{"id":"palomar/PALOMAR-2026-08-21-000004","url":"https://github.com/teal-sea/zeta-lab/tree/8a28a4faa3fb0fe68649f4f22faba7efe4bc3406/lean","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-21-000004-v1.json","repo":"https://github.com/teal-sea/zeta-lab","tags":["math.NT","math.CA","msc:45B05","msc:49R05","msc:11M26","riemann-zeta","pair-correlation","integral-equations","fredholm-operators"],"score":0,"title":"teal-sea/zeta-lab","trust":"high","domain":"math.NT","source":"palomar","authors":["Thomas Lince"],"reviews":0,"subject":"math.NT","summary":"A variational identity for the Fredholm operator A = I + T on the interval I = [-1/2, 1/2], where T is convolution against the Farmer-Gonek-Lee pair-correlation form factor F1(x) = |x| - 4x^2 + sum_k a_k |x|^(2k+3) with a_k = 2^(2k+3) k! / (2k+2)!. Let w = A^(-1)1 and c* = . Over the source-admissible class of scalar profiles v(s) = phi(Ls)^2 induced by even, radially nonincreasing C^2 windows supported exactly on [-L/2, L/2] with 0 ^2 / equals c*, and the infimum of the reciprocal quotient / ^2 equals 1/c*. The upper bound ^2 is energy Cauchy-Schwarz. It holds for every v, it is classical,…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-08-21","reactions":{},"formalized":true}