{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5KDAVAEYPQ4XCPNR473GACSRBT","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":"200459addd10f0b863cf9659c4d59b7996efe1d7d0a2da5a79159dc7a5f845f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-02T13:35:04Z","title_canon_sha256":"a050f39b0409a6d0c64e2f9205f6bd0e6ea14976f2151d1a8e6dcd1758e271ff"},"schema_version":"1.0","source":{"id":"1703.00777","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00777","created_at":"2026-05-18T00:49:40Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00777v1","created_at":"2026-05-18T00:49:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00777","created_at":"2026-05-18T00:49:40Z"},{"alias_kind":"pith_short_12","alias_value":"5KDAVAEYPQ4X","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5KDAVAEYPQ4XCPNR","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5KDAVAEY","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:8667316777b6027d4496cc396caa7c5941b44bb28ef1f5b1e03f71a3a0739d51","target":"graph","created_at":"2026-05-18T00:49:40Z","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 are concerned with the following Schr\\\"odinger-Newton problem\n  \\begin{equation}\n  -\\varepsilon^2\\Delta u+V(x)u=\\frac{1}{8\\pi \\varepsilon^2}\n  \\big(\\int_{\\mathbb R^3}\\frac{u^2(\\xi)}{|x-\\xi|}d\\xi\\big)u,~x\\in \\mathbb R^3. \\end{equation} For $\\varepsilon$ small enough, we show the uniqueness of positive solutions concentrating at the nondegenerate critical points of $V(x)$. The main tools are a local Pohozaev type of identity, blow-up analysis and the maximum principle. Our results also show that the asymptotic behavior of concentrated points to Schr\\\"odinger-Newton problem is quite different ","authors_text":"Chunhua Wang, Peng Luo, Shuangjie Peng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-02T13:35:04Z","title":"Uniqueness of positive solutions with Concentration for the Schr\\\"odinger-Newton problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00777","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":"sha256:41a2ec63f2150ec29cdd6420df02162fcebec50836050ece77505011d0d8bc46","target":"record","created_at":"2026-05-18T00:49:40Z","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":"200459addd10f0b863cf9659c4d59b7996efe1d7d0a2da5a79159dc7a5f845f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-02T13:35:04Z","title_canon_sha256":"a050f39b0409a6d0c64e2f9205f6bd0e6ea14976f2151d1a8e6dcd1758e271ff"},"schema_version":"1.0","source":{"id":"1703.00777","kind":"arxiv","version":1}},"canonical_sha256":"ea860a80987c39713db1e7f6600a510cf14e72ce2aa532430b9c12870e1b5019","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea860a80987c39713db1e7f6600a510cf14e72ce2aa532430b9c12870e1b5019","first_computed_at":"2026-05-18T00:49:40.785693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:40.785693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"28YqSS5XRmhlrb6NLQyUByqCO2UzXPDpxpAQfhabCXDqwbph7u9EJXt3aKEa02eoHUsOKohmT93qwtuuJNA3Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:40.786188Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.00777","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41a2ec63f2150ec29cdd6420df02162fcebec50836050ece77505011d0d8bc46","sha256:8667316777b6027d4496cc396caa7c5941b44bb28ef1f5b1e03f71a3a0739d51"],"state_sha256":"b69934294e0bff4531c4462c4b2433d0fbb905d9651e2449ae9b96b81d39f584"}