Learning iterated function systems from time series of partial observations

The paper correctly formalizes delay-embedded IFSs and provides a sound graph-theoretic unembedding of the time-delay embedded Markov chain (Algorithm 3.1 with Theorem 3.6), and a conditional bundle-conjugacy statement (Theorem 4.1). However, its main theorem relies on an unproven step: that one can actually construct/learn generators g_i whose delay-space evolution exactly realizes the reduced dynamics (5) from partial observations, which the paper motivates via optimization but does not establish rigorously. The candidate model goes further by attempting an explicit construction on a disjoint union of charts but (i) incorrectly infers a positive Euclidean gap δ from Whitney C^q separation and (ii) defines generators g_i that depend implicitly on future symbols, so they are not well-defined as fixed maps independent of the base sequence. Hence both are incomplete relative to the posed problem.