Variance of Goldbach representations in residue classes / Variância das representações de Goldbach em classes residuais

We study the variance of Goldbach representations of an even integer N across the k_n admissible residue classes modulo n, for odd n>1 coprime to 6. The exact identity V_N = diag_N + 2 W_off(N) fixes the normalisation: the variance ratio is R_n = 1 + 2 sum W_off / sum diag. Four-form local factors are recorded with the correct branch at primes dividing N. A leading term W_off ~ -(1/4) D_n S_2(N) N (log N)^2 would be compatible with R_n -> 1/2; we do not prove that asymptotic, nor a conditional limit 1/2. Non-negativity of the four-form singular series does not determine the sign of the signed off-diagonal sum. Under an l^1 hypothesis we bound W - W_rho. Unconditionally we bound the resonant linear piece of h_ell after an O(X^2) remainder. Two empirical conjectures are stated. We claim no progress on the Riemann hypothesis or on pointwise Goldbach. Portuguese and English sources and the reproduction code are included.