e9","first_computed_at":"2026-05-18T03:00:50.955475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:50.955475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+L6Ob0feUK/EpdEqlvrShrmhTG9DtgIt+Ejwel4qcpoBqDAJyaE5HbSh9R5RzwlSIGYARw7cP/P/SlnsyckoCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:50.956044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7066","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cae0acb9cda4c8bcdf1d9de2565604337989187586bbed89958ca959f4e97dd9","sha256:c4865e57666a2e0def0f3fa91e4d33aa492cf9bfc1e130157f0caa1a0f57d009"],"state_sha256":"504ed5e842c24e83cd01cdfd256119f11eab387f7b658f94f9bf53623fc833da"}