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```python
# AI Dev Tool: PostgreSQL Vector Search Extension with FastAPI and Supabase
# ========================================================================
# This production-ready developer code asset provides a starter boilerplate
# for building scalable and efficient vector search applications using
# PostgreSQL, FastAPI, and Supabase.

import os
import uvicorn
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, Optional

# 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 the VectorSearch model
class VectorSearch(BaseModel):
    query: str
    limit: int = 10
    offset: int = 0

# Define the SearchResult model
class SearchResult(BaseModel):
    id: int
    score: float
    data: dict

# Create the FastAPI app
app = FastAPI()

# Define the vector search endpoint
@app.post("/search", response_model=List[Search

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