{"paper":{"title":"On the Gardner Transition in the Ising Pure $p$-Spin Glass II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Yuxin Zhou","submitted_at":"2026-08-06T19:08:04Z","abstract_excerpt":"In previous work, we identified, for every $p\\geq3$, a unique first critical temperature $\\beta_1^p$ and proved that the Parisi measure is replica symmetric (RS) for $0<\\beta\\leq\\beta_1^p$ and one-step replica symmetry breaking (1-RSB) on a nonempty interval immediately above $\\beta_1^p$. In this sequel, we determine the rest of the phase diagram. We prove that there is a unique second critical temperature $\\beta_2^p>\\beta_1^p$ such that the Parisi measure is 1-RSB for $\\beta_1^p<\\beta\\leq\\beta_2^p$, while for $\\beta>\\beta_2^p$, $\\operatorname{supp}\\mu_\\beta=\\{0\\}\\cup[q_\\beta,q'_\\beta],$ for s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06523","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/2608.06523/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"}