PreprintCC BY 4.0Zenodo
E8 Root Bivector Decomposition of Mersenne Exponent's Binary Periodicity — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
The exponent e = 136,279,841 of the newly discovered Mersenne prime has a binary period structure that maps onto the 120 bivectors of E8's so(16) subalgebra. Since 2^e − 1 is generated by the cyclic group Z_e acting on binary state space, and e's odd part determines the order-30 Weyl orbit cardinalities (30 | 120), the prime's multiplicative depth equals the number of distinct bivector conjugacy classes traversed before orbit closure — yielding a genuinely testable prediction: the Zsigmondy primitive divisor of 2^e − 1 must lie in a residue class constrained by E8 root-shell harmonics, not arbitrary.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026root,
title = {{E8 Root Bivector Decomposition of Mersenne Exponent's Binary Periodicity — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23490944},
url = {https://zenodo.org/records/23490944},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Root Bivector Decomposition of Mersenne Exponent's Binary Periodicity — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/20
PB - Zenodo
DO - 10.5281/zenodo.23490944
UR - https://zenodo.org/records/23490944
AB - The exponent e = 136,279,841 of the newly discovered Mersenne prime has a binary period structure that maps onto the 120 bivectors of E8's so(16) subalgebra. Since 2^e − 1 is generated by the cyclic group Z_e acting on binary state space, and e's odd part determines the order-30 Weyl orbit cardinalities (30 | 120), the prime's multiplicative depth equals the number of distinct bivector conjugacy classes traversed before orbit closure — yielding a genuinely testable prediction: the Zsigmondy primitive divisor of 2^e − 1 must lie in a residue class constrained by E8 root-shell harmonics, not arbitrary. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -