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We present a comprehensive statistical analysis of Swift X-ray light-curvesof Gamma-Ray Bursts (GRBs) collecting data from more than 650 GRBs discoveredby Swift and other facilities. The unprecedented sample size allows us toconstrain the REST FRAME X-ray properties of GRBs from a statisticalperspective, with particular reference to intrinsic time scales and theenergetics of the different light-curve phases in a common rest-frame 0.3-30keV energy band. Temporal variability episodes are also studied and theirproperties constrained. Two fundamental questions drive this effort: i) Doesthe X-ray emission retain any kind of "memory"of the prompt gamma-ray phase?ii) Where is the dividing line between long and short GRB X-ray properties? Weshow that short GRBs decay faster, are less luminous and less energetic thanlong GRBs in the X-rays, but are interestingly characterized by similarintrinsic absorption. We furthermore reveal the existence of a number ofstatistically significant relations that link the X-ray to prompt gamma-rayparameters in long GRBs; short GRBs are outliers of the majority of these2-parameter relations. However and more importantly, we report on the existenceof a universal 3-parameter scaling that links the X-ray and the gamma-rayenergy to the prompt spectral peak energy of BOTH long and short GRBs:E_{X,iso}\propto E_{gamma,iso}^{1.00\pm 0.06}/E_{pk}^{0.60\pm 0.10}.

The prompt-afterglow connection in Gamma-Ray Bursts: a comprehensive statistical analysis of Swift X-ray light-curves