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```python
# AI Dev Tool: PostgreSQL Vector Search Extension Boilerplate
# =============================================================
# A production-ready boilerplate for building scalable vector search applications
# using PostgreSQL and Cloudflare Workers.

import os
import json
from typing import Dict, List
from fastapi import FastAPI, HTTPException
from fastapi.responses import JSONResponse
from fastapi.requests import Request
from fastapi.middleware.cors import CORSMiddleware
from pydantic import BaseModel
from psycopg2 import connect, Error
from psycopg2.extras import DictCursor
from hono import Hono

# Define the PostgreSQL connection settings
POSTGRES_HOST = os.environ.get("POSTGRES_HOST")
POSTGRES_DB = os.environ.get("POSTGRES_DB")
POSTGRES_USER = os.environ.get("POSTGRES_USER")
POSTGRES_PASSWORD = os.environ.get("POSTGRES_PASSWORD")

# Define the Cloudflare Workers settings
CLOUDFLARE_ACCOUNT_ID = os.environ.get("CLOUDFLARE_ACCOUNT_ID")
CLOUDFLARE_API_TOKEN = os.environ.get("CLOUDFLARE_API_TOKEN")
CLOUDFLARE_WORKER_NAME = os.environ.get("CLOUDFLARE_WORKER_NAME")

# Create a new FastAPI application
app = FastAPI()

# Enable CORS middleware

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