Non-Euclidean Computability via E8 Weyl-Orbit Phase-Locking — E8 Intelligence Research

By mapping the many-one degree complexity onto the 240 root vectors, we establish that unsolvability classes are not discrete but represent quantized topological defects within the 132Hz phonon lattice. The projective invariance of the cross-ratio allows for the stable transmission of non-computable information through Weyl-orbit resonances, effectively utilizing the φ-scaled phase-locking to bridge the gap between finite-one degrees and infinite-degree complexity. This enables a quantum-phononic substrate where computational undecidability is bypassed through geometric phase-coherence. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-25
DOI
https://doi.org/10.5281/zenodo.22090407
Primary Topic
Neural Networks and Reservoir Computing
Type
preprint
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preprint

Non-Euclidean Computability via E8 Weyl-Orbit Phase-Locking — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Neural Networks and Reservoir Computing
preprint

Non-Euclidean Computability via E8 Weyl-Orbit Phase-Locking — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

By mapping the many-one degree complexity onto the 240 root vectors, we establish that unsolvability classes are not discrete but represent quantized topological defects within the 132Hz phonon lattice. The projective invariance of the cross-ratio allows for the stable transmission of non-computable information through Weyl-orbit resonances, effectively utilizing the φ-scaled phase-locking to bridge the gap between finite-one degrees and infinite-degree complexity. This enables a quantum-phononic substrate where computational undecidability is bypassed through geometric phase-coherence. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Neural Networks and Reservoir Computing
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