{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:C4RCKPBJX7HIQU6K26WSOAEPDD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0e4a9f1f047c6a8ecac8fc81a61133906140b4f9d08166410de984081ca7b412","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-01T09:34:53Z","title_canon_sha256":"8054e50bc15670c9b5275692940a59a5e11fffc998356315c2d241c957a5f303"},"schema_version":"1.0","source":{"id":"1905.00232","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.00232","created_at":"2026-05-17T23:47:13Z"},{"alias_kind":"arxiv_version","alias_value":"1905.00232v1","created_at":"2026-05-17T23:47:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00232","created_at":"2026-05-17T23:47:13Z"},{"alias_kind":"pith_short_12","alias_value":"C4RCKPBJX7HI","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"C4RCKPBJX7HIQU6K","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"C4RCKPBJ","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:74feb8cb2f38709c566174d11fc7494559617a19202d98bc0a2918ed7e72dfb9","target":"graph","created_at":"2026-05-17T23:47:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the existence of a solution to the mixed boundary value problem for Helmholtz and Poisson type equations in a bounded Lipschitz domain $\\Omega\\subset\\mathbb{R}^N$ and in $\\mathbb{R}^N\\setminus\\Omega$ for $N\\geq3$. The boundary $\\partial\\Omega$ of $\\Omega$ is the decomposition of $\\Gamma_1,\\Gamma_2\\subset\\partial\\Omega$ such that $\\partial\\Omega=\\Gamma=\\overline{\\Gamma}_1\\cup\\Gamma_2=\\Gamma_1\\cup\\overline{\\Gamma}_2$ and $\\Gamma_1\\cap\\Gamma_2=\\emptyset$. We have shown that if the Neumann data $f_2\\in H^{-\\frac{1}{2}}(\\Gamma_2)$ and the Dirichlet data $f_1\\in H^{\\frac{1}{2}}(\\Gamma_1)$ t","authors_text":"Akasmika Panda, Debajyoti Choudhuri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-01T09:34:53Z","title":"Existence results of two mixed boundary value elliptic PDEs in $\\mathbb{R}^n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00232","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d90a1da02e2008ae8df3264fbfd9ba494411dcc0426ebbe849e015a61e4db5fd","target":"record","created_at":"2026-05-17T23:47:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0e4a9f1f047c6a8ecac8fc81a61133906140b4f9d08166410de984081ca7b412","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-01T09:34:53Z","title_canon_sha256":"8054e50bc15670c9b5275692940a59a5e11fffc998356315c2d241c957a5f303"},"schema_version":"1.0","source":{"id":"1905.00232","kind":"arxiv","version":1}},"canonical_sha256":"1722253c29bfce8853cad7ad27008f18fe845a84ee2d92436e170e514e6c26a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1722253c29bfce8853cad7ad27008f18fe845a84ee2d92436e170e514e6c26a6","first_computed_at":"2026-05-17T23:47:13.405432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:13.405432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nAVpSDv+MaNmVgO1zAIRf62FCKLnqGNW/oiwV6DFwblBiJM04O8U+iLNSm84u6JCJOaBmnbXiRQ/XJPs7byFBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:13.405893Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.00232","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d90a1da02e2008ae8df3264fbfd9ba494411dcc0426ebbe849e015a61e4db5fd","sha256:74feb8cb2f38709c566174d11fc7494559617a19202d98bc0a2918ed7e72dfb9"],"state_sha256":"47bd5fe145caa08426836fd75d3051b8664863569eb7666d8e5181e170e3f31c"}