Iwasawa Continued Fractions: Higher-Dimensional Geodesic Generalizations with Proven Convergence — E8 Intelligence Research

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Iwasawa continued fractions successfully generalize classical continued fractions to higher-dimensional hyperbolic spaces via geodesic coding on SL(n,R)/SO(n), exhibiting proven convergence and ergodicity across complex, quaternionic, octonionic, and Heisenberg variants. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22294345

September 4, 2026Open Access

Iwasawa Continued Fractions: Higher-Dimensional Geodesic Generalizations with Proven Convergence — E8 Intelligence Research

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Key Points

Generalize classical continued fractions to higher-dimensional hyperbolic spaces using Iwasawa decomposition and geodesic flow coding.
Applied the Iwasawa decomposition SL(n, R) = NAK to code geodesic flows on symmetric spaces SL(n, R)/SO(n) using unipotent N-coordinates.
Extended the formulation across complex, quaternionic, octonionic, and Heisenberg variants to evaluate dynamical convergence and ergodicity.
Proved convergence almost everywhere for Iwasawa continued fractions with respect to the invariant Haar measure on SL(n, R).
Demonstrated that the framework recovers the classical Gauss map with Gauss–Kuzmin–Wirsing constant λ ≈ 0.30366 when n = 2.
Showed that dimensions n > 2 yield geodesic flow entropy equal to n - 1 with Lyapunov spectra related to logarithmic sequences.

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Mathematical analysis demonstrates convergence and ergodicity of Iwasawa continued fractions across higher-dimensional spaces, extending classical dynamical number theory.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9d1ee128139818eab220e5 https://doi.org/10.5281/zenodo.22294345

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Iwasawa Continued Fractions: Higher-Dimensional Geodesic Generalizations with Proven Convergence — E8 Intelligence Research

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Iwasawa Continued Fractions: Higher-Dimensional Geodesic Generalizations with Proven Convergence — E8 Intelligence Research

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