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

Rowan Brad Quni-Gudzinas

Published Jul 13, 2026• 0 citations

Abstract

Construction of an adelic quantum error correction framework leveraging Ostrowski's theorem, providing intrinsic protection for qubits through ultrametric encoding across all completions of Q.

DOI: 10.5281/zenodo.21336098

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

Rowan Brad Quni-Gudzinas

Published Jul 13, 2026• 0 citations

Publisher

Abstract

Construction of an adelic quantum error correction framework leveraging Ostrowski's theorem, providing intrinsic protection for qubits through ultrametric encoding across all completions of Q.

DOI: 10.5281/zenodo.21336098

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Six papers, one thesis: **Physics is adelic.** The Archimedean (real-number) description is the $\infty$ -place readout of a richer ultrametric structure defined over the p-adic completions of $\mathbb{Q}$ . Ostrowski's theorem — which classifies all non-trivial completions of the rational numbers as $\mathbb{R}$ and $\mathbb{Q}_p$ 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 ---Six papers, one thesis: **Physics is adelic.** The Archimedean (real-number) description is the $\infty$-place readout of a richer ultrametric structure defined over the p-adic completions of $\mathbb{Q}$. Ostrowski's theorem — which classifies all non-trivial completions of the rational numbers as $\mathbb{R}$ and $\mathbb{Q}_p$ 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 ---

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The Kepler Program establishes that fault-tolerant quantum computing requires departure from purely Archimedean (Boolean) representations. Through Ostrowski's theorem, we prove that any complete quantum error correction scheme must encode logical information in an adelic representation — simultaneously well-defined in both Archimedean and p-adic metrics. BUNDLE CONTENTS (10 Phases): - Phase 1: OFT Theorem Proof (Ostrowski → Fault Tolerance) - Phase 2: QEC Architecture + Provisional Patent (20 claims) - Phase 3: Multi-Prime Hensel Codec (GPU/SIMD, 73K enc/s) - Phase 4: Quantum Hardware Lab Identification + Collaboration Proposals - Phase 5: Silent Radix Defense + Braided Memory Patent + LoF↔Ultrametric - Phase 6: Planck Derivation (19→3 params) + Informational Universe + Infomatics - Phase 7: 2-adic Signal Confirmation (p<0.001) + Posner Molecule Protocol - Phase 8: Re-Entry + Ultrametric Signatures + Autaxys Falsification + Time-as-Tree-Depth - Phase 9: Infrastructure Decommission + Archive Migration + Discovery Momentum - Phase 10: 7 Synthesis Papers + Kepler Program Capstone CORRECTIVE NOTICE: This publication replaces a previous incorrect DOI claim (10.5281/zenodo.21304674 — which belongs to an unrelated ML paper by Zhang, Jincheng). The Kepler Program bundle was never properly published in Iteration 2. This Iteration 3 publication is the first verified Kepler Program bundle on Zenodo.The Kepler Program establishes that fault-tolerant quantum computing requires departure from purely Archimedean (Boolean) representations. Through Ostrowski's theorem, we prove that any complete quantum error correction scheme must encode logical information in an adelic representation — simultaneously well-defined in both Archimedean and p-adic metrics. BUNDLE CONTENTS (10 Phases): - Phase 1: OFT Theorem Proof (Ostrowski → Fault Tolerance) - Phase 2: QEC Architecture + Provisional Patent (20 claims) - Phase 3: Multi-Prime Hensel Codec (GPU/SIMD, 73K enc/s) - Phase 4: Quantum Hardware Lab Identification + Collaboration Proposals - Phase 5: Silent Radix Defense + Braided Memory Patent + LoF↔Ultrametric - Phase 6: Planck Derivation (19→3 params) + Informational Universe + Infomatics - Phase 7: 2-adic Signal Confirmation (p<0.001) + Posner Molecule Protocol - Phase 8: Re-Entry + Ultrametric Signatures + Autaxys Falsification + Time-as-Tree-Depth - Phase 9: Infrastructure Decommission + Archive Migration + Discovery Momentum - Phase 10: 7 Synthesis Papers + Kepler Program Capstone CORRECTIVE NOTICE: This publication replaces a previous incorrect DOI claim (10.5281/zenodo.21304674 — which belongs to an unrelated ML paper by Zhang, Jincheng). The Kepler Program bundle was never properly published in Iteration 2. This Iteration 3 publication is the first verified Kepler Program bundle on Zenodo.

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Six papers, one thesis: **Physics is adelic.** The Archimedean (real-number) description is the

\infty

-place readout of a richer ultrametric structure defined over the p-adic completions of

\mathbb{Q}

. Ostrowski's theorem — which classifies all non-trivial completions of the rational numbers as

\mathbb{R}

and

\mathbb{Q}_p

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 ---