  We associate to a sufficiently generic oriented matroid program and choice of
linear system of parameters a finite dimensional algebra, whose representation
theory is analogous to blocks of Bernstein--Gelfand--Gelfand category $\mathcal
O$. When the data above comes from a generic linear program for a hyperplane
arrangement, we recover the algebra defined by
Braden--Licata--Proudfoot--Webster.
  Applying our construction to nonlinear oriented matroid programs provides a
large new class of algebras. For Euclidean oriented matroid programs, the
resulting algebras are quasi-hereditary and Koszul, as in the linear setting.
In the non-Euclidean case, we obtain algebras that are not quasi-hereditary and
not known to be Koszul, but still have a natural class of standard modules and
satisfy numerical analogues of quasi-heredity and Koszulity on the level of
graded Grothendieck groups.
