{"id":"palomar/PALOMAR-2026-10-22-000012","url":"https://github.com/RGConj/fourth-consecutive-ratio-palomar/tree/55ff1f42612a01b2fbe4a1eafc618cdcf83c3b75","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-22-000012-v1.json","repo":"https://github.com/RGConj/fourth-consecutive-ratio-palomar","tags":["math.SP","math.AP","msc:35P15","msc:35J05","msc:68V20","spectral-theory","dirichlet-eigenvalues","lean"],"score":0,"title":"The fourth consecutive Dirichlet eigenvalue ratio","trust":"high","domain":"math.SP","source":"palomar","authors":["Jiachen Shi","Quanyu Tang"],"reviews":0,"subject":"math.SP","summary":"An unconditional Lean proof of the strict inequality lambda_5 / lambda_4 < C_N for every nonempty bounded connected open subset of Euclidean space of dimension at least two, with variational Dirichlet eigenvalues and the sharp Bessel-zero constant. No boundary regularity is assumed.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-22","reactions":{},"formalized":true,"formalizes":[{"title":"A sharp bound for the fourth consecutive Dirichlet eigenvalue ratio","identifier":"","relationship":"formalizes"}]}