Integral Parahoric Comparison and Diagonal Bockstein Obstruction Cancellation at p = 41

Let \(p=41\) and consider the integral chamber-glued parahoric source \(J_{\mathrm{geom}}\) and hyperspecial target lattice \(L_K\) associated with a specified principal series of \(GSp_4(Q_{41})\). We determine the \(H\)-fixed subspace of the residual kernel of the summation map \(J_{\mathrm{geom}}/41J_{\mathrm{geom}}\to L_K/41L_K\), where \(H\) is the elementary abelian Klingen unipotent quotient. We establish an integral comparison of the original 42-leaf source with its normalized presentation, a restricted Bockstein criterion, and an integral identification of the target relation lattice with a three-step intertwiner image. The source class in the 40-dimensional Levi constituent has two diagonal components. Their target contributions combine as \(g_Y^{\mathrm{diag}}=g_Y^{(v=5)}+\Delta\) with \(\Delta=-41e_2+41e_{1054}\) modulo \(41^2\); although the isolated single-channel target is obstructed, the diagonal target has an explicit preimage under the relation matrix. Together with the corresponding $20$-dimensional constituent, this yields \(V_{41}^{H}\cong X_{20}\oplus Y_{40},\qquad \dim_{F_{41}}V_{41}^{H}=60.\) The argument is confined to \(p=41\). The integral source and Levi-module statements needed for this conclusion are proved within the appendices. Reproducible finite-ring computations and falsification tests are supplied separately as supporting evidence.