Finite-precision chaotic generators are deterministic finite-state systems whose structure is not established by continuous-domain chaos indicators or by ciphertext statistics. We study a map on (Z/2wZ)d coupled to a Weyl counter and prove that every eventual joint cycle length is divisible by the counter period, while the image fraction and the normalized indegree distribution are preserved exactly. A simple instance attains this period floor and is predictable from two words of its own output. We then audit fifteen specified quantized realizations, thirteen from recent image-encryption designs and classical maps and two validation controls, under two quantizers at reduced widths, measuring reachability, recurrence, cycle-length distributions and output-equivalence classes. An exponential enhancer that improves every dynamical indicator its authors report lowers the image fraction for three of its four base maps and raises it for the fourth. Across the sampled one-dimensional cases the section-cycle multiplier is at most three, while the two- and three-dimensional examples reach the tens; a permutation counterexample rules out a universal dimension-based claim. Under the common post-update decimal readout, the non-affine one-dimensional realizations approach the image-size bound within six output symbols. These findings motivate reporting finite-state structure alongside conventional tests. The measurements characterize the specified reduced-width realizations; they neither establish native-precision behaviour nor prove or disprove the security of the source ciphers.
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Abu-Faraj et al. (2026) studied this question.