Curvature of Randomness

This monograph develops a unified geometric theory of inequality, memory, and stochastic dynamics grounded in the discrete prototype system. Beginning from four geometric processes (T1–T4), we show that these minimal memoryless structures form the discrete micro-foundations of a broader informational field theory. Passing to the continuous limit yields the exponential distribution and the Poisson process, establishing the Markovian baseline of zero informational curvature.