Cyclic Measurement and Silent Radix: Ultrametric Foundations for Quantum State Tomography

This paper synthesizes the cyclic measurement formalism with the silent radix concept, establishing ultrametric foundations for quantum state tomography. The silent radix is formalized as a valuation-theoretic primitive. Combined with cyclic measurement protocols, this yields a robust framework for quantum state reconstruction with provable error bounds grounded in p-adic analysis. Includes Lean-formalized proofs of core theorems: valuation properties, rollover mechanics, reentry dynamics, and complete 6-case ultrametric inequality analysis.