⚡ Live Sandbox: AI Dev Tool: PostgreSQL Vector Search Extension

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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS Starter
# ================================================
# A production-ready starter boilerplate for building micro-SaaS applications
# using FastAPI, Pydantic v2, and PostgreSQL Vector Search Extension.

import os
import uvicorn
from fastapi import FastAPI, Depends
from fastapi.responses import JSONResponse
from pydantic import BaseModel
from typing import Optional
from sqlalchemy import create_engine
from sqlalchemy.orm import sessionmaker
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy import Column, Integer, String
from sqlalchemy.types import JSON

# Initialize the FastAPI application
app = FastAPI()

# Define the database connection URL
DATABASE_URL = os.environ.get("DATABASE_URL")

# Create a database engine
engine = create_engine(DATABASE_URL)

# Create a session maker
Session = sessionmaker(bind=engine)

# Create a base class for declarative models
Base = declarative_base()

# Define a sample model
class SampleModel(Base):
    """A sample model for demonstration purposes."""
    __tablename__ = "samples"
    id = Column(Integer, primary_key=True)
    name = Column(String)
    data = Column(JSON)

# Create the database

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