The fundamental principle or abstract pattern connecting all these examples is **branching hierarchy**, which refers to a system where a single source or main pathway splits into progressively smaller and more numerous branches. This principle can be observed in both natural and artificial systems, where a central structure distributes resources, energy, or information through a series of increasingly intricate pathways.

### Explanation of the Principle:
- **River Delta**: A river delta forms as a river branches out into multiple distributaries when it reaches a body of water like an ocean or lake. Each branch further divides into smaller channels.
- **Lightning Bolt**: Lightning follows a path of least resistance, often branching into smaller forks as it seeks the ground.
- **Vascular System of a Leaf**: The leaf's veins start with a main vein (the midrib) that branches into smaller veins, distributing water and nutrients to every part of the leaf.
- **Hierarchical Corporate Management Structure**: In a company, decisions and authority flow from the top (executive level) down through various levels of management, with each level potentially subdividing into more specific roles.

### Additional Example:
**Computer File System**: In a computer’s file system, data is organized in a hierarchical manner. The root directory branches into subdirectories, each of which may contain further subdirectories and files. This structure allows for efficient organization and retrieval of information.

In summary, the branching hierarchy principle involves a central source or main channel that divides into progressively finer divisions, facilitating distribution or organization across a broader area or system.