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Using a refined compactness lemma, we extend the mass concentration of finite time blow-up solutions established in the attractive case by the first author in [Bensouilah] to $c<\\lambda(d)$. By means of a simple and short limiting profile theorem, we get the same classification result obtained by Csobo"},"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":"1804.08752","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-23T21:43:49Z","cross_cats_sorted":[],"title_canon_sha256":"8e9a8d9398f7334fc2e4838d1e50c2cd45d7d41a741ad0d802bbb3228a07a40c","abstract_canon_sha256":"82bc868d012a534f15f015e72a830ed18cb7bc6324fa48472418c7bce8238adf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:16.200760Z","signature_b64":"D4P+flUXjFJjXAZKUG8/VICeS0Jzzsk+qXhuigRybw2OsvehzYQJrGwWNKl60u9RpPlnLB7fyEE+4Y0d53CqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"166fd7f248f70d91989ada917e6c8093da52164b97cddb0f389b154e55ea8558","last_reissued_at":"2026-05-18T00:17:16.200255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:16.200255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mass concentration and characterization of finite time blow-up solutions for the nonlinear Schr\\\"odinger equation with inverse-square potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelwahab Bensouilah, Van Duong Dinh","submitted_at":"2018-04-23T21:43:49Z","abstract_excerpt":"We consider the $L^2$-critical NLS with inverse-square potential\n  $$\n  i \\partial_t u +\\Delta u + c|x|^{-2} u = -|u|^{\\frac{4}{d}} u, \\quad u(0) = u_0, \\quad (t,x) \\in \\mathbb{R}^+ \\times \\mathbb{R}^d,\n  $$\n  where $d\\geq 3$ and $c\\ne 0$ satisfies $c<\\lambda(d) := \\left(\\frac{d-2}{2}\\right)^2$. Using a refined compactness lemma, we extend the mass concentration of finite time blow-up solutions established in the attractive case by the first author in [Bensouilah] to $c<\\lambda(d)$. By means of a simple and short limiting profile theorem, we get the same classification result obtained by Csobo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08752","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1804.08752","created_at":"2026-05-18T00:17:16.200346+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.08752v2","created_at":"2026-05-18T00:17:16.200346+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08752","created_at":"2026-05-18T00:17:16.200346+00:00"},{"alias_kind":"pith_short_12","alias_value":"CZX5P4SI64GZ","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"CZX5P4SI64GZDGE2","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"CZX5P4SI","created_at":"2026-05-18T12:32:19.392346+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.04609","citing_title":"Nonlinear Schr\\\"{o}dinger equations with critical Hardy potential and Choquard nonlinearity","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CZX5P4SI64GZDGE23KIX43EASP","json":"https://pith.science/pith/CZX5P4SI64GZDGE23KIX43EASP.json","graph_json":"https://pith.science/api/pith-number/CZX5P4SI64GZDGE23KIX43EASP/graph.json","events_json":"https://pith.science/api/pith-number/CZX5P4SI64GZDGE23KIX43EASP/events.json","paper":"https://pith.science/paper/CZX5P4SI"},"agent_actions":{"view_html":"https://pith.science/pith/CZX5P4SI64GZDGE23KIX43EASP","download_json":"https://pith.science/pith/CZX5P4SI64GZDGE23KIX43EASP.json","view_paper":"https://pith.science/paper/CZX5P4SI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.08752&json=true","fetch_graph":"https://pith.science/api/pith-number/CZX5P4SI64GZDGE23KIX43EASP/graph.json","fetch_events":"https://pith.science/api/pith-number/CZX5P4SI64GZDGE23KIX43EASP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CZX5P4SI64GZDGE23KIX43EASP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CZX5P4SI64GZDGE23KIX43EASP/action/storage_attestation","attest_author":"https://pith.science/pith/CZX5P4SI64GZDGE23KIX43EASP/action/author_attestation","sign_citation":"https://pith.science/pith/CZX5P4SI64GZDGE23KIX43EASP/action/citation_signature","submit_replication":"https://pith.science/pith/CZX5P4SI64GZDGE23KIX43EASP/action/replication_record"}},"created_at":"2026-05-18T00:17:16.200346+00:00","updated_at":"2026-05-18T00:17:16.200346+00:00"}