Gamma-Convergence and the Relativistic Continuum Limit in the Fractal Consistency Law

Gamma-Convergence and the Relativistic Continuum Limit in the Fractal Consistency Law This paper presents the continuum-limit sector of the Fractal Consistency Law (FCL) in a corrected and internally ordered form. Its purpose is to show, within a controlled class of discrete geometric-textural configurations, that the passage from a simplicial microscopic substrate to an effective relativistic continuum can be formulated as a genuine variational convergence problem rather than as an intuitive matching exercise. The manuscript defines the discrete FCL-Regge action, states the admissibility hypotheses with unified notation, derives the compactness and lower-semicontinuity structure required for the bridge theorem, constructs the recovery sequence, and formulates the resulting Gamma-convergence statement. It then integrates the frozen-limit hardening that yields the Einstein-Lambda branch and the statistical Regge-consistency module induced by the Principle of Minimal Inconsistency (PMI). The result is a coherent paper in which the variational bridge, the asymptotic relativistic branch, and the statistical selection of good geometry are treated as parts of a single structural argument. The paper also distinguishes clearly between what is already closed within the present class and what remains open only at higher levels of generality.