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```python
# AI Dev Tool: PostgreSQL Vector Search Extension Boilerplate
# Description: A production-ready boilerplate for building scalable vector search applications with PostgreSQL

import os
import psycopg2
from psycopg2 import Error
from typing import List, Dict

# PostgreSQL connection settings
POSTGRES_HOST = os.environ.get('POSTGRES_HOST', 'localhost')
POSTGRES_DB = os.environ.get('POSTGRES_DB', 'vector_search')
POSTGRES_USER = os.environ.get('POSTGRES_USER', 'postgres')
POSTGRES_PASSWORD = os.environ.get('POSTGRES_PASSWORD', 'postgres')

# Establish a connection to the PostgreSQL database
def connect_to_postgres() -> psycopg2.connection:
    """
    Connect to the PostgreSQL database.

Returns:
        psycopg2.connection: The established connection.
    """
    try:
        connection = psycopg2.connect(
            host=POSTGRES_HOST,
            database=POSTGRES_DB,
            user=POSTGRES_USER,
            password=POSTGRES_PASSWORD
        )
        return connection
    except Error as e:
        print(f"Error connecting to PostgreSQL: {e}")
        return None

# Create the vector search extension
def create_vector_search_extension(connection: psycopg2.connection) -> None:
    """
    Create the vector search extension

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