{"paper":{"title":"A turning point principle for liquid Lane-Emden stars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"King Ming Lam","submitted_at":"2026-07-27T15:08:37Z","abstract_excerpt":"Upon fixing the adiabatic index, the spherically symmetric liquid Lane-Emden stars governed by the Euler-Poisson system with a \"stiffened gas\" equation of state $p=\\rho^\\gamma-1$ form a one-parameter family, naturally parametrised by the central density $\\kappa=\\bar\\rho_\\kappa(0)\\in(1,\\infty)$. In contrast to the gaseous case, the liquid free boundary breaks the self-similarity of the family and bends the mass-radius curve, creating extrema of the mass when $\\gamma<2(d-1)/d$. We formulate a turning point principle in the spirit of Zel'dovich, Wheeler and Thorne, and of its rigorous relativisti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24530","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.24530/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}