Erratum and extension to Lemma L2 §1.⑤ of the Verrou A K=2 program: universal constants +2 and +23 mod p for g_R(p²+p+4) and g_R(p²+p+5)

We report an erratum and extension to Lemma L2 §1.⑤ of the Verrou A K=2 note v8.1 (associated with Zenodo 10.5281/zenodo.20310879). The original statement g_R(p²+p+a) ≡ 0 mod p for a ∈ {0, 1, 2} extends without modification to a = 3. Starting from a = 4, the identity fails strictly, with universal constants: g_R(p²+p+4) ≡ +2 mod p for all p ≥ 5 prime, g_R(p²+p+5) ≡ +23 mod p for all p ≥ 5 prime. Here g_R(m) := Σ_{M ≥ 1} [u^M] Q_m(u) · C(p²-2, M-1), with Q_m(u) := ∏_{i=1}^{m-2} (1 - i·u). Numerical verification: 18/18 across p ∈ {5, 7, 11, 13, 17, 19} and a ∈ {0, 1, 2, 3, 4, 5}, using two independent implementations (sympy/Poly and manual polynomial convolution). The deposit DOI 10.5281/zenodo.20310879 (Verrou A K=2, 20 May 2026) is not affected: it uses only the cases a ∈ {0, 1, 2}, all of which remain valid. The extension and the universal constants (ii)-(iii) are reported for transparency and for future applications that may extend beyond a = 4.