{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:35LPMBPR3DJKNK6ZYWS5JXDHAK","short_pith_number":"pith:35LPMBPR","schema_version":"1.0","canonical_sha256":"df56f605f1d8d2a6abd9c5a5d4dc67029465fed69af41a6f8e136bd2df2fea1c","source":{"kind":"arxiv","id":"1305.2312","version":2},"attestation_state":"computed","paper":{"title":"Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Amp\\`ere type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Barbara Brandolini, Carlo Nitsch, Cristina Trombetti, Nunzia Gavitone","submitted_at":"2013-05-10T11:28:17Z","abstract_excerpt":"The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow."},"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":"1305.2312","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-10T11:28:17Z","cross_cats_sorted":[],"title_canon_sha256":"e16cf08061534b3f37cdf36f17c2e423d09039e4cf0e6239cd538b12db066d08","abstract_canon_sha256":"62bc2b4818b77242f43b91024a175aebf3539676ce558cebabdfcdf99c3fbe71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:45.782846Z","signature_b64":"oUfmzU65e8igXQj+ySsbDAZK+lzWnaQdddE5My4et6srEO4H73VBV2wZMM5QKxxi/Iypz2JT8cbrJHBhvu+nBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df56f605f1d8d2a6abd9c5a5d4dc67029465fed69af41a6f8e136bd2df2fea1c","last_reissued_at":"2026-05-18T03:10:45.782303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:45.782303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Amp\\`ere type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Barbara Brandolini, Carlo Nitsch, Cristina Trombetti, Nunzia Gavitone","submitted_at":"2013-05-10T11:28:17Z","abstract_excerpt":"The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2312","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":"1305.2312","created_at":"2026-05-18T03:10:45.782400+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.2312v2","created_at":"2026-05-18T03:10:45.782400+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2312","created_at":"2026-05-18T03:10:45.782400+00:00"},{"alias_kind":"pith_short_12","alias_value":"35LPMBPR3DJK","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"35LPMBPR3DJKNK6Z","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"35LPMBPR","created_at":"2026-05-18T12:27:32.513160+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/35LPMBPR3DJKNK6ZYWS5JXDHAK","json":"https://pith.science/pith/35LPMBPR3DJKNK6ZYWS5JXDHAK.json","graph_json":"https://pith.science/api/pith-number/35LPMBPR3DJKNK6ZYWS5JXDHAK/graph.json","events_json":"https://pith.science/api/pith-number/35LPMBPR3DJKNK6ZYWS5JXDHAK/events.json","paper":"https://pith.science/paper/35LPMBPR"},"agent_actions":{"view_html":"https://pith.science/pith/35LPMBPR3DJKNK6ZYWS5JXDHAK","download_json":"https://pith.science/pith/35LPMBPR3DJKNK6ZYWS5JXDHAK.json","view_paper":"https://pith.science/paper/35LPMBPR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.2312&json=true","fetch_graph":"https://pith.science/api/pith-number/35LPMBPR3DJKNK6ZYWS5JXDHAK/graph.json","fetch_events":"https://pith.science/api/pith-number/35LPMBPR3DJKNK6ZYWS5JXDHAK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/35LPMBPR3DJKNK6ZYWS5JXDHAK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/35LPMBPR3DJKNK6ZYWS5JXDHAK/action/storage_attestation","attest_author":"https://pith.science/pith/35LPMBPR3DJKNK6ZYWS5JXDHAK/action/author_attestation","sign_citation":"https://pith.science/pith/35LPMBPR3DJKNK6ZYWS5JXDHAK/action/citation_signature","submit_replication":"https://pith.science/pith/35LPMBPR3DJKNK6ZYWS5JXDHAK/action/replication_record"}},"created_at":"2026-05-18T03:10:45.782400+00:00","updated_at":"2026-05-18T03:10:45.782400+00:00"}