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```python
# AI Dev Tool: Tailscale Vector Search API
# Description: A production-ready API integration wrapper for PostgreSQL Vector Search Extension over Tailscale's data plane.

import os
import logging
from typing import Dict, List
from fastapi import FastAPI, HTTPException
from fastapi.responses import JSONResponse
from fastapi.requests import Request
from fastapi.middleware.cors import CORSMiddleware
from pydantic import BaseModel
import psycopg2
import psycopg2.extras
import tailscale

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

# Initialize Tailscale
ts_key = os.environ.get("TS_KEY")
ts_host = os.environ.get("TS_HOST")
ts = tailscale.Tailscale(ts_key, ts_host)

# Initialize PostgreSQL connection
pg_host = os.environ.get("PG_HOST")
pg_port = os.environ.get("PG_PORT")
pg_db = os.environ.get("PG_DB")
pg_user = os.environ.get("PG_USER")
pg_password = os.environ.get("PG_PASSWORD")

try:
    conn = psycopg2.connect(
        host=pg_host,
        port=pg_port,
        database=pg_db,
        user=pg_user,
        password=pg_password

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