Instability of Absolute Nothingness K: Algebraic Degeneration of Higher-Dimensional Numbers and the Isomorphism of Failed Universe Mathematical Structures
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2026
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| _version_ | 1866901057581350912 |
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| author | zhou, changzheng zhou, ziqing |
| author_facet | zhou, changzheng zhou, ziqing |
| 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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19426459 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Instability of Absolute Nothingness K: Algebraic Degeneration of Higher-Dimensional Numbers and the Isomorphism of Failed Universe Mathematical Structures zhou, changzheng zhou, ziqing sedenions; Cayley-Dickson construction; failed universe; information dynam ics; algebraic degeneration; zero divisor <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> |
| title | Instability of Absolute Nothingness K: Algebraic Degeneration of Higher-Dimensional Numbers and the Isomorphism of Failed Universe Mathematical Structures |
| topic | sedenions; Cayley-Dickson construction; failed universe; information dynam ics; algebraic degeneration; zero divisor |
| url | https://doi.org/10.5281/zenodo.19426459 |