Scale Graphs VII: Cross-System Observed Renormalization: A Negative Scalar Taxonomy and an Operator-Valued Reformulation

We perform a frozen cross-system test of observed renormalization for three dissipative model families: Kuramoto-Sivashinsky, complex Ginzburg-Landau, and Gray-Scott reaction-diffusion dynamics. The experiment was designed prospectively after the first five Scale Graphs papers and leaves those papers unchanged. We first formalize what a transferable observed class must contain. A scalar spectral radius, or even an eigenvalue multiset, is not a complete metric invariant of an observed tangent operator. We therefore define an operator-valued observed class as a projective resolution family equipped with explicit inter-resolution identification maps, matched spectra and invariant subspaces, singular-value and pseudospectral profiles, canonical responses, and a resolution-compatibility law. Under surjective isometric conjugacy and compatible resolution maps we prove invariance of these components. We also prove an exact matrix-native production theorem for a cross-diffusive system: the dissipative block is positive semidefinite shell by shell, and channel elimination is governed by the Schur complement. The frozen numerical programme gives a deliberately negative taxonomic result. Stagewise anchor compatibility is recovered for the published shell, Cheeger, PDE-near-unit, and matrix-Schur records, but a full historical field-to-graph round trip is not claimed because the necessary raw fields were not archived. In the initial broad campaign, nine group-resolution rows were non-identifiable and nine were underpowered. A powered follow-up with sixteen candidate group-resolution rows yields sixteen instances of NO_IDENTIFIABLE_RG_CLASS: no row is shell-like, PDE-near-unit-like, or a stable new class. The reasons are structured rather than uniform. All six complex Ginzburg-Landau rows fail stationarity despite a successful U(1)-invariant instrument gate; all six Gray-Scott rows fail resolution stability, with additional null or conditioning failures; the four Kuramoto-Sivashinsky rows fail through conditioning, null indistinguishability, or resolution instability. Several low-resolution Gray-Scott radii are near one, but they do not transfer across resolution and therefore cannot be promoted by widening the frozen bands. The matrix-native benchmark gives the complementary positive result. An equation-derived cross-diffusion matrix remains strictly positive definite, satisfies the Schur identity to 5.6e-17, and produces reproducible paired changes relative to a diagonal control. By contrast, a globally identified SPD surrogate for the natural systems does not transfer out of sample, and no native exact cross-coupled certificate is obtained there. A subsequent operator-valued control suite recognizes known conjugate systems and separates an isospectral nonnormal control, but the separation is carried primarily by the resolution-law component; no physical group is stationarity-eligible, so the preregistered prospective operator-class holdout is cancelled with the typed verdict NO_PROSPECTIVE_OPERATOR_CLASS_TEST. Thus the scalar taxonomy is falsified in its tested form, whereas the operator-valued reformulation is mathematically well posed but not yet physically validated. The result supports a three-level view of dissipative universality: universal algebraic structure, system-specific realizability and closure, and regime- and instrument-dependent observed phenomenology.