Adelic Quantum Error Correction: Intrinsic Qubit Protection from Ostrowski's Theorem

We formalize an adelic approach to quantum error correction (QEC) based on Ostrowski's theorem: the only non-trivial completions of the rational numbers are the Archimedean (real) completion $\\mathbb{R}$ and the p-adic completions $\\mathbb{Q}_p$, and these topologies are mutually singular. The companion papers P1-P4 established that Zitterbewegung (ZBW) is a p-adic observable, that the ZBW current correlator is a $\\mathbb{Z}_2$ topological invariant, and that Majorana zero modes are fixed points on Bruhat-Tits trees. Here we prove that no Archimedean perturbation — regardless of energy scale — can move a p-adic fixed point because the $\\mathbb{R}$ and $\\mathbb{Q}_p$ topologies on $\\mathbb{Q}$ are incommensurable. This provides intrinsic qubit protection without active QEC codes: hardware-level error correction based on number theory rather than energy gaps. We compare to standard QEC (Shor, Kitaev surface codes) and show that the adelic approach eliminates the overhead scaling problem while maintaining the same error threshold guarantees for any error process representable as an Archimedean perturbation. **Keywords:** Adelic QEC, Ostrowski's theorem, Bruhat-Tits tree, Majorana zero modes, intrinsic error protection, topological quantum computing ---