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| Main Authors: | , |
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| Format: | Recurso digital |
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Zenodo
2026
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| Subjects: | |
| Online Access: | https://doi.org/10.5281/zenodo.19426459 |
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Table of Contents:
- <p>Hurwitz’s theorem states that finite-dimensional normed division algebras over<br>the real numbers exist only in dimensions 1, 2, 4, and 8, corresponding to the real<br>numbers, complex numbers, quaternions, and octonions. Continuing the Cayley<br>Dickson construction beyond the octonions yields the sedenions and higher-dimensional<br>algebras, which successively lose normed multiplicativity, divisibility, and even<br>power-associativity, and develop zero divisors. Meanwhile, the cosmic informa<br>tion dynamics framework, based on the axioms of information conservation and<br>computability, predicts that in the parameter region where the inverse constraint<br>temperature β < 0.5, the universe is in a “failed phase”: the effective spacetime<br>dimension freezes at about 1.2, the causal structure fragments, continuous mathe<br>matics cannot be established, and fundamental forces exist only as potentials. This<br>paper demonstrates that there exists a strict mathematical isomorphism between<br>the degeneracy ladder of higher-dimensional number algebras and the failure pat<br>terns of mathematical structures in the failed universe. This isomorphism not only<br>provides a concrete algebraic model for the failed universe but also reveals a deep<br>correspondence between information dynamics and hypercomplex algebras.</p>