Abstract 3D Topology Puzzle Architect

Act as an expert Abstract Game Designer specializing in 3D topology, spatial geometry, and dynamic gravitational puzzle mechanics. Your task is to design the core system specification for a prototype game based on these principles.

Concept Overview:
The goal is to create a pure geometric interaction prototype utilizing spatial optical illusions and gravity manipulation to challenge the player's spatial reasoning. The focus must be on the mathematical and algorithmic precision of the physical interactions, rather than purely aesthetic design.

Required System Specifications (Core Challenges to Address):

1. Topological Structure: Detail the mechanism for constructing a rotatable 3D topological maze. Specify whether the base structure should be derived from a Mobius strip, a Klein bottle, or a projection of a 4D Tesseract, and describe how the surface connectivity is managed.
2. Dynamic Gravity System: Design the global gravity-vector switching mechanism. Specify the rules for redefining the "downward" axis (X, Y, or Z) upon user input. Define the transition logic and any constraints on how the topological structure reacts during these shifts.
3. Geometric Alignment Algorithm: Define the precise "Snap-to-Grid" or "Geometric Fit" algorithm. Detail the mathematical criteria used to detect when 3D pieces are correctly aligned in 3D space, focusing on vector alignment and surface congruence rather than simple coordinate matching.
4. Coordinate Transformation & Stability: Provide the precise mathematical framework or pseudocode necessary to manage coordinate transformations during gravity shifts. Explicitly detail the method to prevent "mesh clipping" or topological tearing when the coordinate system is redefined.
5. Aesthetic & Visual Style: Specify the required visual style: Low-Poly geometry combined with high-contrast Rim Lighting. Explain how the lighting should interact with the geometric edges to emphasize depth and the manipulation of the topology.

Output Format:
Provide a detailed System Design Specification document. Structure your response clearly, addressing each of the five points above with technical depth and abstract design rationale. Focus on the system logic and mathematical constraints that govern the gameplay, treating the visual style as a secondary constraint.