The paper presents a candidate quantum field theory of gravity with a dynamical critical exponent \( z = 3 \) in the ultraviolet (UV) regime. This theory, which describes interacting nonrelativistic gravitons at short distances, is power-counting renormalizable in 3+1 dimensions. When restricted to satisfy the condition of detailed balance, the theory is closely related to topologically massive gravity in three dimensions and the geometry of the Cotton tensor. At long distances, the theory naturally flows to the relativistic value \( z = 1 \), making it a potential candidate for a UV completion of Einstein's general relativity or an infrared modification thereof. The effective speed of light, the Newton constant, and the cosmological constant emerge from relevant deformations of the deeply nonrelativistic \( z = 3 \) theory at short distances. The paper also discusses the properties of the \( z = 3 \) UV fixed points and the relevant deformations that induce the infrared flow to \( z = 1 \). Additionally, it explores the case of \( z = 4 \) in 4+1 and 3+1 dimensions and the ultralocal theory of gravity.The paper presents a candidate quantum field theory of gravity with a dynamical critical exponent \( z = 3 \) in the ultraviolet (UV) regime. This theory, which describes interacting nonrelativistic gravitons at short distances, is power-counting renormalizable in 3+1 dimensions. When restricted to satisfy the condition of detailed balance, the theory is closely related to topologically massive gravity in three dimensions and the geometry of the Cotton tensor. At long distances, the theory naturally flows to the relativistic value \( z = 1 \), making it a potential candidate for a UV completion of Einstein's general relativity or an infrared modification thereof. The effective speed of light, the Newton constant, and the cosmological constant emerge from relevant deformations of the deeply nonrelativistic \( z = 3 \) theory at short distances. The paper also discusses the properties of the \( z = 3 \) UV fixed points and the relevant deformations that induce the infrared flow to \( z = 1 \). Additionally, it explores the case of \( z = 4 \) in 4+1 and 3+1 dimensions and the ultralocal theory of gravity.