The Universal Object: dρ and the Margin Between Field-Determined and Seed-Determined Geometry

The SFE-06 series established the joint observer manifold: a three-dimensional state space (x_a, x_b, ρ_ab) in which two observers coupled to the same Ornstein–Uhlenbeck (OU) field produce a geometry whose eigenvalue structure encodes field confinement strength k. The principal observable reported was the eigenvalue ratio e₂/e₃, which was observed to rise monotonically with k and to be largely invariant with respect to window size W and observer offset δ. SFE-07 attempted to derive a closed-form expression f(k) for this ratio. The derivation failed in a productive way: it revealed that the ratio e₂/e₃ is not a universal function of field parameters, but rather a ratio of two seed-dependent quantities whose…