  We extend Geisser and Hesselholt's result on ``bi-relative K-theory'' from
discrete rings to connective ring spectra. That is, if $\mathcal A$ is a
homotopy cartesian $n$-cube of ring spectra (satisfying connectivity
hypotheses), then the $(n+1)$-cube induced by the cyclotomic trace $$K(\mathcal
A)\to TC(\mathcal A)$$ is homotopy cartesian after profinite completion. In
other words, the fiber of the profinitely completed cyclotomic trace satisfies
excision.
