Build Halves, a web app for splitting shared expenses with roommates. It needs a landing page that explains the product, and the working app: add an expense (what it was for, the amount, who paid, and who it's split between), see the list of expenses, and see who owes whom using the fewest payments. Keep the data in localStorage so it's still there after a reload. Deliver one self-contained index.html. No external images; CDN libraries are fine. I want this to be as perfect as Linear's website or Apple Notes: simple purpose, simple architecture, simple design, simple implementation. Cut taglines, helper text and secondary labels. If a screen needs them to make sense, fix the layout. Every decision should elevate the user experience (UX), developer experience (DX) and agent experience (AX) at once, without breaking anything.