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```python
# AI Dev Tool: FastAPI PostgreSQL Vector Search Extension
# Description: A production-ready API integration wrapper for PostgreSQL Vector Search Extension
# Author: [Your Name]

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

# Define the FastAPI app
app = FastAPI(
    title="PostgreSQL Vector Search Extension API",
    description="A production-ready API integration wrapper for PostgreSQL Vector Search Extension",
    version="1.0.0",
)

# Define the PostgreSQL connection settings
POSTGRES_HOST = "localhost"
POSTGRES_PORT = 5432
POSTGRES_USER = "postgres"
POSTGRES_PASSWORD = "postgres"
POSTGRES_DB = "postgres"

# Define the PostgreSQL connection
def get_postgres_connection():
    """Get a PostgreSQL connection"""
    try:
        return psycopg2.connect(
            host=POSTGRES_HOST,
            port=POSTGRES_PORT,
            user=POSTGRES_USER,
            password=POSTGRES_PASSWORD,
            database=POSTGRES_DB,
        )
    except psycopg2.Error as e:

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