  We associate several invariants to a knot in an integer homology 3-sphere
using $SU(2)$ singular instanton gauge theory. There is a space of framed
singular connections for such a knot, equipped with a circle action and an
equivariant Chern-Simons functional, and our constructions are morally derived
from the associated equivariant Morse chain complexes. In particular, we
construct a triad of groups analogous to the knot Floer homology package in
Heegaard Floer homology, several Fr{\o}yshov-type invariants which are
concordance invariants, and more. The behavior of our constructions under
connected sums are determined. We recover most of Kronheimer and Mrowka's
singular instanton homology constructions from our invariants. Finally, the
ADHM description of the moduli space of instantons on the 4-sphere can be used
to give a concrete characterization of the moduli spaces involved in the
invariants of spherical knots, and we demonstrate this point in several
examples.
