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```python
# AI Dev Tool: PostgreSQL Vector Search Extension with FastAPI and Supabase
# ========================================================================
# This is a production-ready boilerplate for building a vector search API
# using PostgreSQL, FastAPI, and Supabase.

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, Optional
import os
import logging

# Initialize the logger
logging.basicConfig(level=logging.INFO)
logger = logging.getLogger(__name__)

# Define the 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 the FastAPI app
app = FastAPI()

# Define the vector search model
class VectorSearchModel(BaseModel):
    query: str
    limit: Optional[int] = 10

# Define the vector search response model
class VectorSearchResponse(BaseModel):
    results: List[dict]

# Define the vector search endpoint
@app.post("/vector_search", response_model=VectorSearchResponse)

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