Physical phenomena emerge from the combined contributions of all ”places” – including the real continuum and p-adic number fields. We present a concrete implementation of this principle through precise numerical integration, demonstrating how these divergent contributions can be reconciled to produce normalized physical quantities. Adelic integration emerged in reconciling quantum field theoretic models with number-theoretic methods. In this work, we develop a quantum-consistent framework wherein contributions from the real continuum and the p-adic spectrum are integrated with Euler-like prime factors. A critical aspect of our model is the anomaly detection mechanism, which is essential for ensuring that recursive expansions do not propagate numerical instabilities

Physical phenomena emerge from the combined contributions of all ”places” – including the real continuum and p-adic number fields. We present a concrete implementation of this principle through precise numerical integration, demonstrating how these divergent contributions can be reconciled to produce normalized physical quantities. Adelic integration emerged in reconciling quantum field theoretic models with number-theoretic methods. In this work, we develop a quantum-consistent framework wherei