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```python
# AI Dev Tool: PostgreSQL Vector Search Extension with FastAPI and Supabase
# ========================================================================
# This is a production-ready developer code asset that integrates PostgreSQL
# Vector Search Extension with FastAPI and Supabase for building scalable
# and efficient search systems.

import os
import sys
from fastapi import FastAPI, HTTPException
from fastapi.responses import JSONResponse
from fastapi.requests import Request
from pydantic import BaseModel
from supabase import create_client, Client
from typing import List, Dict

# Initialize FastAPI app
app = FastAPI(title="PostgreSQL Vector Search Extension with FastAPI and Supabase")

# Initialize Supabase client
SUPABASE_URL = os.environ.get("SUPABASE_URL")
SUPABASE_KEY = os.environ.get("SUPABASE_KEY")
supabase: Client = create_client(SUPABASE_URL, SUPABASE_KEY)

# Define data models
class SearchQuery(BaseModel):
    """Search query data model"""
    query: str

class SearchResult(BaseModel):
    """Search result data model"""
    id: int
    title: str
    description: str
    vector: List[float]

# Define API endpoints
@app.post("/search")
async def search(query:

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