= Solution
For <inexact information in the SCI hierarchy>, replace every exact evaluation $\lambda\in\Lambda$ by a family of admissible approximations $\lambda_m$ satisfying
$$
d(\lambda_m(A),\lambda(A))\leq2^{-m}.
$$
An algorithm must converge for every admissible choice of approximations, not merely for one favored encoding.
For continuous nonsingular maps $F:X\to X$, take the evaluations to be arbitrary point queries. At precision $m$, a query at $x\in X$ returns any $y$ satisfying
$$
\boxed{d_X(y,F(x))\leq2^{-m}.}
$$
Thus the information set contains all triples $(x,m,y)$ satisfying this inequality. This is a <perfect measurement device for a dynamical system>: it can sample any state, at any requested accuracy, with no fixed noise floor. The finite-information rule still requires each terminating computation to make only finitely many such measurements.
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