A full-list uniform generator bounds circuit size and width

Initially the input $1^n$ occupies $n$ cells. In $T(n)$ transitions the head visits at most $T(n)+1$ additional positions, and each transition writes only one symbol by [F2]. At halting, the output convention [F3] therefore gives a binary word of length at most $n+T(n)+1$. The description is self-delimiting by [F1], so the number of its symbols is bounded by this polynomial quantity.

Each gate record contains at least one symbol, so its number of gates is no greater than the description length. The total wire count is explicitly unary in the same description, so it too is no greater than the description length. With $T(n)\le c(n+1{)}^k$, both quantities are $O(n+c(n+1{)}^k+1)$ and hence polynomial in $n$. The argument makes no claim that an indexed-gate generator can be converted to a full list.