The pointed weak energy for an arbitrarily evolving quantum state defines a complex valued phase which is the sum of a dynamic phase and a purely geometric phase—the pointed geometric phase. The pointed geometric phase is concisely expressed as a time integral which depends upon the energy uncertainty, the associated evolving state, and its orthogonal companion state. The real part of the pointed geometric phase is to within a sign the geometric phase for arbitrary evolutions defined by Mukunda and Simon and that of Aharonov and Anandan for cyclic evolutions. The imaginary part of the pointed geometric phase governs the survival probability of the initial state. Several general rate of change relationships associated with the real and imaginary parts of the pointed geometric phase are deduced from this concise expression, and it is used to calculate the pointed geometric phase acquired as a spin- particle precesses under the influence of a uniform magnetic field.