# Prior-art boundary and target status

Checked against the following primary sources during preparation on 2026-10-01:

1. Shigeki Akiyama, De-Jun Feng, Tom Kempton and Tomas Persson, *On the Hausdorff Dimension of Bernoulli Convolutions*, arXiv:1801.07118; IMRN 2020(19), 6569–6595; DOI 10.1093/imrn/rny209. https://arxiv.org/abs/1801.07118
2. Joachim Breitner and Maciej Skorski, *Analytic Formulas for Renyi Entropy of Hidden Markov Models*, arXiv:1709.09699 (2017). https://arxiv.org/abs/1709.09699
3. Chengyu Wu, Yonglong Li, Li Xu and Guangyue Han, *Renyi Entropy Rate of Stationary Ergodic Processes*, arXiv:2207.07554 (2022). https://arxiv.org/abs/2207.07554
4. Péter P. Varjú, *Entropy rates in the dimension theory of self-similar measures*, arXiv:2509.22042v2, 22 March 2026. https://arxiv.org/html/2509.22042v2

The iid entropy-approximation framework, arithmetic carries, integer-order replicas, and ordinary HMM spectral theory have prior art. The candidate extension is the exact block-output boundary matrix with a subexponential factor bound and its correlated/asynchronous arithmetic implementation. Merely combining named ingredients or renaming them does not establish priority.

The continuity theorem is confined to the finite-state factor model; it is not a universal continuity claim for stationary ergodic processes. The latter is false in general, as the third source explains.

The 2026 survey distinguishes the delicate fair-Salem maximal-entropy equality from algorithms that approximate the entropy. This release supplies no proof of that equality. Search results cannot establish that no differently formulated prior theorem exists; external novelty review is still required.