Inspiration
Physics is hard to picture. A textbook diagram doesn't move, so students memorise formulas without seeing what forces actually do. AI can now build 3D worlds from a sentence, but a simulation that is quietly wrong is worse than none. We wanted simulations students can trust, and a fair way to pay for the AI behind them.
What it does
- Solve and simulate: paste a textbook problem. The AI solves it step by step, a separate pass builds a 3D simulation without seeing the answer, and the app measures the answer inside the simulation. Example: a stone thrown from a cliff, 2.93 s and 38.0 m, "Verified by simulation".
- Video or sentence to simulation: a short clip or one sentence becomes a live 3D scene you can pause, rewind, measure, and change just by asking.
- Credits with PayPal: each new scene costs 1 credit; demos and edits are free. Every visitor starts with 5 free credits.
- 60% student discount: 10 credits for $0.80 instead of $2.00, 50 for $3.20 instead of $8.00.
- Verified or free: every scene must pass an automatic physics test. If it never does, the credit is refunded automatically.
- AI payment assistant: tell it what you need; it checks your balance, picks the right pack, and creates the PayPal order. It can never pay by itself: only PayPal's own window completes a payment.
- Receipts and history: every payment shows PayPal's order and transaction IDs.
- Pay it forward: anyone can gift credits into a shared pool that students who've run out can draw from each day.
How we built it
- PayPal Orders v2 (create and capture) on a Node server, PayPal JavaScript SDK buttons and card fields, and verified Webhooks (CHECKOUT.ORDER.APPROVED, PAYMENT.CAPTURE.COMPLETED). Captures are idempotent; credits are added only for a completed capture of the exact server-set price, once.
- Google Gemini: scene design as code, visual self-review, repair from test failures, video measurement, step-by-step problem solving, and function calling for scene edits and payments.
- A server-side AI proxy metered by "generation passes", so the AI can't be used for free by bypassing the page.
- React 19, TypeScript, Three.js, cannon-es, Vite, Tailwind 4, deployed on Render.
Challenges we ran into
One scene is many AI calls (design, test, repairs, review), so we meter per generation instead of per request. Making "verified or free" fair without being farmable. Giving an AI agent payment tools while keeping the human in control.
Accomplishments that we're proud of
Simulations tested before anyone sees them, a payment model tied to that verification, a real student discount, and an assistant that turns "I'm a student and out of credits" into the right PayPal order.
What we learned
How PayPal Orders v2, idempotent captures and verified webhooks fit together, and how to give an LLM payment tools without letting it spend money on its own.
What's next for Equilibria
Teacher accounts with class codes, PayPal Subscriptions for schools, and more languages for students worldwide.
