  A search in energetic, high-multiplicity final states for evidence of physics
beyond the standard model, such as black holes, string balls, and electroweak
sphalerons, is presented. The data sample corresponds to an integrated
luminosity of 35.9 fb$^{-1}$ collected with the CMS experiment at the LHC in
proton-proton collisions at a center-of-mass energy of 13 TeV in 2016. Standard
model backgrounds, dominated by multijet production, are determined from
control regions in data without any reliance on simulation. No evidence for
excesses above the predicted background is observed. Model-independent 95%
confidence level upper limits on the cross section of beyond the standard model
signals in these final states are set and further interpreted in terms of
limits on semiclassical black hole, string ball, and sphaleron production. In
the context of models with large extra dimensions, semiclassical black holes
with minimum masses as high as 10.1 TeV and string balls with masses as high as
9.5 TeV are excluded by this search. Results of the first dedicated search for
electroweak sphalerons are presented. An upper limit of 0.021 is set on the
fraction of all quark-quark interactions above the nominal threshold energy of
9 TeV resulting in the sphaleron transition.
