From Quantum Graph To Spacetime Dimensionality: A Computational Finitism Derivation of 4D Spacetime, Matter, and the Standard Mode

We present a complete derivation of 4-dimensional spacetime and the Standard Model from discrete computational principles within the framework of Computational Finitism. Through four sequential phases, we demonstrate: (1) How Feynman path summation on a quantum causal graph yields an effective dimensionality of D = 4.074, intrinsically linking the fine structure constant α ≈ 1/137 to spatial dimensionality through the coupling constant λ ≈ √α; (2) How topological defects (Trefoil knots) in the causal graph manifest as massive particles with 1/r gravitational fields; (3) How discrete knot topology derives Standard Model properties (Charge, Spin, Mass) without continuous mathematics; (4) Universal validation across multiple prime moduli. This work establishes that spacetime dimensionality, matter, and physical constants are not background assumptions but emergent properties of quantum computational dynamics on a finite causal graph.