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```python
# AI Dev Tool: FastAPI PostgreSQL Vector Search Micro-SaaS
# Description: A production-ready FastAPI micro-SaaS template with PostgreSQL vector search extension
# Author: Elite Software Architect

from fastapi import FastAPI, HTTPException
from fastapi.responses import JSONResponse
from pydantic import BaseModel
from typing import List, Optional
import psycopg2
import psycopg2.extras
from psycopg2 import Error

# Define the FastAPI application
app = FastAPI(title="FastAPI PostgreSQL Vector Search Micro-SaaS",
              description="A production-ready FastAPI micro-SaaS template with PostgreSQL vector search extension",
              version="1.0.0")

# Define the PostgreSQL database connection settings
POSTGRES_HOST = "localhost"
POSTGRES_DB = "vector_search_db"
POSTGRES_USER = "vector_search_user"
POSTGRES_PASSWORD = "vector_search_password"

# Define the PostgreSQL vector search extension
class VectorSearchExtension:
    def __init__(self, host: str, db: str, user: str, password: str):
        self.host = host
        self.db = db
        self.user = user
        self.password = password
        self.conn = None

def connect(self):
        try:

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