Dirichlet Form and Reconstruction of Macroscopic Geometry

This preprint develops the operator-geometric closure of the spatial sector of the Theory of Structural Articulation (TSA). It shows how macroscopic geometry can be reconstructed from the effective operator theory of a coarse-grained structural substrate, rather than introduced as an a priori background. The work builds on the companion TSA-GEOM-R3 preprint, which establishes the rank-three transport carrier, and provides the next step in the geometry line of TSA. It constructs the effective Dirichlet-form framework, derives the corresponding macroscopic elliptic operator, and identifies the reconstructed metric and curvature quantities as operator-level invariants. The paper serves as a bridge between the emergence of a three-dimensional transport phase and subsequent TSA works on spectral stability, structural diffusion, and correlation-scale normalization.