What question did this study set out to answer?

The aim is to establish K_crit as a universal fixed point within self-organized criticality and renormalization group theory.

March 8, 2026Open Access

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

Key Points

The aim is to establish K_crit as a universal fixed point within self-organized criticality and renormalization group theory.
Derived K_crit as a fixed point using various theoretical frameworks like GCT cubic and Landauer analysis.
Identified K_max and the second zero of the RG beta function for upper stability boundary.
Predicted coherence collapse events follow a specific power law and explored implications across different fields.
K_crit is derived as approximately 0.127 and signifies a renormalization fixed point.
K_max is established around 6.87, indicating an upper limit of stability.
Predictions imply coherence collapse events follow a power law, with critical exponent τ pending further derivation.

Abstract

The critical coherence threshold Kcrit ≈ 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; Kcrit 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 Kₘax ≈ 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* = Kcrit + ε, not K ≫ Kcrit; (3) K ≫ Kcrit 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).

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

Key Points

Abstract

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