Recursive Quantum Number Theory

Recursive Quantum Number (RQN) Theory proposes a new mathematical framework for encoding space-time as a time-evolving, energy-filtered number system. Extending classical ppp-adic arithmetic, RQNs introduce a dynamic scaling base tied to cosmic expansion and impose quantum energy thresholds on digit-level contributions. This results in a non-Archimedean, partially closed ring structure that evolves with time and reflects both hierarchical recursion and physical constraints. The theory models space-time as a recursive arithmetic object, where each valid digit corresponds to a causally ordered, energy-permitted quantum event. RQNs support algebraic operations, recursive harmonic analysis, and filtered sheaf structures, while naturally embedding concepts from spin foam models, causal set theory, and holographic entropy bounds. The framework offers a novel arithmetic lens on discrete geometry, quantum gravity, and cosmological information flow.