Formally verified polygon intersection – Opus 4.8 oneshots, prev failed
To my knowledge, this is the first formally verified implementation of an intersection algorithm for polygons. The experience of working with AI agents on this project changed a lot with recent model releases, as I describe in the readme. Opus 4.8 is able to provide algorithm implementation with formal proof in one shot, whereas previous models required me to provide proof strategies in multiple steps. Trust in the correctness comes entirely from the Lean checker and human review of a small specification, not from the LLM. Also check out the web demo built around the verified core linked in…
Formally verified polygon intersection – Opus 4.8 oneshots, prev failed launched on June 4, 2026 with 93 votes, #434 of 22,647 launches that month and more than 95% of that year's launches.
In plain words
Formally verified polygon intersection is a Lean implementation of a polygon intersection algorithm with mathematical proof of correctness. Designed for developers who need reliable geometric computation, it stands out as apparently the first formally verified polygon intersection algorithm. The implementation handles complex cases including multipolygons with holes, self-intersections, and overlapping edges. Correctness is guaranteed by Lean's proof checker and human review rather than relying on AI output alone. A web demo is available for testing the verified core.
written from the facts on this page · September 2026
From the sources
Formally verified polygon intersection. Contribute to schildep/verified-polygon-intersection development by creating an account on GitHub.
To my knowledge, this is the first formally verified implementation of an intersection algorithm for polygons. (Also compare with Related work ) The experience of working with AI agents on this project changed a lot with recent model releases. Latest models are able to provide algorithm implementation with formal proof in one shot, whereas previous models required me to provide proof strategies in multiple steps. ( Capabilities of AI agents ) Trust in the correctness comes entirely from the Lean checker and human review of a small specification, not from the LLM. (See Use of AI agents ) Try out the web demo built around the verified core, where you can draw and intersect multipolygons.…from github.com
In the maker’s words, at launch
To my knowledge, this is the first formally verified implementation of an intersection algorithm for polygons. The experience of working with AI agents on this project changed a lot with recent model releases, as I describe in the readme. Opus 4.8 is able to provide algorithm implementation with formal proof in one…
Does a similar job
all alternatives →
Formally verified 3D CSG: Trust 93 lines spec, not 1000 lines AI codeJul 2026 · github.com · ▲115To my knowledge, this is the first formally verified implementation of a 3D constructive solid geometry (CSG) operation: mesh intersection, implemented in Lean 4 and verified against a concise specification that pins down the surface of the resulting mesh exactly and guarantees practical well-formedness conditions on the triangulation. This project is also an experiment in avoiding having to trust AI-generated code. A human reviewer only needs to read 93 lines of formal specification and run the Lean checker to certify the correctness of the kernel, skipping the intricate 1000+ lines of…
Formalizing Principia Mathematica using Lean2025 · github.com · ▲188This project aims to formalize the first volume of Prof. Bertrand Russell’s Principia Mathematica using the Lean theorem prover. Throughout the formalization, I tried to rigorously follow Prof. Russell’s proof, with no or little added statements from my side, which were only necessary for the formalization but not the logical argument. Should you notice any inaccuracy (even if it does not necessarily falsify the proof), please let me know as I would like to proceed with the same spirit of rigour. Before starting this project, I had already found Prof. Elkind’s formalization of the Principia…
HyperLogLog intersections2018 · github.com · ▲88HyperMinHash: Bringing intersections to HyperLogLog - axiomhq/hyperminhash
Formal Verification for Machine Learning Models Using Lean 42025 · github.com · ▲52Framework for specifying and proving properties—such as robustness, fairness, and interpretability—of machine learning models using Lean 4. - fraware/leanverifier
- GCGoldbach Conjecture up to 4*10^18+7*10^132025 · medium.com · ▲244
Achieved a new world record in verifying the Goldbach Conjecture using grid computing, by extending the verification up to 4 quadrillion (4×10¹⁸) + 70 trillion (7×10¹³). My grid computing system - Gridbach is a cloud-based distributed computing system accessible from any PC or smartphone. It requires no login or app installation. The high-performance WASM (WebAssembly) binary code is downloaded as browser content, enabling computation on the user’s browser. [Website] https://gridbach.com/ [Medium]…
Cuq – Formal Verification of Rust GPU Kernels2025 · github.com · ▲94A pipeline that translates Rust GPU code into formal Coq models, as a foundation for memory model proofs - neelsomani/vericuda
More ai this month
the category →
Paintings by AI models: programs run through a simulation of oil paint.
AI · 21d ago · stillwet.art
PixVerse R2▲381A real-time world model you can explore and change
AI · 30d ago · world.pixverse.video
Source: Show HN post ↗ · launch text quoted in part
Launched alongside, June 2026
the whole month →
Fundraisly▲1,537AI fundraising agent that finds investors and books meetings
AI · Jun 2026 · fundraisly.com
Homebrew 6.0.0▲1,481Today, I’m proud to announce Homebrew 6.0.0. The most significant changes since 5.1.0 are a new tap trust security mechanism, the new faster, smaller, default internal Homebrew JSON API, sandboxing on Linux, better defaults informed by our user survey, many brew bundle improvements, improved performance and initial support for macOS 27 (Golden Gate). Happy to discuss any questions here!
Dev tools · Jun 2026 · brew.sh
Hi HN! I was super frustrated at apps like tiktok and wechat preventing me from saving or downloading the animated gifs, so I made a little tool to turn a screen recording into a slack-sized emoji. Hope you get some value from this!
Life & fun · Jun 2026 · vorpus.github.io
Search 18 years of Hacker News and chart how any topic, tool, or person trended. Overlay terms to compare their rise and fall across 45M posts and comments.
Life & fun · Jun 2026 · hackernewstrends.com