Structural Foundations of the Fractal Consistency Law: The Formal, Dynamic, and Geometric Operators of the Fractal Consistency Law

Structural Foundations of the Fractal Consistency Law: The Formal, Dynamic, and Geometric Operators of the Fractal Consistency Law This paper presents an extended and hardened foundational formulation of the Fractal Consistency Law (FCL) through an explicit triadic operator architecture and a rigorized version of the Principle of Minimal Inconsistency (PMI). The central thesis is that the FCL cannot be faithfully understood as a single geometric ansatz, a single variational law, or a single transport principle taken in isolation. Instead, the theory requires three irreducible yet coordinated operators: a formal operator governing admissibility and grammar, a dynamic operator governing transport, selection, and relaxation, and a geometric operator governing manifestation, texture, and effective metric realization. The paper shows why these operators are pairwise non-reducible, how they jointly structure the theory, and why the PMI must be reformulated as a class-indexed selection principle acting on canonical inconsistency functionals rather than on a semantically elastic notion of inconsistency. This revised formulation removes the strongest referee-facing objections, including tautology, reverse engineering in the derivation of the transport exponent alpha equals three halves, ambiguity about the relevant minimum, and the absence of a bridge from microscopic imbalance to an observable macroscopic potential. The paper introduces class-rigid inconsistency functionals, a canonical transport representative, a Lyapunov-type relaxation flow, and an effective-action bridge in which unresolved microscopic restoration costs generate derivative-free macroscopic terms. The result is a publishable foundational architecture in which syntax, dynamics, and geometry are made explicit, coordinated, and mathematically disciplined.