Computational data and verification code for the paper: "On the decomposable classes $h_0g_s$ and $h_7D_3(0)$ in the cohomology groups ${\rm Ext}_{\mathscr A}^{5,12\cdot2^s+1}(\mathbb F_2,\mathbb F_2)$ and Hung's conjecture"

This deposit contains the computational data supporting the determination of the fifth algebraic transfer in homology degrees $d_s=12\cdot2^s-4$, for all integers $s\geq1$. Let $G=\operatorname{GL}_5(\mathbb F_2)$ and $Q_5(n)=(\mathbb F_2\otimes_{\mathscr A} \mathbb F_2[x_1,\ldots,x_5])_n$, where $\mathscr A$ is the mod-$2$ Steenrod algebra. The main results are\[\dim_{\mathbb F_2}Q_5(d_s)^G=\begin{cases}1,&1\leq s\leq3,\\0,&s\geq4,\end{cases}\qquad\operatorname{Im}\operatorname{Tr}_{5,d_s}=\begin{cases}\langle h_0g_s\rangle,&1\leq s\leq3,\\0,&s\geq4.\end{cases}\] Explicit invariant polynomials and normalized Steenrod-annihilated primitive representatives in degrees $44$ and $92$, together with lambda-algebra boundary identities, establish\[h_0g_2\in\operatorname{Im}\operatorname{Tr}_{5,44},\qquadh_0g_3\in\operatorname{Im}\operatorname{Tr}_{5,92}.\]Thus the manuscript confirms the $h_0g_2$ and $h_0g_3$ cases of Hung's detection conjecture. The degree-$20$ case is taken from Sum's prior result. Equivariant duplication extends the vanishing of the entire transfer domain in degree $188$ to every $s\geq4$. In particular, neither $h_0g_4$ nor $h_7D_3(0)$ belongs to the transfer image in bidegree $(5,193)$. Consequently, the fifth transfer is injective in every bidegree $(5,12\cdot2^s+1)$, $s\geq1$, verifying Singer's injectivity conjecture throughout this degree family. The ZIP includes cohit and invariant bases, normalized primitive duals, quotient projections, group-action and duplication matrices, lambda images, explicit boundaries, nonboundary functionals, and the parameter dependent description of the vanishing domains. It also contains TXT/CSV/JSON coefficient records, Python and C++17 source code, reproduction and independent verification programs, execution records, and SHA-256 checksums.