  Given a compact connected Lie group G endowed with root datum, and an element
w in the corresponding Artin braid group for G, we describe a filtered
G-equivariant stable homotopy type, up to a notion of quasi-equivalence. We
call this homotopy type Strict Broken Symmetries, sB(w). As the name suggests,
sB(w) is constructed from the stack of principal G-connections on a circle,
whose symmetry is broken between consecutive arcs in a manner prescribed by a
presentation of w. We show that sB(w) is independent of the choice of
presentation of w, and also satisfies Markov type properties. Specializing to
the case of the unitary group G = U(r), these properties imply that sB(w) is an
invariant of the link L obtained by closing the r-stranded braid w. As such, we
denote it by sB(L). In the follow up to this article, we will show that the
construction of strict broken symmetries allows us to incorporate twistings.
Under suitable conditions, U(r)-equivariant (twisted) cohomology theories EU(r)
applied to sB(L) give rise to a spectral sequence of link invariants converging
to the cohomology of the direct limit of the filtration of sB(L). For instance
we describe Triply-graded link homology as the E2-term in the spectral sequence
one obtains on applying Borel-equivariant singular cohomology HU(r) to sB(L).
We also study a universal twist of HU(r). Here one recovers sl(n)-link
homologies for any value of n (depending on the choice of specialization of the
universal twist).
