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The vector BSs are characterized by the two conserved quantities, the Arnowitt-Deser-Misner (ADM) mass and the Noether charge associated with the global $U(1)$ symmetry. We show that in comparison"},"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":"1805.09867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-05-24T19:41:31Z","cross_cats_sorted":[],"title_canon_sha256":"25045340f447c79c001d210005b9236663af1170cc97783bf0103a0e0e37900e","abstract_canon_sha256":"1ccb4ff579a5f3791f75c72754c10c1842095bf8ebc1372438c5f2c6f5d3c1f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:58.920400Z","signature_b64":"QzNkeJ0LyUGu+mQWArEGiFKlOgsTYh9E04XNcgtvCM0l65iO0qczF3XE98ZOu6UBMdyM3UPNoeKiaPX/P9agDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27f0cc5c986fd022b1b5fa7f3ca25a209a7de9b756b2cb151cdbe84620b4ef1c","last_reissued_at":"2026-05-18T00:14:58.919953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:58.919953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vector boson star solutions with a quartic order self-interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Masato Minamitsuji","submitted_at":"2018-05-24T19:41:31Z","abstract_excerpt":"We investigate boson star (BS) solutions in the Einstein-Proca theory with the quartic order self-interaction of the vector field $\\lambda (A^\\mu\\bar{A}_\\mu)^2/4$ and the mass term $\\mu \\bar{A}^\\mu A_\\mu/2$, where $A_\\mu$ is the complex vector field and ${\\bar A}_\\mu$ is the complex conjugate of $A_\\mu$, and $\\lambda$ and $\\mu$ are the coupling constant and the mass of the vector field, respectively. The vector BSs are characterized by the two conserved quantities, the Arnowitt-Deser-Misner (ADM) mass and the Noether charge associated with the global $U(1)$ symmetry. 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