A theory for the term structure of interest rates is presented, focusing on the use of discretized forms of the convolution and master equations to model interest rate variations. The paper introduces the concept of a "seed," a discretized form of the infinitesimal generator of a Markov process, which leads to an infinite superposition of Markov processes and allows for a power (rather than exponential) decrease in the empirical probabilities of interest rate variations. The discretized seed is shown to produce distributions that closely match empirical data from the Federal Reserve System (FRS), particularly in reproducing the tails of the distributions. These results suggest the presence of critical exponents related to self-organized systems. The paper also discusses the importance of discretization in modeling interest rate variations, as empirical data are often expressed in discrete units. The theoretical model is applied to FRS data, and the results are used to develop new methods for computing value-at-risk and fixed-income derivative pricing. The analysis shows that the seed can be parametrized to fit the data, with parameters depending on the initial interest rate and maturity. The results indicate that the exponent d, which governs the power law behavior of the seed, is of the order three, consistent with previous findings on the tail behavior of interest rate distributions. The paper concludes that the theory provides a framework for understanding the term structure of interest rates and has potential applications in risk management and financial modeling.A theory for the term structure of interest rates is presented, focusing on the use of discretized forms of the convolution and master equations to model interest rate variations. The paper introduces the concept of a "seed," a discretized form of the infinitesimal generator of a Markov process, which leads to an infinite superposition of Markov processes and allows for a power (rather than exponential) decrease in the empirical probabilities of interest rate variations. The discretized seed is shown to produce distributions that closely match empirical data from the Federal Reserve System (FRS), particularly in reproducing the tails of the distributions. These results suggest the presence of critical exponents related to self-organized systems. The paper also discusses the importance of discretization in modeling interest rate variations, as empirical data are often expressed in discrete units. The theoretical model is applied to FRS data, and the results are used to develop new methods for computing value-at-risk and fixed-income derivative pricing. The analysis shows that the seed can be parametrized to fit the data, with parameters depending on the initial interest rate and maturity. The results indicate that the exponent d, which governs the power law behavior of the seed, is of the order three, consistent with previous findings on the tail behavior of interest rate distributions. The paper concludes that the theory provides a framework for understanding the term structure of interest rates and has potential applications in risk management and financial modeling.