Six papers, one thesis: **Physics is adelic.** The Archimedean (real-number) description is the
∞-place readout of a richer ultrametric structure defined over the p-adic completions of
Q. Ostrowski's theorem — which classifies all non-trivial completions of the rational numbers as
R and
Qp for each prime
p — is the hidden organizing principle behind quantum measurement, quantum error correction, and the structure of spacetime at the Compton scale. We present the unified framework: Zitterbewegung (ZBW) is the physical manifestation of the p-adic channel of the adelic Dirac equation; Majorana zero modes are Bruhat-Tits fixed points encoding adelic topological charge; and adelic quantum error correction replaces active QEC codes with number-theoretic protection. This synthesis paper connects all six companion publications into a coherent research program with specific, falsifiable predictions. **Keywords:** Adelic physics, Ostrowski's theorem, Zitterbewegung, Bruhat-Tits tree, p-adic quantum mechanics, topological quantum computing, grand synthesis ---
We prove that any fault-tolerant quantum error correction (QEC) scheme must encode logical information in an adelic representation — a representation simultaneously well-defined with respect to both the Archimedean valuation and at least one p-adic valuation on Q. The proof proceeds from Ostrowski's theorem on the classification of absolute values on Q and three key lemmas covering metric classification and insufficiency proofs for single-metric error models. Computational verification across 132 code parameter combinations found no counter-examples. We derive corollaries concerning code optimality, dimension constraints (prime-power qudit codes), and the natural fit of the Bruhat-Tits quantum processor architecture. Part of the QNFO Kepler Program, Phase 1.