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```python
# AI Dev Tool: PostgreSQL Vector Search Extension for FastAPI Pydantic v2 Micro-SaaS
# Description: A production-ready developer code asset for integrating PostgreSQL vector search with FastAPI and Pydantic v2.

from fastapi import FastAPI, HTTPException
from pydantic import BaseModel
from typing import List, Optional
import psycopg2
from psycopg2 import Error
from psycopg2.extras import DictCursor
import numpy as np
from sentence_transformers import SentenceTransformer

# Define the FastAPI application
app = FastAPI()

# Define the Pydantic model for search queries
class SearchQuery(BaseModel):
    """Search query model"""
    query: str
    limit: Optional[int] = 10

# Define the Pydantic model for search results
class SearchResult(BaseModel):
    """Search result model"""
    id: int
    text: str
    score: float

# Define the PostgreSQL database connection settings
DB_HOST = "localhost"
DB_NAME = "vector_search"
DB_USER = "postgres"
DB_PASSWORD = "password"

# Establish a connection to the PostgreSQL database
def connect_to_db():
    """Connect to the PostgreSQL database"""
    try:
        return psycopg2.connect(

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