Balanced Ternary Quaternions Generate F3[Q8] Gregory D. Volk July 1, 2026 Abstract This work investigates the non-commutative behavior of quaternionic multiplication operating over a finite, balanced ternary field framework. Specifically, we evaluate the...
More
Balanced Ternary Quaternions Generate F3[Q8] Gregory D. Volk July 1, 2026 Abstract This work investigates the non-commutative behavior of quaternionic multiplication operating over a finite, balanced ternary field framework. Specifically, we evaluate the complete state-space tra- jectories generated by treating elements as localized operators—analogous to eigenvalue transforma- tions—applied within a three-state balanced system (F3 ) characterized by the strict absence of a carry-trit mechanism. By executing an exhaustive combinatorial audit of all 81 structural permuta- tions within this bounded framework, we demonstrate that the resulting global state-space architecture maps with perfect algebraic isomorphism to the group ring F3 [Q8 ]. Furthermore, we show that this discrete 81-state cubic lattice serves as an exact topological blueprint for a wide array of self-contained, periodic physical phenomena manifesting throughout nature, including electrodynamic plasma filaments, subatomic
Less
