The Enchan Field: An Effective Field Framework for Geometric Stabilization and Non-Linear Relaxation

The Enchan Field is proposed as an effective-field framework for geometric stabilization and nonlinear relaxation across continuous and discrete systems. The paper introduces a geometric order field S(x) and interprets its nonlinear screening response as finite field tension: excessive local concentration is regularized by the field response rather than by an externally imposed correction. The same stabilization principle is translated into deterministic graph dynamics. In that discrete reading, high-degree hub nodes act as localized over-concentrations of interaction intensity; unrestricted linear aggregation can drive premature collapse, while finite-tension screening permits relaxation toward stable phase boundaries corresponding to candidate graph cuts. Enchan Cosmic is presented as a discrete realization of this pre-existing field principle, not as the theoretical starting point. The paper's main contributions are the effective geometric-field formulation, the nonlinear finite-tension kinetic framework, the interpretation of screening as over-concentration regularization, and the continuous-to-discrete mapping to deterministic graph optimization. Scope and review focus: This is an effective framework and structural proposal, not a completed fundamental theory or empirical confirmation of a new gravitational law. Review is especially invited on the mathematical consistency of the finite-tension response, the continuous-to-discrete mapping, the interpretation of hub-induced collapse, and the evidentiary boundary between the field proposal and the computational observations. The record contains the manuscript PDF and archived source material. Version update — v1.0.4 (September 16, 2026):This revision is a provenance and citation maintenance release. It adds explicit data- and figure-provenance documentation for the SNAP Web-Google benchmark and the archived computational audit figures, clarifies the official dataset source and the non-bundling of third-party raw data, and adds an explicit citation for the Tabu Search baseline used in the local comparison. The theoretical framework, field equations, reported benchmark values, and scientific conclusions are unchanged from v1.0.3. The original publication date remains May 11, 2026.