{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LZUPGFKTR5WWCOYEY6VJPE6JXU","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":"cb9f29c4a0bbf37b17f2cacfaa15b155f9e1cdff4c3d4cc4128cc4c4767549d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-19T15:28:06Z","title_canon_sha256":"dfe5ec841003c6cbc5a394a0f73795dc1c95fd5e4c50e74d80c03a4adb985293"},"schema_version":"1.0","source":{"id":"1801.06461","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.06461","created_at":"2026-05-18T00:25:30Z"},{"alias_kind":"arxiv_version","alias_value":"1801.06461v1","created_at":"2026-05-18T00:25:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.06461","created_at":"2026-05-18T00:25:30Z"},{"alias_kind":"pith_short_12","alias_value":"LZUPGFKTR5WW","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LZUPGFKTR5WWCOYE","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LZUPGFKT","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:b7ed05e33ea7137fc0dc396f09095009d66aed42b2c36e2afea9de681ea09995","target":"graph","created_at":"2026-05-18T00:25:30Z","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 article, we prove the existence of at least three positive solutions for the following nonlocal singular problem \\begin{equation*} (P_\\la)\\left\\{ \\begin{split} (-\\De)^su &= \\la\\frac{f(u)}{u^q}, \\; \\; u>0 \\;\\; \\text{in}\\;\\; \\Om,\\\\ u &= 0\\;\\; \\text{in}\\;\\; \\mb R^n \\setminus \\Om \\end{split} \\right. \\end{equation*} where $(-\\De)^s$ denotes the fractional Laplace operator for $s\\in (0,1)$, $n>2s$, $q \\in (0,1)$, $\\la>0$ and $\\Om$ is smooth bounded domain in $\\mb R^n$. Here $f :[0,\\infty) \\to [0,\\infty)$ is a continuous nondecreasing map satisfying $\\lim\\limits_{u\\to \\infty}\\frac{f(u)}{u^{q+","authors_text":"Jacques Giacomoni, Konijeti Sreenadh, Tuhina Mukherjee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-19T15:28:06Z","title":"Existence of three positive solutions for a nonlocal singular dirichlet boundary problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06461","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":"sha256:07d7028e207b6159c8b1f9eacab101ce41c09c53ab8e2d4620a5f55b6d457078","target":"record","created_at":"2026-05-18T00:25:30Z","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":"cb9f29c4a0bbf37b17f2cacfaa15b155f9e1cdff4c3d4cc4128cc4c4767549d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-19T15:28:06Z","title_canon_sha256":"dfe5ec841003c6cbc5a394a0f73795dc1c95fd5e4c50e74d80c03a4adb985293"},"schema_version":"1.0","source":{"id":"1801.06461","kind":"arxiv","version":1}},"canonical_sha256":"5e68f315538f6d613b04c7aa9793c9bd0507170b004a9f7bf7de9f69529af413","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e68f315538f6d613b04c7aa9793c9bd0507170b004a9f7bf7de9f69529af413","first_computed_at":"2026-05-18T00:25:30.007799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:30.007799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s6VI4nhiccQb7U1LpTxLbaQYpr5Z5tEQR6c+o2QtnZ9CV2Z4QDN6lhDK28nxLYGcRSIsxLu3JnUOYdAz7huZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:30.008518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.06461","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07d7028e207b6159c8b1f9eacab101ce41c09c53ab8e2d4620a5f55b6d457078","sha256:b7ed05e33ea7137fc0dc396f09095009d66aed42b2c36e2afea9de681ea09995"],"state_sha256":"5691f96f66dcee12cac882bc7653ee51fbcde9378230d05a689968a0bd67d023"}