A generalized pseudostandard prefix with no string attractor of size four

A string attractor of a finite word is a set of positions such that every nonempty factor has an occurrence containing one of them. Binary generalized pseudostandard sequences are built by iterating palindromic and antipalindromic closures along a directive bi-sequence (Δ,Θ), where Δ lists the letters appended and Θ the closures taken, R for palindromic and E for antipalindromic. Dvořáková and Hendrychová (2024) determined minimal string attractors of pseudopalindromic prefixes for several subclasses, among them the standard complementary-symmetric Rote sequences, and conjectured that the pseudopalindromic prefixes of every binary generalized pseudostandard sequence have a minimal string attractor of size at most four. We show that this bound fails at length 36: for Δ beginning $00101$ and Θ beginning $EEEER$, the fifth word of the recurrence, the palindromic prefix $010110010101100101101001101010011010$, has smallest attractor size five. The lower bound is an elementary argument with seven factors; the upper bound is an explicit five-position attractor. Both bounds are also confirmed by computer. A second example has length 43. Computer-assisted; not yet reviewed by experts. Produced by AI models under the author's direction.