We prove that when p = 2n−1 is prime and n is even (equivalently p ≡ 3 mod 4), the right half of the Legendre interval (n−1)², n² has exactly zero quadratic residue skewness modulo p: the number of QR classes equals the number of NR classes. The global asymmetry N⁻ − N⁺ = 1 (proved in Paper IX, Zenodo:18706876) is carried entirely by the left half. The proof uses the negation involution x ↦ p − x on (Z/pZ)*, which swaps QR ↔ NR when (−1/p) = −1, combined with the closure of the right half's residue set under this involution. A complementary result for odd n shows the right half skewness is always even. Verified computationally for all 87 qualifying even n ≤ 500. Source code and manuscript: https://github.com/Ruqing1963/oppermann-parity-law This is Paper X of the Titan Project.
Ruqing Chen (Fri,) studied this question.