Normalized CutOut beyond the Cartan class: constant non-abelian SU(2) configurations and the adjoint-block structure of the Faddeev-Popov operator

This is the eleventh paper of a programme constructing the Feynman functional integral without a Wick rotation, based on the non-absolutely convergent Henstock–Kurzweil (HK) integral and on Kuelbs–Steadman spaces. Its predecessor proved the normalized continuum CutOut for the constant Cartan class of SU(2) on the four-torus, where the Faddeev–Popov operator is simultaneously diagonal in the Fourier and in the root bases. The present paper goes beyond the Cartan class: it treats the constant non-Cartan class, A_mu(x) = A_mu in su(2) arbitrary, for which the Faddeev–Popov operator is still diagonal in the Fourier modes but acts on each mode by the 3x3 adjoint block M^(n)(A) = lambda_n 1_3 - 2 pi i ad(b_n), b_n = n_mu A_mu, lambda_n = |2 pi n|^2, whose direction in su(2) rotates with the mode. Target A of the previous work is achieved in full. The block determinant is computed in closed form, det M^(n)(A) = lambda_n (lambda_n^2 - omega_n^2) with omega_n = 2 pi |b_n|; the first Gribov region of the class is identified with the explicit semialgebraic set Omega = {A : |A_mu| < 2 pi for every mu}, the product of four open balls of radius 2 pi in su(2), which is shown to be independent of the truncation level N >= 1; the normalized truncated determinant obeys the concentration estimate |g_N(A)| <= K_RM_R exp(-N epsilon^2 / (4 pi^2)) on the box B_R in R^12 with constants independent of N, and the non-degeneracy estimate g_N >= 1/2 on the polynomially small box of half-width rho_N = pi / (4(2N+1)^2); and these two estimates assemble into the normalized CutOut limit, with the explicit rate C(2N+1)^24 e-N/3 and a constant C = C(R) depending only on the box. Theorems B.1 and B.2 of the previous work are proved as part of this, and the fallback Target C is therefore not needed; the optional Target D (quasi-abelian perturbations supported on one Fourier mode) is not attempted and is stated as a conjecture only. The Yang–Mills action vanishes identically on constant configurations, so the theorem makes no claim about a dynamical mechanism of cut-out: what is proved is that the normalized Faddeev–Popov determinant of a genuinely non-abelian class concentrates in the first Gribov region and that the Fresnel weight of the premeasure does not obstruct this. The paper does not solve the continuum Gribov problem and claims nothing about non-constant configurations. Every theorem is proved in full in the main text; all statements of Sections 3–7 are additionally machine-verified in Lean 4 with no sorry, no admit and no new axioms, and a deterministic numerical script with two independent quadrature methods and a high-precision cross-check confirms the estimates on a one-dimensional non-Cartan slice.