K_crit as a Universal Fixed Point: Self-Organized Criticality, Renormalization Group, and Cross-Domain Empirical Predictions

The critical coherence threshold K_crit ≈ 0.127 is derived as a renormalization group fixed point — the sixth independent derivation alongside the dynamical (GCT cubic), thermodynamic (Landauer), information-geometric (Cramér–Rao), categorical (natural transformation), and holographic (Ryu–Takayanagi) derivations. Self-organized criticality systems at their critical point are scale-invariant and sit at RG fixed points; K_crit is the RG fixed point of the coherence universality class. This explains cross-scale universality: at the critical point, microscopic details wash out and only the universality class remains. The upper stability boundary K_max ≈ 6.87 is derived from the second zero of the RG beta function using the GCT cubic structure. Three quantitative, falsifiable predictions: (1) coherence collapse events follow a power law P(s) ~ s-τ — the critical exponent τ is identified as an open problem with forthcoming derivation; (2) the evolutionary optimum is K* = K_crit + ε, not K ≫ K_crit; (3) K ≫ K_crit produces over-correction pathology (autoimmune analogue). Cross-domain empirical program covers institutions, molecular biology (Eigen error threshold — structural correspondence established, numerical mapping forthcoming), neuroscience (Beggs–Plenz neural criticality), ecology (May stability threshold), and markets. Part of the Spektre corpus (github.com/spektre-labs/corpus).