Geometric–Structural Layer Closure (Pasev) I: Foundational Structures

This work establishes the foundational mathematical layer of the Geometric–Structural Layer Closure program. It defines a well-founded base space, fibered structural organization, and projection-preserving transformations.

All objects are constructed explicitly within a set-theoretic framework, ensuring termination, non-circularity, and structural consistency. The system is defined as a fibered hierarchy:

• Base space (O, ≤) as a well-founded partially ordered set  
• Fiber assignment Fα over each base element  
• Total space E with projection π : E → O  

Transformation rules enforce invariance:

π ∘ T = π

Spectral constructions are introduced to extract invariant structures, ensuring stability under admissible transformations.

This layer provides a complete, internally consistent structural foundation upon which all subsequent geometric operators and extensions are defined.