{"paper":{"title":"The spectral edge of the quartic SYK model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.OA","math.PR"],"primary_cat":"math-ph","authors_text":"Yukun He","submitted_at":"2026-07-21T11:32:10Z","abstract_excerpt":"We consider the Sachdev--Ye--Kitaev model of $N$ Majorana fermions with random $q$-body interactions. For $q=4$, we show that as $N\\to \\infty$ through even integers, the largest eigenvalue of the model satisfies\n  \\[\n  \\frac{\\lambda_1}{\\sqrt{N}}\\to 4\\int_0^\\infty g_0(t)^4\\,\\mathrm{d}t \\approx 0.32504 \\qquad \\mbox{almost surely}\\,,\n  \\] where $g_0(t)=\\frac{1}{2}\\int \\mathrm{e}^{-Et}\\rho_0(\\mathrm{d}E)$ is the unique solution of the zero-temperature quartic Schwinger--Dyson equation for which $\\rho_0$ is a probability measure, $\\int E^2\\rho_0(\\mathrm{d}E)=1/4$, and $g_0^3\\in L^1(0,\\infty)$. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18998","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/2607.18998/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"}