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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 scalable micro-SaaS applications
#              with AI-powered vector search capabilities using FastAPI, Pydantic v2, and PostgreSQL.

from fastapi import FastAPI, Depends
from fastapi.responses import JSONResponse
from pydantic import BaseModel
from typing import List, Optional
from sqlalchemy import create_engine, Column, Integer, String
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy.orm import sessionmaker, Session
import psycopg2
import numpy as np
from scipy import spatial

# Initialize FastAPI application
app = FastAPI()

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

class SearchResults(BaseModel):
    """Search results model"""
    id: int
    title: str
    description: str
    score: float

# Define PostgreSQL database connection
SQLALCHEMY_DATABASE_URL = "postgresql://user:password@host:port/dbname"
engine = create_engine(SQLALCHEMY_DATABASE_URL)
SessionLocal = sessionmaker(

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