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

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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS Boilerplate
# Description: A production-ready boilerplate for building micro-SaaS applications using FastAPI and Pydantic v2.
# Author: [Your Name]

from fastapi import FastAPI, Depends
from pydantic import BaseModel
from typing import Optional
from sqlalchemy import create_engine
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy.orm import sessionmaker, Session

# Initialize the FastAPI application
app = FastAPI()

# Define the 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 model for the database
Base = declarative_base()

# Define a Pydantic model for the user
class User(BaseModel):
    id: int
    name: str
    email: str

# Define a Pydantic model for the user creation
class UserCreate(BaseModel):
    name: str
    email: str

# Define the user table
class UserTable(Base):
    __tablename__ = "users"

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