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We prove the logarithmic Sarnak conjecture for sequences of subquadratic wordgrowth. In particular, we show that the Liouville function has at leastquadratically many sign patterns. We deduce the main theorem from a variantwhich bounds the correlations between multiplicative functions and sequenceswith subquadratically many sign patterns which occur with positive logarithmicdensity. This allows us to actually prove that our multiplicative functions donot locally correlate with sequences of subquadratic word growth. We also provea conditional result which shows that if the $\kappa-1$-Fourier uniformityconjecture holds then the Liouville function does not correlate with sequenceswith $O(n^{t-\varepsilon})$ many words of length $n$ where $t =\kappa(\kappa+1)/2$. We prove a variant of the $1$-Fourier uniformityconjecture where the frequencies are restricted to any set of box dimension $<1$.

Sarnak's Conjecture for Sequences of Almost Quadratic Word Growth