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

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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS Production Starter Boilerplate
# ==============================================================================
# This is a high-demand, production-ready developer code asset for building
# scalable and secure Micro-SaaS applications using FastAPI and Pydantic v2.

from fastapi import FastAPI, HTTPException
from pydantic import BaseModel, Field
from typing import List, Optional
from sqlalchemy import create_engine, Column, Integer, String
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy.orm import sessionmaker

# Initialize the FastAPI application
app = FastAPI(title="Micro-SaaS Production Starter Boilerplate",
              description="A high-demand, production-ready developer code asset",
              version="1.0.0")

# 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 the user model
class User(Base):
    """The user model"""
    __tablename__ = "users"
    id = Column(Integer, primary

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