Garvit-Agr/T3-Arena ? reverse-engineered prompt

Build me a web app called T3 Arena that feels like a competitive tic tac toe game with a slick sci fi style. It should have a login and registration flow, a lobby where players can see who is online, challenge each other, and get matched in real time, a live match screen with the board syncing instantly, a leaderboard, and a combat log page showing past matches and results. I also want face based login support, so users can sign in securely with their face if that’s available, and normal account login too. Make the backend handle the game logic, winner checking, Elo style rating updates, database storage, and live WebSocket updates. Use a frontend that cleanly separates the pages and makes everything feel polished. If you need to check current docs or best practices for the libraries, go ahead and look them up online.