Beta functions of ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> )-dimensional projectable Ho?ava gravity

We derive the full set of beta functions for marginal essential couplings projectable Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity in ($3+1$)-dimensional spacetime. To this end we compute divergent part one-loop effective action static background with an arbitrary spatial metric. The computation is done several steps: reduction problem to three dimensions, extraction operator square root from fluctuation operator, and evaluation its trace using method universal functional traces. This provides us renormalization potential which combine results kinetic obtained previously. calculation uses symbolic computer algebra performed four different gauges yielding identical functions. additionally check by evaluating on a special spherical slices alternative spectral summation. conclude preliminary discussion properties resulting group flow, identifying candidate asymptotically free fixed points.