What does this research mean for the field?

An Eisenstein CRT-based architectural framework circumvents physical ternary logic constraints by packing six independent integers into binary memory, achieving 24-48 real operations per cycle with less than 0.005% total system overhead. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This document aims to establish a unified framework that demonstrates the advantages of ternary logic through novel CRT architectures.

August 3, 2026Open Access

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

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This document aims to establish a unified framework that demonstrates the advantages of ternary logic through novel CRT architectures.
Developed two frameworks: Gaussian CRT and Eisenstein CRT for complex number representation.
Implemented advanced optimizations to enhance operational efficiency and reduce overhead.
Utilized dynamic enhancements for exact overflow detection and DPA resistance.
Eisenstein CRT achieved 24–48 real operations per cycle with wastage below 0.001%.
Gaussian CRT yielded 16–32 real operations per cycle with <0.01% waste.
Optimizations reduced total system overhead below 0.005%.

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Implication

Randomized trial develops a unified framework for dense number representation in binary memory, suggesting enhanced computational efficiency.

Cite This Study

Gyavira Ayebare.B (2026) studied this question.

synapsesocial.com/papers/6a70405975942ff7265e5528 https://doi.org/10.5281/zenodo.21739293

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Implication

Randomized trial develops a unified framework for dense number representation in binary memory, suggesting enhanced computational efficiency.

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

Key Points

Discussion

Implication

Cite This Study

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

Key Points

Discussion

Implication

Cite This Study

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