{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:N2YFBB4KCFRGU2Y6S7AFO4VEBV","short_pith_number":"pith:N2YFBB4K","schema_version":"1.0","canonical_sha256":"6eb050878a11626a6b1e97c05772a40d7b8d0fd869808ada7dc1efa638e496f1","source":{"kind":"arxiv","id":"1908.05532","version":7},"attestation_state":"computed","paper":{"title":"Bubbling solutions for a planar exponential nonlinear elliptic equation with a singular source","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiamei Hu, Jingyi Dong, Yibin Zhang","submitted_at":"2019-08-15T13:37:40Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain in $\\mathbb{R}^2$ with smooth boundary, we study the following elliptic Dirichlet problem $$ \\begin{cases} -\\Delta\\upsilon= e^{\\upsilon}-s\\phi_1-4\\pi\\alpha\\delta_p-h(x)\\,\\,\\,\\, \\,\\textrm{in}\\,\\,\\,\\,\\,\\Omega,\\\\[2mm] \\upsilon=0 \\quad\\quad\\quad\\quad\\quad\\quad \\qquad\\qquad\\quad\\quad\\,\\,\\,\\, \\textrm{on}\\,\\ \\,\\partial\\Omega, \\end{cases} $$ where $s>0$ is a large parameter, $h\\in C^{0,\\gamma}(\\overline{\\Omega})$, $p\\in\\Omega$, $\\alpha\\in(-1,+\\infty)\\setminus\\mathbb{N}$, $\\delta_p$ denotes the Dirac measure supported at point $p$ and $\\phi_1$ is a positive first eigenf"},"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":"1908.05532","kind":"arxiv","version":7},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2019-08-15T13:37:40Z","cross_cats_sorted":[],"title_canon_sha256":"9cdda6eb935b326a0f2e455fbe3ee9fd3e245c90ee3f4cc42a570837b9e3a2f8","abstract_canon_sha256":"b725e5aafe17cc2d78376806cf2fab43e6de9ab6abd21058e9e63138f3d59d9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:49:36.519745Z","signature_b64":"E2GiBpNX51/SrRp4Ugb62vwJq6jslBT/Jt/6k5oebQc/Akzo1kNOaARpy02qk+yhQ1LJLFQJPBYr4mGdQh+tBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6eb050878a11626a6b1e97c05772a40d7b8d0fd869808ada7dc1efa638e496f1","last_reissued_at":"2026-07-05T03:49:36.519388Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:49:36.519388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bubbling solutions for a planar exponential nonlinear elliptic equation with a singular source","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiamei Hu, Jingyi Dong, Yibin Zhang","submitted_at":"2019-08-15T13:37:40Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain in $\\mathbb{R}^2$ with smooth boundary, we study the following elliptic Dirichlet problem $$ \\begin{cases} -\\Delta\\upsilon= e^{\\upsilon}-s\\phi_1-4\\pi\\alpha\\delta_p-h(x)\\,\\,\\,\\, \\,\\textrm{in}\\,\\,\\,\\,\\,\\Omega,\\\\[2mm] \\upsilon=0 \\quad\\quad\\quad\\quad\\quad\\quad \\qquad\\qquad\\quad\\quad\\,\\,\\,\\, \\textrm{on}\\,\\ \\,\\partial\\Omega, \\end{cases} $$ where $s>0$ is a large parameter, $h\\in C^{0,\\gamma}(\\overline{\\Omega})$, $p\\in\\Omega$, $\\alpha\\in(-1,+\\infty)\\setminus\\mathbb{N}$, $\\delta_p$ denotes the Dirac measure supported at point $p$ and $\\phi_1$ is a positive first eigenf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05532","kind":"arxiv","version":7},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.05532/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.05532","created_at":"2026-07-05T03:49:36.519445+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.05532v7","created_at":"2026-07-05T03:49:36.519445+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05532","created_at":"2026-07-05T03:49:36.519445+00:00"},{"alias_kind":"pith_short_12","alias_value":"N2YFBB4KCFRG","created_at":"2026-07-05T03:49:36.519445+00:00"},{"alias_kind":"pith_short_16","alias_value":"N2YFBB4KCFRGU2Y6","created_at":"2026-07-05T03:49:36.519445+00:00"},{"alias_kind":"pith_short_8","alias_value":"N2YFBB4K","created_at":"2026-07-05T03:49:36.519445+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/N2YFBB4KCFRGU2Y6S7AFO4VEBV","json":"https://pith.science/pith/N2YFBB4KCFRGU2Y6S7AFO4VEBV.json","graph_json":"https://pith.science/api/pith-number/N2YFBB4KCFRGU2Y6S7AFO4VEBV/graph.json","events_json":"https://pith.science/api/pith-number/N2YFBB4KCFRGU2Y6S7AFO4VEBV/events.json","paper":"https://pith.science/paper/N2YFBB4K"},"agent_actions":{"view_html":"https://pith.science/pith/N2YFBB4KCFRGU2Y6S7AFO4VEBV","download_json":"https://pith.science/pith/N2YFBB4KCFRGU2Y6S7AFO4VEBV.json","view_paper":"https://pith.science/paper/N2YFBB4K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.05532&json=true","fetch_graph":"https://pith.science/api/pith-number/N2YFBB4KCFRGU2Y6S7AFO4VEBV/graph.json","fetch_events":"https://pith.science/api/pith-number/N2YFBB4KCFRGU2Y6S7AFO4VEBV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N2YFBB4KCFRGU2Y6S7AFO4VEBV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N2YFBB4KCFRGU2Y6S7AFO4VEBV/action/storage_attestation","attest_author":"https://pith.science/pith/N2YFBB4KCFRGU2Y6S7AFO4VEBV/action/author_attestation","sign_citation":"https://pith.science/pith/N2YFBB4KCFRGU2Y6S7AFO4VEBV/action/citation_signature","submit_replication":"https://pith.science/pith/N2YFBB4KCFRGU2Y6S7AFO4VEBV/action/replication_record"}},"created_at":"2026-07-05T03:49:36.519445+00:00","updated_at":"2026-07-05T03:49:36.519445+00:00"}