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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS Starter with PostgreSQL Vector Search Extension
# ==============================================================================
# This is a production-ready starter boilerplate for building micro-SaaS applications
# using FastAPI, Pydantic v2, and 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
import psycopg2.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"

# Define the Pydantic model for the vector search data
class VectorSearchData(BaseModel):
    id: int
    vector: List[float]
    metadata: Optional[dict]

# Define the route for creating a new vector search index
@app.post("/create-index")
async def create_index():
    """
    Create a new vector search index in the PostgreSQL database.
    """
    try:
        # Establish a connection to the PostgreSQL database
        conn = psycopg2.connect(
            host

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