Pairing-defect formulation of the parity problem

Let $\Delta_Q(x)$ denote the pairing defect function introduced in the paper for the residue-pairing framework associated with the residue-pairing bound $B_Q(x)$. Pairing-defect parity conjecture. There is no known sieve method that can prove

$$\lim_{Q\to\infty}\Delta_Q(x)=0.$$

The statement reformulates the parity obstruction spectrally and is presented as an open direction whose resolution could connect sieve-theoretic estimates with concentration near low frequencies.