Geometric Origin of Physical Constants in an Expanding 3-Sphere Universe

Physical constants such as G, h, and e are conventionally treated as independent empirical inputs — quantities measured to high precision but left unexplained. This paper examines whether their values are instead geometric readouts of an expanding universe. Working within a closed 3-sphere (S³) geometry of cosmic radius R, the gravitational constant G and Hubble parameter H are derived from the topology and expansion dynamics of the manifold: a* = c²/πR, H = πc/R The seven SI base units reduce, within Wave Theory, to two independent scales (the Planck length and Planck time). In this natural unit system mass carries dimensions L², charge is a geometric surface-rate quantity, and impedance is dimensionless. Under this unit map, a* identifies exactly with the numerical value of Newton's G, and every constant becomes an explicit function of Lp, Tp, π, Z₀, and the epoch parameter R. Constants whose R-dependence cancels are genuinely epoch-invariant (c, α, G/Hc = 1/π²). Constants that retain R-dependence (G, H, h, e) are epoch-specific readouts of the same geometric relations at the present cosmic radius. The cosmic radius R is over-determined by four metrologically distinct empirical routes (G, H, h, e), all agreeing within an uncertainty budget dominated by the 22 ppm precision of G. The primary falsifiable prediction is G/(Hc) = 1/π², a dimensionless ratio testable with existing data at zero free parameters. The long-baseline prediction is a fractional drift of h/G at rate +2H, robust to instrument co-scaling.