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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS PostgreSQL Vector Search Extension
# Description: A production-ready developer code asset for building fast and secure micro-SaaS applications
#               with FastAPI, Pydantic v2, and PostgreSQL Vector Search Extension.

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

# Initialize FastAPI app
app = FastAPI()

# Define security scheme
security = HTTPBearer()

# Define Pydantic models
class VectorSearchQuery(BaseModel):
    """Vector search query model"""
    query: str
    limit: int = 10

class VectorSearchResult(BaseModel):
    """Vector search result model"""
    id: int
    vector: List[float]
    score: float

# Define PostgreSQL connection settings
POSTGRES_HOST = "localhost"
POSTGRES_DB = "vector_search"
POSTGRES_USER = "postgres"
POSTGRES_PASSWORD = "postgres"

# Establish PostgreSQL connection
def get_postgres_connection():
    """Get PostgreSQL connection"""
    try:
        connection = psycopg2.connect(

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