The generic point of Wolstenholme determinants: staircase Schur normalizations, the sliding-node derivative, and closed second layers in every corank up to three

We solve the two problems left open by Note 5 of this program by a single change of viewpoint: the harmonic node set (1, 1/2, …, 1/n) underlying the Wolstenholme determinants is replaced by free variables x₁, …, xₙ, and the symbolic engine of Note 5 is rerun at this generic point. Three phenomena, previously verified only at the harmonic point, become polynomial identities: the amplification, the null pairings, and the w-law. The pay-off is structural. In corank one, the normalized first-layer symbol factors as γ_μ = (−1)^g μ s_(g−2,…,1)(x) P_(μ−m_min), a staircase Schur polynomial times a window coefficient, and the residue left open by Note 5 is a derivative: σ_μ = A_μ γ_μ + 𝒟γ_μ with A_μ = −(μ−1)/((μ+1)(2μ+1)) and 𝒟 = Σ xₗ² ∂xₗ, the infinitesimal generator of the node shift l ↦ l−t. In corank two, the entire mod-p² layer closes in four terms; the free parameters of Note 5's higher-corank parametrization are proved to be pure gauge. The staircase unifies: the normalization in corank κ₀ is s(g−2κ₀,…,1). The same four-term law and two coefficient laws are verified through corank four, with the window in every corank the same symbol determinant. A dead-row argument gives, unconditionally and uniformly, rank(e_(2i−l)) ≤ ⌊(g+n)/2⌋, hence corank ≥ κ₀ and the half-amplification v_p ≥ κ₀; the unknown-digit cancellation follows by a bordered-determinant recursion; and the full doubling v_p ≥ 2κ₀ closes uniformly through explicit kernels for the h-matrix (the pairing tower collapses to a single vanishing). The tail expansion is proved as an elementary reflection lemma, so all results are conditional on Sun's congruences alone. All computations are exact and reproducible from the attached scripts.