Geometric–Structural Layer Closure (Pasev): Introduction to Research Program

This work introduces the Geometric–Structural Layer Closure program, a formally defined mathematical framework for constructing geometric systems based on well-founded hierarchical structures, fiber bundle organization, and invariant-preserving transformations. The program addresses the absence of fully explicit and internally closed formulations in geometric unification approaches. It establishes a structure-first methodology in which all primary objects, mappings, and constraints are explicitly defined within a well-founded set-theoretic context. The framework is developed as a layered system: • Geometric Unity I – Foundational Structures • Geometric Unity II – Operators and Relational Geometry • Geometric Unity III – Structural Consistency, Limitations, and Closure Each layer extends the previous while preserving compatibility, invariance, and hierarchical integrity. This document defines the conceptual, methodological, and structural basis of the program and establishes its epistemic position as a pre-physical mathematical framework. The program is developed within the Global Institute of Logic & Cybernetics (GILC) and operates under the formal logic architecture of Digital Fabrica Theory (DFT).