Minimal Strong Generators of the Orthogonal Orbifold of the Heisenberg Vertex Algebra in Every Rank

We determine the minimal strong generators of the orthogonal invariant subalgebra of the chiral algebra of n free bosons. For every n ≥ 1, there is one generator in each even conformal weight from 2 to n² + 3n, resolving Linshaw's conjecture. The free-boson result also gives an independent derivation of the known generic minimal types of the corresponding affine orthogonal coset orbifolds. For n ≥ 2, we identify the Heisenberg orbifold as the simple quotient of the universal even-spin vertex algebra Wᵉᵛ(c, λ) at central charge n and parameter (3n + 2)/[7(n − 1)(5n + 22)]. A Cauchy determinant formula evaluates the diagonal scalar remainders in the decoupling recursion. For consecutive indices, an integral inverse formula makes the relevant trace factor positive. A 2-adic argument proves nonvanishing for every strictly increasing diagonal list and determines its valuation. We also obtain a formula for pairs of lists differing in one entry and an asymptotic expansion of the minimal remainders through the constant term, with error O(n⁻¹).