  Building on earlier work, we propose an elementary Lagrangian for the
unification of the standard model with pre-gravitation, assumed to have an
unbroken $E_8 \times E_8$ symmetry. The Lagrangian is patterned after the
kinetic energy of a free particle in Newtonian dynamics, generalising it to the
matrix-valued Lagrangian dynamics of a 2-brane on a split bioctonionic space.
Symmetry breaking gives rise to the standard model quarks and leptons of three
generations along with the known gauge interactions, and a novel right-handed
counterpart $SU(3)_{grav}\times SU(2)_R \times U(1)_g$ identified as
pre-gravitation. The goal of the present series of papers is to investigate if
this pre-quantum, pre-spacetime matrix-valued Lagrangian dynamics can lead to
the emergence of quantum field theory for the standard model, and classical
general relativity, possibly with some additional corrections. In this paper we
work out the bosonic part of the Lagrangian, and show how the anticipated 32
gauge bosons are recovered from the elementary Lagrangian. As an application,
we show that the asymptotic low energy weak mixing angle $\theta_W$ is given by
a solution of the equation $1 = (1/2)\sqrt{ \cos(\theta_{W}/2)}+ \sqrt
{\sin(\theta_{W}/2)}$, yielding $\sin^2\theta_W \approx 0.24996$.
