We prove that when the length p = 2n−1 of a Legendre interval (n−1) ², n² is prime, the p−1 interior integers form a punctured complete residue system modulo p, missing exactly one quadratic residue class. Consequently, quadratic non-residues always exceed quadratic residues by exactly 1 — an unconditional algebraic identity requiring no unproven conjectures. The theorem is computationally verified for all 549 qualifying intervals with n ≤ 2000. We complement this algebraic result with empirical measurements of the discrete Wronskian compression ratio for maximal prime-free subsequences near n², observing stabilization near qW ≈ 1. 20 across six orders of magnitude. Source code, verification data, and scripts are available at: https: //github. com/Ruqing1963/legendre-spin-asymmetry This is Paper IX of the Titan Project, a programme investigating geometric and algebraic structures underlying classical prime number conjectures.
Ruqing Chen (Fri,) studied this question.