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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS Boilerplate with PostgreSQL Vector Search Extension
# Description: A production-ready starter boilerplate for building micro-SaaS applications with FastAPI, Pydantic v2, and PostgreSQL Vector Search Extension.

from fastapi import FastAPI, HTTPException
from pydantic import BaseModel
from typing import List, Optional
import psycopg2
import psycopg2.extras
from psycopg2 import Error

# Initialize the FastAPI application
app = FastAPI()

# Define the PostgreSQL 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]

# Define the route for creating a new vector search data
@app.post("/vector-search-data/")
async def create_vector_search_data(data: VectorSearchData):
    try:
        # Establish a connection to the PostgreSQL database
        conn = psycopg2.connect(
            host=POSTGRES_HOST,
            database=POSTGRES_DB,
            user=POSTGRES_USER,
            password=POSTGRES_PASSWORD

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