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Additionally, we show that critical points of the corresponding constrained energy functional a"},"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":"2506.18202","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-22T23:36:43Z","cross_cats_sorted":[],"title_canon_sha256":"43e427081d67de1d7ac08925049a916043ac114db64fb9b3d6c1fd154f8f7875","abstract_canon_sha256":"f8dd6eeb348754fc0b2f32665f969b3ac636ededec3b6357a929463a4c06c012"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:04.953158Z","signature_b64":"4vRxkYaXIdPLotnGkO1wIHBLk16TGdKpys38VQal1HUzvq3PKHP7tXXs2H+ocggRpy9j//VhAyKU8hGeqIwHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e881c67f47bc32df00c2f38752e876b7eb7a52cd79591b69eac17d9a39cf5cf0","last_reissued_at":"2026-05-25T02:01:04.952516Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:04.952516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ground states of the planar nonlinear Schr\\\"odinger--Newton system with a point interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gustavo de Paula Ramos","submitted_at":"2025-06-22T23:36:43Z","abstract_excerpt":"We establish sufficient conditions for the existence of ground states of the following normalized nonlinear Schr\\\"odinger--Newton system with a point interaction: \\[ \\begin{cases} - \\Delta_\\alpha u = w u + \\beta u |u|^{p - 2} &\\text{on} ~ \\mathbb{R}^2; \\\\ - \\Delta w = 2 \\pi |u|^2 &\\text{on} ~ \\mathbb{R}^2; \\\\ \\|u\\|_{L^2}^2 = c, \\end{cases} \\] where $p > 2$; $\\alpha, \\beta \\in \\mathbb{R}$ and $- \\Delta_\\alpha$ denotes the Laplacian of point interaction with scattering length $(- 2 \\pi \\alpha)^{- 1}$. 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