We isolate the analytic Type II obstructions that arise in quotient-weighted distribution estimates for the companion Chen--Wu--Richert criterion. The refined formulation separates three tasks: a sub-1/3 quotient P₂ range, which is proved here from Type I estimates and completion; the remaining balanced shifted semiprime-prime problem, i. e. primes of the form qr+2 with q, r prime and y^1/32/7 is treated by a direct triple-prime convolution Bombieri--Vinogradov theorem plus an ordinary upper linear sieve, giving constant 4. We also include a certified special-factor refinement of the fixed P₄ residual; the companion coefficient certificate encloses the refined cost in 0. 13631427, 0. 13710612 and certifies a gain >0. 0165 over the old P₄ residual. These two theorem-level refinements together certify remaining tolerance above 1. 086 for the balanced shifted semiprime-prime sector. This version then reformulates that sector in the more intrinsic language of binary shifted convolution: after a high-order Heath--Brown decomposition of (qr+2), Type I and non-top branches are reduced to standard convolution-Bombieri--Vinogradov and smooth binary additive-divisor inputs, while the primitive top branch is isolated as a shifted convolution with the special HB-small coefficient generated by Lᵦ/Uᵦ, equivalently as CD=qr+2 with two HB-small well-factorable weights on the shifted side. For possible full balanced-P₃ control, the paper further isolates the simultaneous top all-small branch and the quotient-weighted friable progression estimate that would close it; the quotient coefficient is the only part not matched to Pascadi's stated 5/8 friable distribution theorem. The paper is a reduction and target-problem document: standard distribution theorems are quoted only where their coefficient classes, local singular factors, and quotient weights match the stated hypotheses.
Marshall Ratliff (Tue,) studied this question.