Formally Verifying 3D Mesh Intersections with AI-Generated Proofs

We just hit a massive milestone in formal verification: the first formally verified implementation of a 3D constructive solid geometry (CSG) operation—mesh intersection—using the Lean 4 theorem prover. This isn't just an academic 'what if.' It’s a functional workflow where AI agents autonomously churned out over 60,000 lines of formal proofs and 1,000+ lines of implementation code. The kicker? Human reviewers only had to certify 93 lines of formal specification.

Shrinking the Human Review Loop

The real engineering win here is the massive compression of human effort. In traditional formal verification, you’re often stuck auditing thousands of lines of dense, error-prone logic. This project flips that script. The AI does the heavy lifting—navigating the grueling requirements of a formal proof system—while the human acts as a high-level architect. You only need to ensure the 93-line specification is correct. Because the Lean checker guarantees conformance to that spec at compile time, you can treat the AI-generated proofs and code as a verified black box. We’re moving from 'trusting the LLM' to 'verifying the requirements.'

The Reality of Correctness vs. Speed

Let’s be real: this isn't about real-time rendering. The project prioritizes absolute correctness over raw performance. Intersecting two 70k-triangle Stanford bunnies takes 24 seconds. In a game engine, that’s a non-starter. But in aerospace manufacturing, medical robotics, or high-precision CAD, a single geometric error can be catastrophic. For those industries, 'correct-by-construction' geometry isn't a luxury—it's a requirement. This provides a blueprint for building systems where the cost of failure is higher than the cost of latency.

From 'AI as Coder' to 'AI as Proof Assistant'

The big takeaway here is a fundamental shift in how we use LLMs. Anyone can prompt an AI to write a messy Python script for mesh intersection. The real power lies in the AI’s ability to navigate the dense, logical requirements of a formal proof system like Lean 4. The value isn't in the syntax; it's in the logic. The next hurdle for the industry isn't just making these proofs faster—it's finding the sweet spot where formal specifications are small enough for humans to audit but robust enough to handle the messy, unpredictable realities of production data.