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Latent action models offer a promising way to extract such priors from videos, but reconstruction-trained latent codes are not necessarily suitable for policy generation: they may predict future observations while lacking the structure needed to be reused or generated coherently with robot actions. We introduce ALAM (Algebraic Latent Action Model), an Algebraically Consistent Latent Action Model that turns temporal relations in action-free video into structural supervision. Given frame triplets, ALAM learns latent transitions that are grounded by reconstruction while being regularized by composition and reversal consistency, encouraging a locally additive transition space. 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