  The construction of spectral cocycle from the case of 1-dimensional
substitution flows by Bufetov-Solomyak [arXiv:1802.04783] is extended to the
setting of pseudo-self-similar tilings in ${\mathbb R}^d$, allowing expanding
similarities with rotations. The pointwise upper Lyapunov exponent of this
cocycle is used to bound the local dimension of spectral measures of deformed
tilings. The deformations are considered, following Trevi\~no
[arXiv:2006.16980], in the simpler, non-random setting. We review some of the
results on quantitative weak mixing from [arXiv:2006.16980] in this special
case and illustrate them on concrete examples.
