Gyavira Ayebare.B

Adaptive Physical Layer Exploitation for CRT-Packed Arithmetic

Shannon's radix economy establishes base‑3 as the most efficient representation for numerical information, yet binary logic dominates hardware. Recent work circumvented this barrier by using the Chinese Remainder Theorem (CRT) over Eisenstein integers to pack six independent comp...

Resonant Geometric Confinement in a Finite-Approximation Kakeya Fractal

This manuscript presents a theoretical framework for a charged particle confinement mechanism based on a finite-iteration approximation of the Kakeya (Besicovitch) fractal. The core proposal is that a particle guided along the discrete slides and pivots of the Perron tree—under a...

Resonant Geometric Confinement in a Finite-Approximation Kakeya Fractal

This manuscript presents a theoretical framework for a charged particle confinement mechanism based on a finite-iteration approximation of the Kakeya (Besicovitch) fractal. The core proposal is that a particle guided along the discrete slides and pivots of the Perron tree—under a...

A Unified Theory of Dense Number Representation via CRT: From Gaussian to Eisenstein Integers

The theoretical superiority of base-3 arithmetic over binary has been recognised since Shannon's foundational work on radix economy, yet ternary logic remains absent from commercial hardware due to fundamental semiconductor constraints. This document presents a comprehensive fram...