{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZOFU3GB4HUWK4GCNWC6E5SSB3Q","short_pith_number":"pith:ZOFU3GB4","schema_version":"1.0","canonical_sha256":"cb8b4d983c3d2cae184db0bc4eca41dc3c13faa506b56dc7572a853b258b4016","source":{"kind":"arxiv","id":"1706.05684","version":1},"attestation_state":"computed","paper":{"title":"Radial biharmonic $k-$Hessian equations: The critical dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos Escudero, Pedro J. Torres","submitted_at":"2017-06-18T16:35:26Z","abstract_excerpt":"This work is devoted to the study of radial solutions to the elliptic problem \\begin{equation}\\nonumber \\Delta^2 u = (-1)^k S_k[u] + \\lambda f, \\qquad x \\in B_1(0) \\subset \\mathbb{R}^N, \\end{equation} provided either with Dirichlet boundary conditions \\begin{eqnarray}\\nonumber u = \\partial_n u = 0, \\qquad x \\in \\partial B_1(0), \\end{eqnarray} or Navier boundary conditions \\begin{equation}\\nonumber u = \\Delta u = 0, \\qquad x \\in \\partial B_1(0), \\end{equation} where the $k-$Hessian $S_k[u]$ is the $k^{\\mathrm{th}}$ elementary symmetric polynomial of eigenvalues of the Hessian matrix and the dat"},"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":"1706.05684","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-06-18T16:35:26Z","cross_cats_sorted":[],"title_canon_sha256":"3859d47f3bdde50b50fa5bd757e10eba15ebf82171952f14320fead6da78eb03","abstract_canon_sha256":"a02be75a85fbdc9637a793db586c789c4c0f6e0c2e8fed249c3badea05327bca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:09.226082Z","signature_b64":"bTtc2nOAmqKGtIeMas/BEnxexQpVnBNbV9HwVA1XM/4Ry1UQk4zHk+n0jHCQDMkFgbzkPUyjfuV1ue637KqQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb8b4d983c3d2cae184db0bc4eca41dc3c13faa506b56dc7572a853b258b4016","last_reissued_at":"2026-05-18T00:42:09.225346Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:09.225346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Radial biharmonic $k-$Hessian equations: The critical dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos Escudero, Pedro J. Torres","submitted_at":"2017-06-18T16:35:26Z","abstract_excerpt":"This work is devoted to the study of radial solutions to the elliptic problem \\begin{equation}\\nonumber \\Delta^2 u = (-1)^k S_k[u] + \\lambda f, \\qquad x \\in B_1(0) \\subset \\mathbb{R}^N, \\end{equation} provided either with Dirichlet boundary conditions \\begin{eqnarray}\\nonumber u = \\partial_n u = 0, \\qquad x \\in \\partial B_1(0), \\end{eqnarray} or Navier boundary conditions \\begin{equation}\\nonumber u = \\Delta u = 0, \\qquad x \\in \\partial B_1(0), \\end{equation} where the $k-$Hessian $S_k[u]$ is the $k^{\\mathrm{th}}$ elementary symmetric polynomial of eigenvalues of the Hessian matrix and the dat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05684","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.05684","created_at":"2026-05-18T00:42:09.225470+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.05684v1","created_at":"2026-05-18T00:42:09.225470+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05684","created_at":"2026-05-18T00:42:09.225470+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZOFU3GB4HUWK","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZOFU3GB4HUWK4GCN","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZOFU3GB4","created_at":"2026-05-18T12:31:59.375834+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/ZOFU3GB4HUWK4GCNWC6E5SSB3Q","json":"https://pith.science/pith/ZOFU3GB4HUWK4GCNWC6E5SSB3Q.json","graph_json":"https://pith.science/api/pith-number/ZOFU3GB4HUWK4GCNWC6E5SSB3Q/graph.json","events_json":"https://pith.science/api/pith-number/ZOFU3GB4HUWK4GCNWC6E5SSB3Q/events.json","paper":"https://pith.science/paper/ZOFU3GB4"},"agent_actions":{"view_html":"https://pith.science/pith/ZOFU3GB4HUWK4GCNWC6E5SSB3Q","download_json":"https://pith.science/pith/ZOFU3GB4HUWK4GCNWC6E5SSB3Q.json","view_paper":"https://pith.science/paper/ZOFU3GB4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.05684&json=true","fetch_graph":"https://pith.science/api/pith-number/ZOFU3GB4HUWK4GCNWC6E5SSB3Q/graph.json","fetch_events":"https://pith.science/api/pith-number/ZOFU3GB4HUWK4GCNWC6E5SSB3Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZOFU3GB4HUWK4GCNWC6E5SSB3Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZOFU3GB4HUWK4GCNWC6E5SSB3Q/action/storage_attestation","attest_author":"https://pith.science/pith/ZOFU3GB4HUWK4GCNWC6E5SSB3Q/action/author_attestation","sign_citation":"https://pith.science/pith/ZOFU3GB4HUWK4GCNWC6E5SSB3Q/action/citation_signature","submit_replication":"https://pith.science/pith/ZOFU3GB4HUWK4GCNWC6E5SSB3Q/action/replication_record"}},"created_at":"2026-05-18T00:42:09.225470+00:00","updated_at":"2026-05-18T00:42:09.225470+00:00"}