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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS with PostgreSQL Vector Search Extension
# ==============================================================================
# This is a production-ready developer code asset for building high-performance Micro-SaaS applications.
# It combines the power of FastAPI, Pydantic v2, and PostgreSQL Vector Search Extension.

from fastapi import FastAPI, Depends
from pydantic import BaseModel
from sqlalchemy import create_engine, Column, Integer, String
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy.orm import sessionmaker, Session
from typing import List
import psycopg2
import numpy as np
from sklearn.metrics.pairwise import cosine_similarity

# Define the database connection
SQLALCHEMY_DATABASE_URL = "postgresql://user:password@host:port/dbname"
engine = create_engine(SQLALCHEMY_DATABASE_URL)
SessionLocal = sessionmaker(autocommit=False, autoflush=False, bind=engine)

# Define the base class for models
Base = declarative_base()

# Define the model for vector search
class VectorSearchModel(Base):
    __tablename__ = "vector_search"
    id = Column(Integer, primary_key=True)
    vector = Column(String)

# Create the database tables
Base.metadata.create_all(bind=engine)

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