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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, HTTPException
from pydantic import BaseModel
from typing import List, Optional
import psycopg2
from psycopg2 import extras
import json

# Initialize the FastAPI application
app = FastAPI()

# Define the PostgreSQL database connection settings
POSTGRES_HOST = "localhost"
POSTGRES_DB = "mydatabase"
POSTGRES_USER = "myuser"
POSTGRES_PASSWORD = "mypassword"

# Establish a connection to the PostgreSQL database
def get_db_connection():
    """Returns a connection to the PostgreSQL database."""
    return psycopg2.connect(
        host=POSTGRES_HOST,
        database=POSTGRES_DB,
        user=POSTGRES_USER,
        password=POSTGRES_PASSWORD
    )

# Define the Pydantic model for the user data
class User(BaseModel):
    """Represents a user with id, name, and email."""
    id: int
    name: str
    email: str

# Define the Pyd

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