Projective Geometry of the Divisor Lattice: Reconstructing Arithmetic from Quasimodular Residues

In a previous work, we established the algebraic properties of the functional R (n) = (n² − n + 1) σ1 (n) − σ3 (n), identifying prime numbers as its zeros. In this paper, we expand this framework to construct a geometric representation of the integer lattice. We introduce the structural kernel K (n) = n² − 1 as a metric complement to the residue R (n). We prove that the fundamental arithmetic operations—addition, subtraction, multiplication, and division—are not axiomatic primitives but can be derived as projective invariants from the interaction between the residue R and the kernel K within a bidimensional state space. Specifically, we demonstrate that the quotient of two integers is a conformal invariant, independent of the scalar magnitude of the structural metric, and that the interaction of prime numbers embeds naturally into the complex unit circle via a precise trigonometric parameterization. This is Part 2 of the 'Structural Divisor Theory' series