For every prime p ≡ 3 mod 4, the truncated Legendre-symbol determinant evaluates to floor((p-2)/3)^2 x via reduction to Chapman's matrix inverse using Vsemirnov factorization and Schur-Pfaffian identity.
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A Proof of a Conjecture of Zhi-Wei Sun on a Truncated Legendre-Symbol Determinant
For every prime p ≡ 3 mod 4, the truncated Legendre-symbol determinant evaluates to floor((p-2)/3)^2 x via reduction to Chapman's matrix inverse using Vsemirnov factorization and Schur-Pfaffian identity.