The companion TFOFT paper proposes that the universe is a finite computational object defined by a dynamical Apollonian-Soddy sphere-packing fractal quine under Presburger arithmetic. This paper develops the first continuum-limit equations of that framework. The sphere radius is treated as a local clock field; its coarse-grained graph dynamics yields Newtonian gravity and the weak-field time component of general relativity. On the same tangency graph, a one-dimensional chiral transfer channel with a two-state boundary-spin register yields the 1+1 dimensional Dirac equation, with mass interpreted as the chirality-reversal rate per local radius-clock tick. The extension to full curved 3+1 dimensional spinor dynamics is stated as a frame-rotation ansatz, not a theorem. Electromagnetism is sketched as lower-layer callback momentum bookkeeping whose graph form is a candidate edge-phase holonomy limit. The paper also derives a testable Milky Way prediction: if the Fermi bubbles are the polar lobes of a scaled 3dz2 boundary state, then a weaker equatorial "Fermi donut" should appear at roughly 10 to 15 kpc, with an inner shoulder near 8 to 12 kpc and one-quarter the angular density contrast of the polar lobes. This places the key observational test in the Gaia DR3 outer-disk regime.