Improve the exceptional-set exponent for the remaining quasi-Riemann-Hypothesis range

Improve the exponent $7/12+\epsilon$ in the bound for the Goldbach exceptional set E_+(N) under the quasi Riemann Hypothesis $(Q_\Theta)$ for $11/12\leq\Theta<1$.

Background

The paper proves a square-root exceptional-set bound under (QΘ)(Q_\Theta) for 1/2≤Θ<11/121/2\leq\Theta<11/12. It then observes that a similar method should improve the previously cited 7/12+ϵ7/12+\epsilon exponent when Θ\Theta lies in the remaining range 11/12≤Θ<111/12\leq\Theta<1, but does not carry out that improvement.

References

For $11/12 \leq \Theta <1$, by a similar method we can also improve the exponent $7/12+\epsilon$. We leave this to the interested reader.

— Fourth moments of prime exponential sums and exceptional sets for sums and differences of primes  (2610.26756 - Li et al., 19 Oct 2026) in Section 1, immediately after Theorem 2