⚡ Live Sandbox: AI Dev Tool: AGENTSmd AINative SaaS Template

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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS with PostgreSQL Vector Search Extension
# ==============================================================================
# This is a high-demand production-ready developer code asset for building
# scalable and secure Micro-SaaS applications with 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 sqlalchemy import create_engine, Column, Integer, String
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy.orm import sessionmaker, Session
from sqlalchemy.exc import IntegrityError
from psycopg2.extras import Json
from typing import Optional

# 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 SQLAlchemy models
Base = declarative

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