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Frank","submitted_at":"2009-10-14T20:30:17Z","abstract_excerpt":"We consider ground state solutions $u \\geq 0$ for the $L^2$-critical boson star equation $$ \\sqrt{-\\Delta} \\, u - \\big (|x|^{-1} \\ast |u|^2 \\big) u = -u \\quad {in $\\R^3$}. $$ We prove analyticity and radial symmetry of $u$.\n  In a previous version of this paper, we also stated uniqueness and nondegeneracy of ground states for the $L^2$-critical boson star equation in $\\R^3$, but the arguments given there contained a gap. However, we refer to our recent preprint \\cite{FraLe} in {\\tt arXiv:1009.4042}, where we prove a general uniqueness and nondegeneracy result for ground states of nonlinear equ"},"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":"0910.2721","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-10-14T20:30:17Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7e5aaeb547860fe344beb30b7ee5f6a138926d7b26587485c284e6774d0bf375","abstract_canon_sha256":"951f20dc625fd933d2dc8a35a685707a5b726815a8749a328faf1a2b54b2a1e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:48.603551Z","signature_b64":"3ilWpX86JQ0+XDnoA1kGVKAjZ480eFrmu+Isn5gEBtbsYf5OmPbpLvhqdn/UopdrcHDs/YLqkQ4WG1XwwlZ9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c537b4e80591a0348ee695a6810209fbb64266a89fc38c499a3065bcfba5360","last_reissued_at":"2026-05-18T04:38:48.603109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:48.603109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On ground states for the L^2-critical boson star equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Enno Lenzmann, Rupert L. 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