Certified fixed-dimensional special-unitary input

Fix $d\in \{2,5,8\}$ and put $SU(d)=\{T\in M_d(\mathbb{C}):T^{\ast }T=I_d,\det T=1\}\mathrm{.}$ A certified $SU(d)$ matrix input is an exact target $T\in SU(d)$ together with a deterministic Cauchy-name procedure which, on unary input $1^b$ for $b\ge 1$, returns a rational complex matrix $Q_b$ such that each real and imaginary coordinate of each entry differs from the corresponding coordinate of $T$ by at most $2^{-b}$. The interface also specifies a worst-case bit-time bound $t(b)$ for the query. A polynomial-time name has $t(b)\le (b+1{)}^c$ for some fixed integer $c\ge 1$. The target is the matrix specified by the entire Cauchy name; if two targets satisfy these bounds for the same sequence $(Q_b{)}_{b\ge 1}$, every coordinate difference is at most $2^{1-b}$ for all $b$, hence is zero. No individual $Q_b$ is required to be unitary or special unitary. A requested tolerance is a positive binary rational and its numerator/denominator encoding length is recorded separately. For $d=2$ this specializes the unary-name convention of Effective Unitary Matrix Input. For $d=5,8$ it is the same entrywise interface in the fixed block dimensions; no dimension is input to an algorithm as an unbounded parameter.