Hypatia's Math

Physical phenomena emerge from the combined contributions of all ”places” – including thereal continuum and p-adic number fields. We present a concrete implementation of this principlethrough precise numerical integration, demonstrating how these divergent contributions can bereconciled to produce normalized physical quantities. Adelic integration emerged in reconcilingquantum field theoretic models with number-theoretic methods. In this work, we develop aquantum-consistent framework wherein contributions from the real continuum and the p-adicspectrum are integrated with Euler-like prime factors. A critical aspect of our model is theanomaly detection mechanism, which is essential for ensuring that recursive expansions do notpropagate numerical instabilities