  A unified field theory of all known basic forces and elementary particles is
built based on the postulates of gauge invariance and coordinate independence
along with general conformal scaling symmetry. The hyper-spin charge of a
unified hyper-spinor field is conjectured to correlate with the dimension of
hyper-spacetime. The minimal dimension of hyper-spacetime for the unity of
quarks and leptons in the standard model is found to be $D_h=19$ with a
bimaximal symmetry. A unified fundamental interaction is governed by hyper-spin
gauge symmetry SP(1,$D_h$-1). We show gravitational origin of gauge symmetry
characterized by gauge-type Goldstone-like hyper-gravifield, which enables us
to study gauge gravity and gravity geometry correspondences and to reveal gauge
geometry duality.
