This is where the tools show their work. Every claim begins with its header — FINITE:, IDENTITY:, INEQUALITY:, SUM:, GROUP:, COLORING:, GAME: or MODEL: — and is taken up by exactly the tool built for it. Free text never binds. What the animation shows is the recorded log of the run, not a re-enactment. Everything runs in the browser: no network, no model, no cost.