⚡ Live Sandbox: AI Dev Tool: Ancient Library (pu92)

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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS Boilerplate with PostgreSQL Vector Search Extension
# =============================================================================================
# This production-ready boilerplate provides a scalable and secure foundation for building micro-SaaS applications
# using FastAPI, Pydantic v2, and PostgreSQL Vector Search Extension.

from fastapi import FastAPI, Depends, HTTPException
from fastapi.security import HTTPBearer, HTTPAuthorizationCredentials
from pydantic import BaseModel, Field
from typing import List, Optional
import psycopg2
from psycopg2 import extras
import json

# Initialize the FastAPI application
app = FastAPI()

# Define the security scheme for authentication
security = HTTPBearer()

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

# Define the PostgreSQL vector search extension settings
VECTOR_SEARCH_TABLE = "mytable"
VECTOR_SEARCH_COLUMN = "mycolumn"

# Define the Pydantic model for the vector search query
class VectorSearchQuery(BaseModel):
    query: str = Field(..., description="The search query")
    limit: int = Field(10, description="The number of results to

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