Logic-Flow Educational Puzzle

Act as a Senior Game Designer and Technical Architect. Your task is to design the core mechanics and technical specification for an educational, interactive puzzle game based on historical timelines.

Game Concept: Chronos Link

Goal: Design the system for a puzzle game where the objective is for the player to link historical events by establishing causal connections, visualized as "Energy Threads."

Core Mechanics & Visualization:

1. Event Representation (Bubbles): Each historical event must be represented as a distinct, interactive 3D object (a bubble or node) floating within a navigable 3D space.
2. Layout System (Physics Simulation): The arrangement of these event bubbles must be governed by a force-directed layout simulation. This simulation must ensure the bubbles naturally repel and attract each other, allowing them to position themselves dynamically in a natural, force-driven arrangement in 3D space.
3. Connection Mechanism (Energy Threads): The player links two correctly related events by drawing a dynamic connection path, termed an "Energy Thread," between them.
4. Connection Rendering: The drawn Energy Thread must be rendered using a Catmull-Rom Curve3 to ensure smooth, natural interpolation between the two linked nodes.
5. Aesthetics: All visual elements (event bubbles and Energy Threads) must utilize a glowing neon texture effect to emphasize the energetic, educational theme.

Technical Prompt:

Develop a detailed technical specification for the implementation of the Chronos Link system. Focus on the logic required for the physics simulation and the curve generation.

1. Force Simulation Logic: Describe the necessary mathematical framework for the force-directed simulation to manage the 3D positioning of the event bubbles, ensuring collision detection and prevention of overlapping geometry.
2. Interaction/Linking Logic: Detail the algorithm for detecting a valid link between two selected events and generating the corresponding Catmull-Rom curve segment.
3. Rendering Specification: Specify the requirements for applying the glowing neon material/shader to both the static event nodes and the dynamic connecting curves.

Provide the blueprint for how the physics, linking, and rendering systems integrate to create the desired interactive educational experience.