Explicit primitive preimages and lambda certificates for the sixth algebraic transfer in degree $36$

Conjecture~1.7 in arXiv:2509.09455v12 asserts that the nonzero class $t\in\operatorname{Ext}_{\mathscr A}^{6,42}(\mathbb F_2,\mathbb F_2)$ is detected by the sixth algebraic transfer. This deposit contains the computational data supporting Theorem~1.1 of the paper: "Detection of the class $t$ by the sixth algebraic transfer'', which proves this conjecture. Let $G=\operatorname{GL}_6(\mathbb F_2)$, and let $[\zeta_1],[\zeta_2]$ be the previously determined cohit invariant basis in degree $36$. The theorem constructs divided-power polynomials $u_1,u_2\in H_{36}(B((\mathbb Z/2)^6);\mathbb F_2)$, with $9440$ and $124$ terms, respectively, satisfying\[ \operatorname{Sq}_*^r(u_i)=0\quad(r>0),\qquad \langle u_i,\zeta_j\rangle=\delta_{ij}\quad(1\leq i,j\leq2).\]Their coinvariant classes $e_i=[u_i]_G$ form the normalized dual basis of the transfer domain, and\[ \begin{aligned} \operatorname{Tr}_{6,36}(e_1)&=0,& \operatorname{Tr}_{6,36}(e_2)&=t\ne0,\\ \ker\operatorname{Tr}_{6,36}&=\langle e_1\rangle,& \operatorname{Im}\operatorname{Tr}_{6,36} &=\operatorname{Ext}_{\mathscr A}^{6,42}(\mathbb F_2,\mathbb F_2) =\langle t\rangle. \end{aligned}\]Thus the transfer is surjective with a one-dimensional kernel. The archive contains the full invariant and primitive coefficient lists, cohit bases and quotient projections, group-action matrices, lambda images and explicit boundaries, the adjacent differential matrices, and a separating functional certifying that the cycle for $t$ is not a boundary.