Toward full LHC coverage of natural supersymmetry

We argue that combining just a handful of searches for new physics at Run I of the LHC is sufficient to exclude most supersymmetric extensions of the Standard Model in which the gluino is kinematically accessible and the spectrum is natural. Such models typically give rise to significant ET, top quarks and/or high object multiplicity, and we show that having even one of these signatures generally results in stringent limits. We also identify, among models that lack these signatures, the few gaps in coverage remaining, and propose search strategies to close these gaps. Our results are general and independent of the details of the spectrum, assumptions about minimality, R-parity, etc. Our analysis strategy should remain applicable when the LHC moves to higher energy. Central to our argument are ATLAS and CMS searches for many jets and low ET, a proposed lepton + many jets search, an ATLAS search for 6-7 high-pi, jets, and a reexamination of the control and signal regions of the CMS black hole search.