{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ZKRO63YSRQMTCKRDA3VYMZVMNY","short_pith_number":"pith:ZKRO63YS","schema_version":"1.0","canonical_sha256":"caa2ef6f128c19312a2306eb8666ac6e0f3898b1a221cd7b5d364fef38dacd76","source":{"kind":"arxiv","id":"1611.04111","version":3},"attestation_state":"computed","paper":{"title":"Null Controllability of the Kuramoto-Sivashinsky Equation on star-shaped trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Ademir F. Pazoto, Cristian M. Cazacu, Liviu I. Ignat","submitted_at":"2016-11-13T10:43:43Z","abstract_excerpt":"In this paper we treat controllability properties for the linear Kuramoto-Sivashinsky equation on a network with two types of boundary conditions. More precisely, the equation is considered on a star-shaped tree with Dirichlet and Neumann boundary conditions. By using the moment theory we can derive null-controllability properties with boundary controls acting on the external vertices of the tree. In particular, the controllability holds if the anti-diffusion parameter of the involved equation does not belong to a critical countable set of real numbers. We point out that the critical set for w"},"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":"1611.04111","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-13T10:43:43Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"41ed810a7467334273e245c2edc546de814e0624e3de3d49b6fab9fb034a7788","abstract_canon_sha256":"d9e3a8d15eab40ffdc4b450f5c39a0fa53a56b6d49594b227a0e5b2b484c8723"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:15.753581Z","signature_b64":"lCmofZ0NFB2DC6y0xDRJzajdy/d7FupdfDPQvv1YtVNdyX6W6u1yPqluPox9hB15lZmP/NeSO8nYbSG5bKJkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"caa2ef6f128c19312a2306eb8666ac6e0f3898b1a221cd7b5d364fef38dacd76","last_reissued_at":"2026-05-18T00:13:15.752830Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:15.752830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Null Controllability of the Kuramoto-Sivashinsky Equation on star-shaped trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Ademir F. Pazoto, Cristian M. Cazacu, Liviu I. Ignat","submitted_at":"2016-11-13T10:43:43Z","abstract_excerpt":"In this paper we treat controllability properties for the linear Kuramoto-Sivashinsky equation on a network with two types of boundary conditions. More precisely, the equation is considered on a star-shaped tree with Dirichlet and Neumann boundary conditions. By using the moment theory we can derive null-controllability properties with boundary controls acting on the external vertices of the tree. In particular, the controllability holds if the anti-diffusion parameter of the involved equation does not belong to a critical countable set of real numbers. We point out that the critical set for w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04111","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.04111","created_at":"2026-05-18T00:13:15.752944+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.04111v3","created_at":"2026-05-18T00:13:15.752944+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04111","created_at":"2026-05-18T00:13:15.752944+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZKRO63YSRQMT","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZKRO63YSRQMTCKRD","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZKRO63YS","created_at":"2026-05-18T12:30:53.716459+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZKRO63YSRQMTCKRDA3VYMZVMNY","json":"https://pith.science/pith/ZKRO63YSRQMTCKRDA3VYMZVMNY.json","graph_json":"https://pith.science/api/pith-number/ZKRO63YSRQMTCKRDA3VYMZVMNY/graph.json","events_json":"https://pith.science/api/pith-number/ZKRO63YSRQMTCKRDA3VYMZVMNY/events.json","paper":"https://pith.science/paper/ZKRO63YS"},"agent_actions":{"view_html":"https://pith.science/pith/ZKRO63YSRQMTCKRDA3VYMZVMNY","download_json":"https://pith.science/pith/ZKRO63YSRQMTCKRDA3VYMZVMNY.json","view_paper":"https://pith.science/paper/ZKRO63YS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.04111&json=true","fetch_graph":"https://pith.science/api/pith-number/ZKRO63YSRQMTCKRDA3VYMZVMNY/graph.json","fetch_events":"https://pith.science/api/pith-number/ZKRO63YSRQMTCKRDA3VYMZVMNY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZKRO63YSRQMTCKRDA3VYMZVMNY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZKRO63YSRQMTCKRDA3VYMZVMNY/action/storage_attestation","attest_author":"https://pith.science/pith/ZKRO63YSRQMTCKRDA3VYMZVMNY/action/author_attestation","sign_citation":"https://pith.science/pith/ZKRO63YSRQMTCKRDA3VYMZVMNY/action/citation_signature","submit_replication":"https://pith.science/pith/ZKRO63YSRQMTCKRDA3VYMZVMNY/action/replication_record"}},"created_at":"2026-05-18T00:13:15.752944+00:00","updated_at":"2026-05-18T00:13:15.752944+00:00"}