  Here, in \cite{KrumWicb} and in \cite{KrumWicc} we study the nature of an
$n$-dimensional locally area minimising rectifiable current $T$ of codimension
$\geq 2$ near its typical (i.e.\ ${\mathcal H}^{n-2}$ a.e.) singular points.
Our approach relies on an intrinsic frequency function for $T$, which we call
the \emph{planar frequency function}, which is defined geometrically relative
to a given $n$-dimensional plane $P$ and a given base point in the support of
$T$. In the present article we establish that the planar frequency function
satisfies an approximate monotonicity property, and takes values $\leq 1$ on
any cone ($\neq P$) meeting $P^{\perp}$ only at the origin, whenever the base
point is the vertex of the cone. Using these properties we obtain a
\emph{decomposition theorem} for the singular set of $T$, which (roughly
speaking) asserts the following: for any integer $q \geq 2$, the set ${\rm
sing}_{q} \, T$ of density $q$ singularities of $T$ can be written as ${\rm
sing}_{q} \, T = {\mathcal S} \cup {\mathcal B}$ for disjoint sets ${\mathcal
S}$ and ${\mathcal B}$, where: (I) each point $Z \in {\mathcal S}$ has a
neighbourhood ${\mathbf B}_{\rho_{Z}}(Z)$ such that about any point $Z^{\prime}
\in {\mathbf B}_{\rho_{Z}}(Z) \cap {\rm spt} \, T$ with density $\geq q$ and at
any scale $\rho^{\prime} < \rho_{Z}$, $T$ is significantly closer to some
non-planar cone ${\mathbf C}_{Z^{\prime}, \rho^{\prime}}$ than to any plane,
and (II) ${\mathcal B}$ is relatively closed in ${\rm sing}_{q} \, T$ and $T$
satisfies a locally uniform estimate along ${\mathcal B}$ implying decay of $T$
to a unique tangent plane faster than a fixed exponential rate in the scale.
This result is central to the more refined analysis of $T$ we perform in
\cite{KrumWicb} and \cite{KrumWicc}.
