{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:H7DJCP4PFKS4STXCPIQIQV3S4P","short_pith_number":"pith:H7DJCP4P","schema_version":"1.0","canonical_sha256":"3fc6913f8f2aa5c94ee27a20885772e3c6827311ba4287581d0a8677c15a7bcf","source":{"kind":"arxiv","id":"1309.5656","version":1},"attestation_state":"computed","paper":{"title":"Some fourth order nonlinear elliptic problems related to epitaxial growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Carlos Escudero, Ireneo Peral","submitted_at":"2013-09-22T21:33:34Z","abstract_excerpt":"This paper deals with some mathematical models arising in the theory of epitaxial growth of crystal. We focalize the study on a stationary problem which presents some analytical difficulties. We study the existence of solutions. The central model in this work is given by the following fourth order elliptic equation, $$\\begin{array}{rclll} \\Delta^2 u=\\text{det} \\left(D^2 u \\right) &+&\\lambda f, \\quad & x\\in \\Omega\\subset\\mathbb{R}^2\\\\ \\hbox{conditions on} &\\quad& & \\partial \\Omega. \\end{array} $$ The framework to study the problem deeply depends on the boundary conditions."},"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":"1309.5656","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-22T21:33:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"67280074fe81c81aa5af2d1a0a29f413ab6512cc4c75eab4c29bdcfd25e7a894","abstract_canon_sha256":"5bf4685cf0a938f38eb0d21f47508ccc6a7a61468c2d1a9b9182208358a2e49d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:35.634100Z","signature_b64":"qlXymVgGfW5srfDYm3FAL6lLhpxD+ndO0EmxN30oHqagWZNiWQWLYVA+UMkCxcgCZKGOlmDR3dFtwhdDjlTvCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fc6913f8f2aa5c94ee27a20885772e3c6827311ba4287581d0a8677c15a7bcf","last_reissued_at":"2026-05-18T03:12:35.633404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:35.633404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some fourth order nonlinear elliptic problems related to epitaxial growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Carlos Escudero, Ireneo Peral","submitted_at":"2013-09-22T21:33:34Z","abstract_excerpt":"This paper deals with some mathematical models arising in the theory of epitaxial growth of crystal. We focalize the study on a stationary problem which presents some analytical difficulties. We study the existence of solutions. The central model in this work is given by the following fourth order elliptic equation, $$\\begin{array}{rclll} \\Delta^2 u=\\text{det} \\left(D^2 u \\right) &+&\\lambda f, \\quad & x\\in \\Omega\\subset\\mathbb{R}^2\\\\ \\hbox{conditions on} &\\quad& & \\partial \\Omega. \\end{array} $$ The framework to study the problem deeply depends on the boundary conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5656","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":"1309.5656","created_at":"2026-05-18T03:12:35.633502+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.5656v1","created_at":"2026-05-18T03:12:35.633502+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5656","created_at":"2026-05-18T03:12:35.633502+00:00"},{"alias_kind":"pith_short_12","alias_value":"H7DJCP4PFKS4","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"H7DJCP4PFKS4STXC","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"H7DJCP4P","created_at":"2026-05-18T12:27:46.883200+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/H7DJCP4PFKS4STXCPIQIQV3S4P","json":"https://pith.science/pith/H7DJCP4PFKS4STXCPIQIQV3S4P.json","graph_json":"https://pith.science/api/pith-number/H7DJCP4PFKS4STXCPIQIQV3S4P/graph.json","events_json":"https://pith.science/api/pith-number/H7DJCP4PFKS4STXCPIQIQV3S4P/events.json","paper":"https://pith.science/paper/H7DJCP4P"},"agent_actions":{"view_html":"https://pith.science/pith/H7DJCP4PFKS4STXCPIQIQV3S4P","download_json":"https://pith.science/pith/H7DJCP4PFKS4STXCPIQIQV3S4P.json","view_paper":"https://pith.science/paper/H7DJCP4P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.5656&json=true","fetch_graph":"https://pith.science/api/pith-number/H7DJCP4PFKS4STXCPIQIQV3S4P/graph.json","fetch_events":"https://pith.science/api/pith-number/H7DJCP4PFKS4STXCPIQIQV3S4P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H7DJCP4PFKS4STXCPIQIQV3S4P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H7DJCP4PFKS4STXCPIQIQV3S4P/action/storage_attestation","attest_author":"https://pith.science/pith/H7DJCP4PFKS4STXCPIQIQV3S4P/action/author_attestation","sign_citation":"https://pith.science/pith/H7DJCP4PFKS4STXCPIQIQV3S4P/action/citation_signature","submit_replication":"https://pith.science/pith/H7DJCP4PFKS4STXCPIQIQV3S4P/action/replication_record"}},"created_at":"2026-05-18T03:12:35.633502+00:00","updated_at":"2026-05-18T03:12:35.633502+00:00"}