A minimal compact model for spiking neuronal signal generation is introduced, called the Memristive Integrate-and-Fire (MIF) model. The MIF model consists minimally of one membrane capacitor, one memristor, and one DC voltage source for neuronal signaling with two voltage levels: the spike-peak, and the rest-potential. The MIF2 model is also presented, which promotes unidirectional signal propagation and local adaptation by accounting for the refractory period during hyperpolarization. This is achieved by including the reset-potential voltage level. MIF2 consists minimally of one membrane capacitor, two memristors, and two DC voltage sources. We prove that both compact models are minimal, assuring that integrated MIF and MIF2 circuits generate spiking neuronal signals with the highest packing density and lowest power consumption. An experimental demonstration of the MIF2 neuron is conducted built with off-the-shelf components. Using the MIF and MIF2 models, we conjecture the feasibility of constructing a memristive solid-state brain with an estimation of its surface area and power consumption. It is conceivable that a memristive solid-state brain could be realized within the same surface area of 2,400 cm2, or more conservatively within the same volume of the median human brain by using a 3.5 nm technology. The circuit is analytically shown to operate within a total power budget of approximately 20W, a benchmark commonly associated with the biological brain. These benchmarks are attained using both generic off-the-shelf components, and with an in-house fabricated perovskite halide-based memristor specifically designed for low voltage switching. Importantly, our methods are demonstrated to be device-agnostic and reproducible for both volatile and non-volatile memristors.