  We introduce a strategy to tackle some known obstructions of current
approaches to the Fourier uniformity conjecture. Assuming GRH, we then show the
conjecture holds for intervals of length at least $(\log X)^{\psi(X)}$, with
$\psi(X) \rightarrow \infty$ an arbitrarily slowly growing function of $X$. We
expect the methods should adapt to nilsequences, thus also showing that the
Generalised Riemann Hypothesis implies close to exponential growth in the sign
patterns of the Liouville function.
