Affine Point–Line Structure Associated with the Modular ℤ₉ Tessellation

This paper presents the geometric structure associated with the modular tessellation introduced in Paper 1. The fundamental 3×3 modular tile over ℤ9 is shown to admit a natural combinatorial interpretation as the affine plane AG(2,3). Within this framework the entries of the tile correspond to points (SQV — Singular Quantum Vertices), while specific triples correspond to affine lines (ARG — Affine Resonant Generators). When the tessellation propagates across the lattice, adjacent tiles form a doubled affine configuration. The periodic nature of the modular propagation rules further allows the system to be represented in a compact toroidal geometry. This work provides the geometric layer of the modular tessellation structure and establishes the combinatorial foundation for further algebraic and structural analysis. Series: Modular Tessellation Paper 1 — Modular Tessellation and Local Propagation Rules (Zenodo DOI)Paper 2 — Affine Point–Line Structure Associated with the Modular ℤ9 Tessellation