{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:7KZBTYYTIGKMSSWQOO2RYKLQYK","short_pith_number":"pith:7KZBTYYT","schema_version":"1.0","canonical_sha256":"fab219e3134194c94ad073b51c2970c29b9146465cd6320043c5ffa8c7284dd7","source":{"kind":"arxiv","id":"1509.00863","version":2},"attestation_state":"computed","paper":{"title":"Carleman estimates for parabolic equations with interior degeneracy and Neumann boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Genni Fragnelli, Idriss Boutaayamou, Lahcen Maniar","submitted_at":"2015-09-02T20:15:12Z","abstract_excerpt":"We consider a parabolic problem with degeneracy in the interior of the spatial domain and Neumann boundary conditions. In particular, we will focus on the well-posedness of the problem and on Carleman estimates for the associated adjoint problem. The novelty of the present paper is that for the first time it is considered a problem with an interior degeneracy and Neumann boundary conditions so that no previous result can be adapted to this situation. As a consequence new observability inequalities are established."},"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":"1509.00863","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-02T20:15:12Z","cross_cats_sorted":[],"title_canon_sha256":"4eed92510fc6f43a9892afd45263c0e96fd5dab78a7b358a33958a5f126872b6","abstract_canon_sha256":"4f6f8b97c97bea9da7a3c12a9c71a07a87940bf440c73b68386a01e5826ce17a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:36.893112Z","signature_b64":"CGziKLYPX1qRutpwEmx8Ygqpg1UvPnY+DS0i2+Ne+ky9hIwo6qbqZ7PazONaQ0g06hq0/CHdVaXSdUAwtr7pAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fab219e3134194c94ad073b51c2970c29b9146465cd6320043c5ffa8c7284dd7","last_reissued_at":"2026-05-18T00:27:36.892497Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:36.892497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Carleman estimates for parabolic equations with interior degeneracy and Neumann boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Genni Fragnelli, Idriss Boutaayamou, Lahcen Maniar","submitted_at":"2015-09-02T20:15:12Z","abstract_excerpt":"We consider a parabolic problem with degeneracy in the interior of the spatial domain and Neumann boundary conditions. In particular, we will focus on the well-posedness of the problem and on Carleman estimates for the associated adjoint problem. The novelty of the present paper is that for the first time it is considered a problem with an interior degeneracy and Neumann boundary conditions so that no previous result can be adapted to this situation. As a consequence new observability inequalities are established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00863","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":""},"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":"1509.00863","created_at":"2026-05-18T00:27:36.892605+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.00863v2","created_at":"2026-05-18T00:27:36.892605+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00863","created_at":"2026-05-18T00:27:36.892605+00:00"},{"alias_kind":"pith_short_12","alias_value":"7KZBTYYTIGKM","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"7KZBTYYTIGKMSSWQ","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"7KZBTYYT","created_at":"2026-05-18T12:29:10.953037+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/7KZBTYYTIGKMSSWQOO2RYKLQYK","json":"https://pith.science/pith/7KZBTYYTIGKMSSWQOO2RYKLQYK.json","graph_json":"https://pith.science/api/pith-number/7KZBTYYTIGKMSSWQOO2RYKLQYK/graph.json","events_json":"https://pith.science/api/pith-number/7KZBTYYTIGKMSSWQOO2RYKLQYK/events.json","paper":"https://pith.science/paper/7KZBTYYT"},"agent_actions":{"view_html":"https://pith.science/pith/7KZBTYYTIGKMSSWQOO2RYKLQYK","download_json":"https://pith.science/pith/7KZBTYYTIGKMSSWQOO2RYKLQYK.json","view_paper":"https://pith.science/paper/7KZBTYYT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.00863&json=true","fetch_graph":"https://pith.science/api/pith-number/7KZBTYYTIGKMSSWQOO2RYKLQYK/graph.json","fetch_events":"https://pith.science/api/pith-number/7KZBTYYTIGKMSSWQOO2RYKLQYK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7KZBTYYTIGKMSSWQOO2RYKLQYK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7KZBTYYTIGKMSSWQOO2RYKLQYK/action/storage_attestation","attest_author":"https://pith.science/pith/7KZBTYYTIGKMSSWQOO2RYKLQYK/action/author_attestation","sign_citation":"https://pith.science/pith/7KZBTYYTIGKMSSWQOO2RYKLQYK/action/citation_signature","submit_replication":"https://pith.science/pith/7KZBTYYTIGKMSSWQOO2RYKLQYK/action/replication_record"}},"created_at":"2026-05-18T00:27:36.892605+00:00","updated_at":"2026-05-18T00:27:36.892605+00:00"}