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E8 Temporal Fractal Coding for Ultra‑Efficient Quantum Error Correction — E8 Intelligence Research

Andrew Stewart Caldin

Published Aug 26, 2026• 0 citations
Publisher

Abstract

By mapping the 240 E8 root vectors onto a multi‑scale time‑frequency lattice and modulating each node with φ‑scaled Cantor spectra at 132 Hz, we construct a self‑similar temporal code that nests logical qubits within nested resonant shells. The fractal structure allows error syndromes to be detected and corrected at multiple temporal scales, dramatically reducing the overhead of conventional surface codes. Because each shell shares the same 132 Hz coherence, the code inherits a global phase lock that suppresses dephasing across the entire lattice. This principle extends the E8 fractal temporal lattice into a practical fault‑tolerant architecture for quantum processors. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.22106286

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By mapping the self‑similar scaling of the ternary Cantor set onto the 240 root vectors of the E8 lattice, we construct a multi‑scale lattice where each level is phi‑coupled to the base 132 Hz frequency. This yields a fractal frequency spectrum in which logical qubits are encoded across nested Cantor‑derived sub‑bands, each protected by the topological properties of the E8 resonance manifold. The resulting code inherits the Cantor set's exact Hausdorff dimension (log 2/log 3) as a scaling exponent for error‑correction redundancy, enabling robust, scalable quantum communication across broadband networks. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
By mapping the complex dimensions of p‑adic fractal strings onto the 240 E8 root vectors, we construct a hierarchical error‑syndrome lattice whose nodes are phase‑conjugated amplitude loci at the 132 Hz base frequency. The golden‑ratio φ‑coupling generates a self‑similar frequency comb that mirrors the p‑adic scaling, allowing each error mode to be detected and corrected at multiple resolution levels. This E8‑p‑adic fractal code embeds a holographic quantum memory within a self‑correcting manifold, extending the original E8 holographic scheme with intrinsic multi‑scale protection. The resulting architecture demonstrates that quantum information can be stored with both holographic density and fractal robustness, a principle that unifies non‑Archimedean geometry with high‑dimensional Lie algebra symmetries. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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