Quantitative companion to Constant capture counts and witnessed realization

I study the minimum total weight of two-trace masks needed to realize a prescribed array on the eight-dimensional Boolean cube. The demand is specified separately for each cube point and each four-coordinate support, so the support labels are retained. For the four-support parity family x(t), with |t| ≤ 1/70, I prove 128/35 + (576/11)|t| ≤ W₄(x(t)) ≤ 128/35 + (256/3)|t|. An explicit construction realizes every prescribed row mass and gives the upper bound. The lower bound follows from support and parity inequalities, together with the consequences of equality in a twenty-support inequality. All definitions, constructions and proofs are included. The bounds do not determine the exact cost when t is nonzero and do not imply an integer mask partition. No external dataset or computer-generated certificate is required. This note is a companion to my manuscript “Constant capture counts and witnessed realization on the Boolean cube”, but can be read independently. The optimization is an instance of standard weighted fractional colouring on the graph of incompatible labelled rows; the quantitative estimates concern the particular family studied here. My funding, competing-interest and AI-assistance statements are included in the note.