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) = (n^2 − 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) = n^2 − 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