We present a unified theory of computation and physics based on the GLLYFES-NDIC formalism. This framework postulates that physical spacetime emerges from a non-deterministic graph-rewriting system (Interaction Combinators) constrained by thermodynamic bounds. We define the Non-Deterministic Interaction Combinator (NDIC) agent σ and formally map its reduction dynamics to a Jónsson-Tarski Algebra realized within a linear memory Arena 𝒜. We introduce the paradigm of "Data as Types" (DaT), asserting that physical structure is indistinguishable from logical type constraints. To resolve the tension between the infinite ideal algebra and its finite physical realization, we introduce Topological Impedance, which manifests as spacetime curvature. Finally, we employ Differential Cohesive Homotopy Type Theory (DC-HoTT) to rigorously bridge discrete combinatorics with smooth geometry, offering specific, falsifiable predictions regarding vacuum birefringence and modified dispersion relations at the Planck scale.