A ninth-order linear recurrence for the moment ladder of the E8 Voronoi cell

This record documents a ninth order linear recurrence with integer polynomial coefficients for the even moments of the Voronoi cell of the E8 lattice, together with a machine certified identification theorem proving that the recurrence is the one produced by elimination from the cell geometry, that its order is minimal over the rational function field at every degree, and that it holds at every index from ten onward. The scaled moments a(n) = mu_n (8+2n)! 360^n / 8! are integers beginning 18580, the first term encodes the Conway and Sloane quantizer constant 929/12960, and the sequence is OEIS A399083. The leading coefficients factor as 7 times the product of (x - 1440 s) over the squared circumradii of the nine facet classes, the minimal integer scale of the ladder is 18 with rescaled first term 929, the tail constant is 5443200 with a cone derivation, and the two adic valuation of the ladder obeys a min plus law away from a fixed set of residues. Every claim reproduces from the Gram matrix alone with the included instruments, a Lean 4 package checks integer instances in the kernel, and a text audit instrument, included with its report, re derives every number stated in the announcement from the deposit files. Version 3 rebuilds the documentation in full; the comparative results across the root lattice family appear in a companion record linked from the metadata.