arXiv:2610.33218v1 Announce Type: new Abstract: We prove the existence of maximizing measures for subadditive and almost-additive families of upper semicontinuous, bounded-above potentials $\mathcal F=\{f_n\}_{n\geq1}$ on closed subshifts over countable alphabets. Under a coercivity condition on $f_1$, we prove that every maximizing sequence, that is, $\{\mu_k\}_{k\geq1}\subset\mathcal M_\sigma(X)$ satisfying $\bar{\mathcal F}(\mu_k)\to\beta(\mathcal F)$, is uniformly tight, preventing mass from escaping to arbitrarily large symbols. As a consequence, a maximizing measure exists.
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