{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UR3G3E376AI5IOFXLZUJS4GJNT","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":"cf8cc415c1d5c68598fbd7c43d8bf1023138e5753fd502c71e1b52265237b118","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-12T02:48:56Z","title_canon_sha256":"4037c2d8c1efc0f0a59a910f8d1fe564286acfdf90d98ed55fc3f00aa20c6e08"},"schema_version":"1.0","source":{"id":"1702.03480","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03480","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03480v1","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03480","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"pith_short_12","alias_value":"UR3G3E376AI5","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UR3G3E376AI5IOFX","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UR3G3E37","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:70b0994da879ab9b1499b9eb2e8ba0426daffa071fd3294e6f31b2a3963a0700","target":"graph","created_at":"2026-05-18T00:50:53Z","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 asymptotic behavior of a sequence of positive solutions $(u_{\\epsilon})_{\\epsilon >0}$ as $\\epsilon \\to 0$ to the family of equations \\begin{equation*} \\left\\{\\begin{array}{ll} \\Delta u_{\\epsilon}+a(x)u_{\\epsilon}= \\frac{u_{\\epsilon}^{2^*(s_{\\epsilon})-1}}{|x|^{s_{\\epsilon}}}& \\hbox{ in }\\Omega\\\\ u_{\\epsilon}=0 & \\hbox{ on }\\partial\\Omega. \\end{array}\\right. \\end{equation*} where $(s_{\\epsilon})_{\\epsilon >0}$ is a sequence of positive real numbers such that $\\lim \\limits_{\\epsilon \\rightarrow 0} s_{\\epsilon}=0$, $2^{*}(s_{\\epsilon}):= \\frac{2(n-s_{\\epsilon})}{n-2}$ and $\\Omega \\s","authors_text":"Saikat Mazumdar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-12T02:48:56Z","title":"Hardy-Sobolev equations with asymptotically vanishing singularity: Blow-up analysis for the minimal energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03480","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:f12cd745c49ca621b6b65a0361aa2e7eca32990808f20cc445d96a6e1a65aecc","target":"record","created_at":"2026-05-18T00:50:53Z","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":"cf8cc415c1d5c68598fbd7c43d8bf1023138e5753fd502c71e1b52265237b118","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-12T02:48:56Z","title_canon_sha256":"4037c2d8c1efc0f0a59a910f8d1fe564286acfdf90d98ed55fc3f00aa20c6e08"},"schema_version":"1.0","source":{"id":"1702.03480","kind":"arxiv","version":1}},"canonical_sha256":"a4766d937ff011d438b75e689970c96cfccc540f60491a56a0d7cd8174deedc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4766d937ff011d438b75e689970c96cfccc540f60491a56a0d7cd8174deedc1","first_computed_at":"2026-05-18T00:50:53.682719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:53.682719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K08RJ+QZYrBXpLtYwp2H1Gw/wtEdjFWeSTz5KyALeI+i0KUrFST//g2mKKzXFMOVx3dgt26wLilhQbAQ0NnbCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:53.683273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03480","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f12cd745c49ca621b6b65a0361aa2e7eca32990808f20cc445d96a6e1a65aecc","sha256:70b0994da879ab9b1499b9eb2e8ba0426daffa071fd3294e6f31b2a3963a0700"],"state_sha256":"aaac08702ba9e7e8fda932d9a71773943f287350cbc058e6723ae13b46f96fac"}