Primitive Factorisation of the Evans Lattice Zeta

Research Note 38 in the "Geometry of the Critical Line" programme. This note proves a canonical factorisation of the leading-WKB Evans lattice zeta. The integer scaling action (n,m') → (dn,dm') partitions the lattice into primitive orbits (gcd(n,m') = 1) and their integer multiples. Standard Möbius inversion gives Z_Evans(s) = ζ(2s) · Z_prim(s), where Z_prim is the primitive lattice zeta and ζ(2s) is the Riemann zeta function at argument 2s. The factorisation is verified numerically to six significant figures. It shows that the Riemann zeta function is already present as the common-scaling multiplicity factor of the Evans lattice. The geometric factor Z_prim(s) carries the pole at s = 1; the arithmetic factor…