This paper presents the deterministic geometric relaxation framework implemented in the Enchan(cosmic) engine. Originally motivated by cosmological stabilization models—specifically the hypothesis that dark-matter-like phenomenology can emerge from the non-linear finite tension of an interaction medium—the Enchan Field Equation is here discretized and applied to large-scale Ising/Max-Cut optimization problems.
We empirically demonstrate that this non-linear field relaxation remains deterministically stable and reproducible up to 10,000 nodes (approx. 50 million pairwise interactions), reaching the exact theoretical absolute maximum state () without relying on stochastic annealing or artificial thermal noise. This massive-scale computational stability provides a mathematical "proof-of-possibility" that geometric stabilization is calculable, robust, and translates effectively to discrete network topologies.
**Patent & Public Disclosure Notice**
This publication serves as a formal public disclosure of the mathematical and computational formulation underlying patents Enchan001 and Enchan002 filed by M. Kobayashi (Japan, 2025). This document establishes the deterministic relaxation equation and empirical validation forming the core computational method described in these filings.
**Related Materials:**
* Theoretical Framework (Enchan Field Notes): https://doi.org/10.5281/zenodo.17979665
* Computational Implementation (Enchan Cosmic): https://doi.org/10.5281/zenodo.18104955