  We describe the linearized supergeometry of eleven dimensional supergravity
with four off-shell local supersymmetries. We start with a background Minkowski
11D, N=1 superspace, and an additional ingredient of a global, constant,
$G_2$-structure which facilitates the definition of a $4|4+7$ background
superspace. A bottom-up construction of linear fluctuations of the geometric
constituents (such as supervielbein, spin connection, and the super 3-form of
11D supergravity) is given in terms of 4D, N=1 prepotential superfields. This
is complemented by a top-down description of the linearized supergeometry of
the $4|4+7$ superspace dealing directly with torsion, curvature, and Bianchi
identities. Torsion constraints that (combined with the Bianchi identities)
lead to the preceding prepotential expressions of the gauge fields are
identified. All irreducible consequences of the torsion and 4-form Bianchi
identities are systematically derived except for dimension 2 Bianchi identities
of the 4-form, and dimension $\tfrac 52$ Bianchi identities of torsion, which
set bosonic curls of components of one lower dimension to zero.
