A geometric characterization of divisibility via the COMP operator from GCA theory

We present an exact geometric interpretation of integer divisibility within the framework of the Generalized Complementary Algebra (GCA). Integers are represented by additive configurations (partitions), and a complement operator, denoted COMP, measures their deviation from rectangular closure. We prove that configurations with empty complement are in bijection with the divisors of the integer, so that the associated invariant N_empty(n) coincides exactly with the divisor function τ(n). As a direct consequence, primality admits a precise geometric characterization: an integer n ≥ 2 is prime if and only if N_empty(n) = 2. The result is deterministic and exact, providing a conceptual bridge between additive geometry and multiplicative arithmetic. Although not intended as an efficient algorithmic test, this characterization clarifies the theoretical role of COMP and explains related spectral phenomena observed in numerical experiments.