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```python
# AI Dev Tool: PostgreSQL Vector Search Extension FastAPI Boilerplate
# =====================================================================
# This is a production-ready starter boilerplate for building micro-SaaS applications
# using FastAPI, PostgreSQL, and the PostgreSQL Vector Search Extension.

from fastapi import FastAPI, Depends, HTTPException
from fastapi.security import HTTPBearer, HTTPAuthorizationCredentials
from pydantic import BaseModel
from sqlalchemy import create_engine, Column, Integer, String
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy.orm import sessionmaker, Session
from sqlalchemy.exc import SQLAlchemyError
from typing import List
import os
import psycopg2
from psycopg2 import extras

# Initialize FastAPI application
app = FastAPI()

# Initialize PostgreSQL database connection
SQLALCHEMY_DATABASE_URL = os.environ.get("DATABASE_URL")
engine = create_engine(SQLALCHEMY_DATABASE_URL)
SessionLocal = sessionmaker(autocommit=False, autoflush=False, bind=engine)

# Initialize PostgreSQL Vector Search Extension
vector_search_extension = "pgvector"

# Define the database model
Base = declarative_base()

class VectorSearchModel(Base):
    """Database model for vector search"""
    __tablename__ = "vector_search"
    id = Column(Integer, primary_key=True)

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