The Diophantine Vacuum

All values increase monotonically with dimension, confirming the dimensional ordering. The measured wd values sit between two candidate ladder formulae: Ladder A (w = -1 + (d-1)/3) and Ladder B (w = -1 + (d-2)/3), with A fitting better at low d and B at high d. We also confirm: (i) the yield-memory reservoir model drives w -> -1 at saturation, (ii) Sigma2 ~ 10-123 at Planck-lattice cosmic scale (conditional on the Gauss Circle Conjecture), (iii) the Pythagorean defect hierarchy has Berends-Giele recursion structure with 6% coupling, and (iv) Boltzmann growth tests show 3-5% f*sigma8 suppression.