inference Line-by-line referee report (referee_report.md) covering: the orthogonality/second-moment identity (also machine-verified exactly at q=61,101 against brute-force enumeration over all dilations, verify.py --check fourier); the |S_B(χ)| ≤ 2M(χ) bound for difference-p progressions via multiplicativity (machine-checked per character); the Montgomery–Vaughan input verified against the primary source; Cauchy–Schwarz/Chebyshev bookkeeping; the off-by-one fix computation p(⌊(q−1)/(pk)⌋−1)+i ≤ (q−1)/k − 1; splicing and transport lemmas (machine-checked by exhaustive signed-sum enumeration on random instances); the pullback and contradiction structure; the recursion arithmetic.