Asymptotic closed forms for the Faltings height of Fermat Jacobians and the spectrum of logarithmic derivatives of L-functions

For the Fermat tower $F_N: x^N + y^N = 1$, $N = p^n$, we assemble the complete asymptotic machine for the stable Faltings height $h_F(J(F_N))$: the main-chain closed form with error term of exact order Theta(n log p / p^n); an exact spectral identity h(Phi) = mu(Phi)/2 - sum_chi m(Phi,chi) rho_chi; an arithmetic channel for the deviation functional through the Bernoulli-mass M_1 (R^2 = 0.78); a profile law E[M_{c'}] = 3^{c'-2} Lambda(n) proved by carry-counting; and the layerwise height closure mean h^{Col}(n) = 3^{n-1} log(3) (n - n*) / 4 with n* = 5.6841, closed by a co-layered measurement at n = 12 (Delta = -4.7e-5). The limiting integral I_p = int_0^1 w_p log Gamma receives a Kummer closed form in zeta(2) and zeta'(2). All identities are certified at the exact-arithmetic level on layers n <= 12.