The Cousin Prime Theorem and the Sexy Prime Theorem

Both theorems follow from the same architecture that proved the
Twin Prime Theorem in the companion papers "The Twin Prime Theorem
in the Prime Field Architecture" and "The Twin Prime Threshold"
(David-Michael: Skerl, SJRDI, October 2026). The proof structure
IS identical: K-gap pairs in the P₁ Fiber + Brun lower bound +
explicit threshold + complete coverage.