Prime-Structured Entropy Wells: A Mathematical Framework for Observer Emergence

We present a mathematical framework connecting prime number theory to fundamental physics through entropy minimization processes. Starting from the hypothesis that stable physical structures emerge as prime-resonant entropy wells, we develop rigorous foundations including symbolic entropy measures, prime Hilbert space construction, and dynamical evolution equations. The theory predicts specific patterns in astrophysical data and provides a mechanism for the emergence of spacetime, quantum mechanics, and consciousness from discrete prime-structured dynamics. While speculative, the framework offers testable predictions and addresses long-standing questions about the effectiveness of mathematics in describing physical reality.