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Two subclasses of this family correspond to compactly supported density profiles suitably modulated by the dynamic radius of the star that expands at the self-similar rate $\\lambda(t)_{t\\to\\infty}\\sim t^{\\frac23}$ and linear rate $\\lambda(t)_{t\\to\\infty}\\sim t$ respectively. We prove two results: any linearly expanding Goldreich-Weber star is nonlinearly stable, while any given self-similarly expanding Goldreich-Weber star is codimension-4 nonlinearly stable "},"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":"2212.11420","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-12-22T00:04:28Z","cross_cats_sorted":[],"title_canon_sha256":"33acfd6dd491b619cd73371b104da0ea2623e08478fc0004b357a229d1ca7044","abstract_canon_sha256":"397167ea9f530bc1c538c286a63915ac1aff01faebe3f13c4f9a96258e387354"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:17:55.820135Z","signature_b64":"HQiHLxCejSKjky6rouDKdT3jM29jWl42L/+0leU15Uvrqu60LxGvJDWF91VF/MkDiicHc++55OhO30wjpzd5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff4c285c2a05d9c6bbfadcf71e35613b4f7aee0c7da1f763e1a7d35a9fad99e9","last_reissued_at":"2026-07-05T08:17:55.819533Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:17:55.819533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonradial stability of expanding Goldreich-Weber stars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juhi Jang, King Ming Lam, Mahir Had\\v{z}i\\'c","submitted_at":"2022-12-22T00:04:28Z","abstract_excerpt":"Goldreich-Weber solutions constitute a finite-parameter of expanding and collapsing solutions to the mass-critical Euler-Poisson system. 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