A Closure-Based Substrate Model: Emergent Quantum Behavior and Gravity

This manuscript presents a constructive substrate-based theory where quantum behavior, measurement, and gravitational geometry emerge from a unified closure dynamics acting on a discrete relational structure called the Octahedral Fractal Lattice (OFL). The framework replaces standard quantum postulates with two fundamental principles: Global Closure Consistency (SR1) and Frustration Minimization (SR2). By applying a quantitative microscopic update schema, the model demonstrates the following emergent properties: Geometric Unification: The Weak Equivalence Principle arises from a triadic Möbius architecture, ensuring that all emergent gravitype excitations couple identically to a universal orientation manifold. Planck Scale Derivation: The reduced Planck constant (ℏ) is formally identified as a geometric property of the substrate, defined by the product of microscopic lattice tension (𝜎) and the fundamental update interval (Δ𝜏). Topological Confinement: A discrete Z_3 defect index emerges from triad closure constraints, yielding a linear energy scaling E(L) ~ σL for separated defects without the need for independent gauge fields. Empirical Falsifiability: The model provides explicit, testable predictions for modified dispersion relations ω(k) and substrate-dependent stabilization times for quantum outcomes. This work offers a coherent, mechanistically transparent alternative to the "landscape" paradigm, grounding unified field theory in observable structural dynamics.