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```python
# AI Dev Tool: PostgreSQL Vector Search Extension Boilerplate
# =========================================================
# A production-ready starter boilerplate for PostgreSQL Vector Search Extension
# using FastAPI and Supabase.

from fastapi import FastAPI, HTTPException
from fastapi.responses import JSONResponse
from fastapi.encoders import jsonable_encoder
from pydantic import BaseModel
from supabase import create_client, Client
from typing import List, Dict

# Initialize FastAPI app
app = FastAPI()

# Initialize Supabase client
SUPABASE_URL = "https://your-supabase-url.supabase.co"
SUPABASE_KEY = "your-supabase-key"
SUPABASE_SECRET = "your-supabase-secret"
supabase: Client = create_client(SUPABASE_URL, SUPABASE_KEY)

# Define PostgreSQL Vector Search Extension model
class VectorSearchModel(BaseModel):
    id: int
    vector: List[float]

# Define API endpoint for vector search
@app.post("/vector-search")
async def vector_search(query: Dict[str, str]):
    """
    Perform vector search using PostgreSQL Vector Search Extension.

Args:
    query (Dict[str, str]): Search query with vector and k parameters.

Returns:
    JSONResponse: Search results with scores

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