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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS Boilerplate with PostgreSQL Vector Search Extension
# =================================================================================================

from fastapi import FastAPI, HTTPException
from fastapi.responses import JSONResponse
from pydantic import BaseModel
from typing import List, Optional
import psycopg2
from psycopg2 import Error
import json

# Initialize FastAPI app
app = FastAPI(title="FastAPI Pydantic v2 Micro-SaaS Boilerplate",
              description="A production-ready boilerplate for building micro-SaaS applications",
              version="1.0.0")

# Define Pydantic models
class User(BaseModel):
    """User model"""
    id: int
    name: str
    email: str

class Item(BaseModel):
    """Item model"""
    id: int
    name: str
    description: str
    vector: List[float]

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

# Create a PostgreSQL database connection
def create_connection():
    """Create a PostgreSQL database connection"""
    try:
        connection = psycopg2.connect(
            host=

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