{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7WZ2IBLBESXJM5FTJD5YGMVB7N","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":"d8d34bf5f1fd657faa05bb41f026960f82a25aeac921c83f8ec5265cf0d5ba4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-11T13:46:20Z","title_canon_sha256":"1f4d65f665ee0e56b505be15cf71a34dbb7c35a2a65c7f6998f72ebf5a1452a5"},"schema_version":"1.0","source":{"id":"1506.03669","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03669","created_at":"2026-05-18T00:50:52Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03669v2","created_at":"2026-05-18T00:50:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03669","created_at":"2026-05-18T00:50:52Z"},{"alias_kind":"pith_short_12","alias_value":"7WZ2IBLBESXJ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7WZ2IBLBESXJM5FT","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7WZ2IBLB","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:128f14ee9c56e4a352542bc40a3388fc055cc444233047e93c03d19e1591197d","target":"graph","created_at":"2026-05-18T00:50:52Z","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":"In this paper we are concerned with a general singular Dirichlet boundary value problem whose model is the following $$ \\begin{cases}\n  -\\Delta u = \\frac{\\mu}{u^{\\gamma}} & \\text{in}\\ \\Omega, u=0 &\\text{on}\\ \\partial\\Omega, u>0 &\\text{on}\\ \\Omega\\,.\n  \\end{cases} $$ Here $\\mu$ is a nonnegative bounded Radon measure on a bounded open set $\\Omega\\subset\\mathbb{R}^N$, and $\\gamma>0$.","authors_text":"Francesco Petitta, Luigi Orsina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-11T13:46:20Z","title":"A Lazer-McKenna type problem with measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03669","kind":"arxiv","version":2},"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":"sha256:0a633ef99a25046e55dc51c4f10b34cc87018b902fca3fc48c35f86f9b077cf1","target":"record","created_at":"2026-05-18T00:50:52Z","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":"d8d34bf5f1fd657faa05bb41f026960f82a25aeac921c83f8ec5265cf0d5ba4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-11T13:46:20Z","title_canon_sha256":"1f4d65f665ee0e56b505be15cf71a34dbb7c35a2a65c7f6998f72ebf5a1452a5"},"schema_version":"1.0","source":{"id":"1506.03669","kind":"arxiv","version":2}},"canonical_sha256":"fdb3a4056124ae9674b348fb8332a1fb4018e0ace213c900b8009fc915f20ce2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fdb3a4056124ae9674b348fb8332a1fb4018e0ace213c900b8009fc915f20ce2","first_computed_at":"2026-05-18T00:50:52.511274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:52.511274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"biBZXAp4kA79994rW2HnXqYkh9Posf6zwHlTtJlvzf8V5UyU2Zwgwf0ThJ9aI/plF2g4yXmNC5HmHoogvFFXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:52.511762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03669","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a633ef99a25046e55dc51c4f10b34cc87018b902fca3fc48c35f86f9b077cf1","sha256:128f14ee9c56e4a352542bc40a3388fc055cc444233047e93c03d19e1591197d"],"state_sha256":"6f1e29d9723f4f0bb8aded3eb5fc4c6c2b835bf25fdbf9f78a5f384d50af9b9f"}