The Geometric Standard Model: Self-Reference from Four Integers

This Zenodo release presents “The Geometric Standard Model: Self-Reference from Four Integers,” a discrete, geometry-driven framework that connects a Gauss-constrained cubic lattice to elliptic-curve structure and then to quantitative predictions for fundamental constants. Starting from flux on a 3D lattice with toroidal boundary conditions, the paper derives an elliptic fibration for the moduli space of harmonic configurations and uses complex multiplication (CM) selection to single out the lemniscatic case ($j=1728$), yielding a distinguished geometric constant $G_{\\text{lem}} = \\sqrt{2}\\,\\Gamma(1/4)^2/(2\\pi)$. With the minimal lattice ($2\\times2\\times2$) fixing the coefficient 16 via a degrees-of-freedom count, the framework produces a “master quadratic” whose coefficients are determined by the geometry. Evaluated at $c=G_{\\text{lem}}$, its roots are $x_+ \\approx 137.036$ and $x_- \\approx 3.024$: the larger root matches the inverse fine structure constant $1/\\alpha$ at the ppm level, and the smaller root sits near the SU(3) color value, motivating an explicit projection/interpretation discussion. The manuscript is structured to distinguish rigorous theorems from argued selection principles and conjectural physical interpretation, and it states concrete falsifiability targets (e.g., whether the residual discrepancy is accounted for and whether associated structural predictions hold up under scrutiny).