{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:O7L46MNO63456TLKRPZR5OLCLP","short_pith_number":"pith:O7L46MNO","schema_version":"1.0","canonical_sha256":"77d7cf31aef6f9df4d6a8bf31eb9625bfc0f2d0871667ac213eba78350717d23","source":{"kind":"arxiv","id":"2508.00812","version":2},"attestation_state":"computed","paper":{"title":"On the controllability of the Kuramoto-Sivashinsky equation on multi-dimensional cylindrical domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Subrata Majumdar, V\\'ictor Hern\\'andez-Santamar\\'ia","submitted_at":"2025-08-01T17:45:59Z","abstract_excerpt":"In this article, we investigate null controllability of the Kuramoto-Sivashinsky (KS) equation on a cylindrical domain $\\Omega=\\Omega_x\\times \\Omega_y$ in $\\mathbb R^N$, where $\\Omega_x=(0,a),$ $a>0$ and $\\Omega_y$ is a smooth domain in $\\mathbb R^{N-1}$. We first study the controllability of this system by a control acting on $\\{0\\}\\times \\omega$, $\\omega\\subset \\Omega_y$, through the boundary term associated with the Laplacian component. The null controllability of the linearized system is proved using a combination of two techniques: the method of moments and Lebeau-Robbiano strategy. We pr"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2508.00812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-08-01T17:45:59Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e8f006ce5ab543d4a01342833abc33d44f595b6e2c87e2b2f0d9180ffa617442","abstract_canon_sha256":"cea0f0ed4ce75067d79b0ba9669296bd3ab72fdb5152f58de5173d6f139ac4d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:58:33.930617Z","signature_b64":"DDjV/gD2jN0WoCrEyUV/4JAuON6eoxbrkTPqmE8SgprBjCKCxuvNPYneG8OV1zz9OvEwxyNiyl4EtifwV+mKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77d7cf31aef6f9df4d6a8bf31eb9625bfc0f2d0871667ac213eba78350717d23","last_reissued_at":"2026-07-05T11:58:33.930167Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:58:33.930167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the controllability of the Kuramoto-Sivashinsky equation on multi-dimensional cylindrical domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Subrata Majumdar, V\\'ictor Hern\\'andez-Santamar\\'ia","submitted_at":"2025-08-01T17:45:59Z","abstract_excerpt":"In this article, we investigate null controllability of the Kuramoto-Sivashinsky (KS) equation on a cylindrical domain $\\Omega=\\Omega_x\\times \\Omega_y$ in $\\mathbb R^N$, where $\\Omega_x=(0,a),$ $a>0$ and $\\Omega_y$ is a smooth domain in $\\mathbb R^{N-1}$. We first study the controllability of this system by a control acting on $\\{0\\}\\times \\omega$, $\\omega\\subset \\Omega_y$, through the boundary term associated with the Laplacian component. The null controllability of the linearized system is proved using a combination of two techniques: the method of moments and Lebeau-Robbiano strategy. We pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.00812","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.00812/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2508.00812","created_at":"2026-07-05T11:58:33.930221+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.00812v2","created_at":"2026-07-05T11:58:33.930221+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.00812","created_at":"2026-07-05T11:58:33.930221+00:00"},{"alias_kind":"pith_short_12","alias_value":"O7L46MNO6345","created_at":"2026-07-05T11:58:33.930221+00:00"},{"alias_kind":"pith_short_16","alias_value":"O7L46MNO63456TLK","created_at":"2026-07-05T11:58:33.930221+00:00"},{"alias_kind":"pith_short_8","alias_value":"O7L46MNO","created_at":"2026-07-05T11:58:33.930221+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.00806","citing_title":"Adacc: An Adaptive Framework Unifying Compression and Activation Recomputation for LLM Training","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O7L46MNO63456TLKRPZR5OLCLP","json":"https://pith.science/pith/O7L46MNO63456TLKRPZR5OLCLP.json","graph_json":"https://pith.science/api/pith-number/O7L46MNO63456TLKRPZR5OLCLP/graph.json","events_json":"https://pith.science/api/pith-number/O7L46MNO63456TLKRPZR5OLCLP/events.json","paper":"https://pith.science/paper/O7L46MNO"},"agent_actions":{"view_html":"https://pith.science/pith/O7L46MNO63456TLKRPZR5OLCLP","download_json":"https://pith.science/pith/O7L46MNO63456TLKRPZR5OLCLP.json","view_paper":"https://pith.science/paper/O7L46MNO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.00812&json=true","fetch_graph":"https://pith.science/api/pith-number/O7L46MNO63456TLKRPZR5OLCLP/graph.json","fetch_events":"https://pith.science/api/pith-number/O7L46MNO63456TLKRPZR5OLCLP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O7L46MNO63456TLKRPZR5OLCLP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O7L46MNO63456TLKRPZR5OLCLP/action/storage_attestation","attest_author":"https://pith.science/pith/O7L46MNO63456TLKRPZR5OLCLP/action/author_attestation","sign_citation":"https://pith.science/pith/O7L46MNO63456TLKRPZR5OLCLP/action/citation_signature","submit_replication":"https://pith.science/pith/O7L46MNO63456TLKRPZR5OLCLP/action/replication_record"}},"created_at":"2026-07-05T11:58:33.930221+00:00","updated_at":"2026-07-05T11:58:33.930221+00:00"}