= Solution
Fix an acceptable effective enumeration $f_{e,n}$ of the $n$-ary <partial computable functions>. The <S-m-n theorem> states that for every $m,n\geq1$ there is a <total computable function> $s_n^m$ such that
$$
f_{s_n^m(e,x_1,\ldots,x_m),n}(y_1,\ldots,y_n)
\simeq f_{e,m+n}(x_1,\ldots,x_m,y_1,\ldots,y_n),
$$
where $\simeq$ means that both sides have the same value when defined and are otherwise both undefined.
The <recursion theorem> states that every total computable transformation $h$ of program indices has a semantic fixed point: there is an $e$ such that
$$
\boxed{f_{e,1}\simeq f_{h(e),1}.}
$$
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