How Temporal Measurement Resolution Shapes Entropy-Based Complexity of Signed Texts: A Bifurcation-Diagram Analysis with Application to Quantitative Linguistics

Entropy-based measures of textual complexity depend on how finely the underlying quantities are measured. For signed texts, the durations of sentences and signs are recorded only up to some rounding, and we ask a practical measurement question: how does the choice of temporal resolution affect an entropy estimate, and is there a principled way to choose it? We address this by computing the topological entropy of multivalued sequences built from duration time-series of two Czech Sign Language “texts”, and by sweeping the rounding accuracy to obtain bifurcation diagrams of entropy versus resolution, separately at the levels of sentences and signs. The resulting curves are piecewise constant (a property we prove) and share a robust, unimodal [Formula: see text]-shaped envelope that recurs across both texts and both linguistic levels. We characterize the finite set of critical resolutions exactly, identify the elementary merge/split mechanism behind each jump, and use continuous spline approximations to derive three interpretable criteria for choosing the resolution (maximal entropy, closeness to the symbolic-count entropy, and maximal stability), which we combine into a practical recommendation. The sudden onset of positive entropy is discussed, as an interpretive analogy, in terms of a cusp-type catastrophe in the sense of Thom, and the implications for complexity comparison between texts are outlined. The study is a methodological case study. Its limitations at the present sample size are stated explicitly.