Scale Graphs IV: Observed Renormalization, Critical Crossovers, and a Production-Selection Principle

This is the fourth paper in the Scale Graphs sequence. The first paper introduced finite Onsager-Prigogine scale graphs and minimum-production renormalization. The second paper used Cheeger geometry and a corrected tail-drainage mechanism on dissipative attractors. The third paper showed that the resulting graph observables act as operational order parameters in a finite Navier-Stokes scale model. The present paper formulates the corresponding notion of observed universality. The main conceptual point is that dissipative universality is not encoded by a single numerical constant. It is a class of observed renormalization data: fixed points, cycles or saddles of an observed RG map, gauge choices, locality class, dissipative scaling, and relevant eigendata. We prove a compact-window fixed point principle for observed RG maps, a gauge-reduced hyperbolicity statement for one-periodic fixed points, and a conditional critical-crossover theorem: if an observed RG saddle has a one-dimensional unstable eigenspace with eigenvalue delta_u > 1, then parameter windows scale by delta_u and the shadowing time grows like log(1/|eta - eta_c|)/log(delta_u). The same theorem contains a production-selection statement: in the abstract saddle model, the critical state has production no smaller than either terminal attracting state. We derive the required production-monotonicity hypothesis from the strict Lyapunov identity of the first paper for the class of production-preserving normalizations, and we show by an explicit two-cell example that the hypothesis cannot be dropped. The numerical part is deliberately narrow. The shell model provides an isolated real observed RG eigenvalue delta_u(shell) = 1.4187394, with confidence interval [1.4002, 1.4366] and gap about 3.95. This is the data set that instantiates the one-dimensional unstable hypothesis. The PDE data from Scale Graphs III show only a weakly unstable near-unit sector: rho(PDE) = 1.0332277003, with confidence interval [1.0086, 1.0562], paired leading modes and an independent near-unit cluster {1.096, 0.998, 0.971}. Thus the abstract transition theorem is proved in the observed RG setting, instrumented in the shell model, and only sign-level in the PDE data. We then freeze and execute two production-selection tests on the archived seven-run EDGE/RELAM/ACTIVE data set, with identical window, eligibility and verdict rules. Test 1 uses the archived field pi_j, which the campaign diagnostic defines as the cumulative spectral energy flux; the resulting statistic is a flux-based production proxy, declared as such. Test 2, frozen after the first and before any computation of its statistic, uses the nonnegative Onsager-Dirichlet quadratic production Pi^D = sum over scales and edges of a_e (Delta mu_e)^2, reconstructed from the published CANONICAL containers, so no sign cancellation is possible. This second statistic is a quadratic mobility-production instantiation, not the full edgewise Onsager polynomial. Both tests are eligible and both return FAIL: the upper 95 percent confidence bounds are negative, and the ACTIVE terminal regime dominates the EDGE runs by three to four orders of magnitude in either normalized statistic. This falsifies the flux-proxy and the nonnegative Onsager-Dirichlet quadratic instantiations of production selection on this archived data set, while leaving the abstract theorem intact: its saddle and monotonicity hypotheses are not instantiated by the archived PDE data. Numerical reproduction dataset (v1.4): https://doi.org/10.6084/m9.figshare.33086183Paper I of the series: https://doi.org/10.6084/m9.figshare.32942279Paper II of the series: https://doi.org/10.6084/m9.figshare.33002558Paper III of the series: https://doi.org/10.6084/m9.figshare.33067973