# Computational and Categorical Frameworks of Finite Ternary Gamma-Semirings: Foundations, Algorithms, and Industrial Modeling Applications

arXiv: https://arxiv.org/abs/2511.12323 · HTML: https://mlsanity.com/paper/2511.12323/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2025.

## Built on by (most cited first, 1 of 1)

- [Ternary Gamma Semirings: From Neural Implementation to Categorical Foundations](https://mlsanity.com/paper/2603.19317/) (2026)

## Abstract (arXiv)

Purpose: This study extends the structural theory of finite commutative ternary Gamma-semirings into a computational and categorical framework for explicit classification and constructive reasoning. Methods: Constraint-driven enumeration algorithms are developed to generate all non-isomorphic finite ternary Gamma-semirings satisfying closure, distributivity, and symmetry. Automorphism analysis, canonical labeling, and pruning strategies ensure uniqueness and tractability, while categorical constructs formalize algebraic relationships.  textitResults: The implementation classifies all systems of order |T|!≤!4 and verifies symmetry-based subvarieties. Complexity analysis confirms polynomial-time performance, and categorical interpretation connects ternary Gamma-semirings with functorial models in universal algebra.  Conclusion: The work establishes a verified computational theory and categorical synthesis for finite ternary Gamma-semirings, integrating algebraic structure, algorithmic enumeration, and symbolic computation to support future industrial and decision-model applications.