⚡ Live Sandbox: AI Dev Tool: PostgreSQL Vector Search (rha0)

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

from fastapi import FastAPI, Depends, HTTPException
from fastapi.security import OAuth2PasswordBearer, OAuth2PasswordRequestForm
from pydantic import BaseModel, EmailStr
from pydantic.validators import UUID4
from typing import Optional
from sqlalchemy import create_engine, Column, Integer, String
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy.orm import sessionmaker
from sqlalchemy.exc import IntegrityError
from psycopg2.extras import Json
import json
import uuid

# Initialize the FastAPI application
app = FastAPI()

# Define the OAuth2 password bearer
oauth2_scheme = OAuth2PasswordBearer(tokenUrl="token")

# Define the PostgreSQL database connection
SQLALCHEMY_DATABASE_URL = "postgresql://user:password@host:port/dbname"
engine = create_engine(SQLALCHEMY_DATABASE_URL)
SessionLocal = sessionmaker(autocommit=False, autoflush=False, bind=engine)

# Define the base class for the database models

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