The Minimal Discrete Geometry

We introduce the class of Discrete Geometric Spaces (DGS): integer-valued metric spaces on Z² satisfying four structural axioms. To each DGS we associate a discrete invariant π■, defined as the asymptotic ratio of sphere cardinality to radius, generalising the classical constant π≈3.14159 to discrete settings. Main Theorem: among all DGS, the value π■=1 is the unique minimum. It is achieved by the metric d■(P,Q)=|Δx|+2|Δy|, and this realisation is unique up to isomorphism. We establish this through three independent invariants (combinatorial, algebraic, metric), show that π■=1 forces dimension 2, and prove that π■ is a strict generalisation of the Euclidean π. This article is fully proven (12 theorems, no conjectures) and self-contained. It is the mathematical foundation of the π■=1 programme.