Computational data and verification code for the paper: "Admissible five-variable cohit bases in the degree family $2^{a+b}+2^a-4$"

This deposit contains explicit monomial bases and computational records for the five-variable cohit spaces\[ Q_5(n)=(\mathbb F_2\otimes_{\mathscr A} \mathbb F_2[x_1,\ldots,x_5])_n, \qquad n=n_{a,b}=2^{a+b}+2^a-4,\]where $\mathscr A$ is the mod-$2$ Steenrod algebra and $a\geq3$, $b\geq1$ are integers. Complete admissible monomial bases are supplied for every $3\leq a\leq5$ and $b\geq1$, including the full lists in degrees $20$, $44$, and $92$. The finite exponent lists and parameter-dependent formulas specify every basis monomial, with the exceptional replacements at $b=5$ included explicitly. For $a\geq6$, the records provide initial bases and explicit transports under duplication isomorphisms; transported monomial bases are distinguished from admissible bases. The dimensions in Theorem~1.1 of the accompanying manuscript are\[\begin{array}{c|rrrrr} \dim_{\mathbb F_2}Q_5(n_{a,b}) & b=1 & b=2 & b=3 & b=4 & b\geq5 \\ \hline a=3 & 641 & 1189 & 1910 & 2480 & 2790 \\ a=4 & 1426 & 1954 & 2635 & 3255 & 3565 \\ a=5 & 1706 & 2263 & 2945 & 3565 & 3875 \\ a\geq6 & 1705 & 2263 & 2945 & 3565 & 3875\end{array}\] The files are organized by parameter values or ranges and the corresponding degrees. The archive includes TXT monomial lists, CSV/JSON coefficient records, quotient coordinates, simultaneous multiplication relations, duplication matrices and explicit kernel representatives, Python and C++17 source code, verification records, and SHA-256 checksums. The supplied export programs produce a monomial basis for any specified pair $(a,b)$ in the stated domain.